How to Handle Calculations

Calculating Destructive Capacity

In order to determine a character's Destructive Capacity, we must first look through the character's feats, and determine how much energy was exerted to perform such a feat. Sometimes the destructive capacity of the feat can be determined easily with no need of a calculation, but most of the time it isn't as simple. Here we will explain some of the methods we use in order to calculate feats.

Destruction/Creation of Planets and Planetoids

For feats that involve the Destruction or the creation of planets or planetoids, we use a term called Gravitational Binding Energy.

Gravitational Binding Energy

Gravitational binding energy is the energy needed to completely disperse a celestial body. If GBE is broken, the particles of the body will not reform or be bound to each other's gravity, but instead drift off infinitely in the direction they were moved towards. There are precise calculations for this via integration, but a good approximation can be achieved with the following formula:

Where U = GBE in joules, M = the mass of the body in question in kilograms, r = its radius in meters, and G = the gravitational constant of 6.67408x10^-11.

For stars, however, the formula is slightly different:

U is GBE in joules, G is the gravitational constant of 6.67408x10^-11, M is mass in kilograms, r is radius in meters, and n is the polytropic value attributed to the type of star. While this formula is not perfectly accurate, it is widely applicable, and is still within the acceptable margin for error.

Ignoring this formula often leads to vast underestimates of the energy required to destroy astronomical objects (for example, some people assume it scales linearly with mass or volume).

Please note that this formula only works on objects that are mostly held together by their own gravity (meaning: large objects in space such as asteroids, moons, planets, stars, etc.) It also doesn't work on black holes, for obvious reasons.

The following is a list of approximate GBE values for various objects:

• Earth's moon (Luna): 1.24e29J
• Earth: 2.487e32J (Calculated with a more accurate method than the above formula)
• OTS 44: 6.906e37J
• VB 10: 3.139e40J
• The sun (Sol): 5.693e41J
• Rigel A: 3.817e42J

SD.net's Planetary Parameter Calculator gives a simplified approach to finding a celestial body's GBE.

Meteors and Kinetic Energy

In order to determine the energy of meteors, we generally use Kinetic energy, as it is the most reliable way to gauge the energy a meteor poses if we are given the required Details.

The equation used:

Ek=0.5*M*V^2

Terms:

Ek=Kinetic Energy

M=mass

V=velocity=speed

There are several speed values that we can use without the need for proof:

If the meteor in question was determined to have come from outer space (or outside of our atmosphere) we will use the value of minimum impact velocity, which is the minimum value of speed an object needs to enter the earth's atmosphere, that value is 11,000 m/s.

If the meteor in question was shown to be Ablated, but didn't come from space, we will use Ablation speeds, which are the minimum speed an object needs to move in order for it to be ablated by its own friction with the atmosphere, the values range from 2000-4000 m/s.

A reasonable high end for meteors that come from outer space is 17,000 m/s, as it is the speed value of most of the meteors that have entered earth's atmosphere.

If the meteor in question wasn't ablated and didn't come from outer space, we will use Potential-Gravitational Energy, as it does not require the use of speed. That is unless we can mathematically find a speed for the meteor.

Potential Gravitational Energy: Energy of falling Objects and Energy to lift Objects

Gravitational potential energy is energy an object possesses because of its position in a gravitational field. If an object from a high position falls towards the ground the kinetic energy the object gets from falling is equal to the difference in its gravitational potential energy before and after the fall, provided no other forces such as air resistance act upon it. Vice versa the energy necessary to lift an object to a certain height is also equal to the change in gravitational potential energy of the object before and after being lifted.

However, lifting should generally not be used to calculate Attack Potency unless it is a fast, explosive form of lift (for example: snatch, clean-and-jerk, etc.). This is based on the biomechanics behind how human type characters attack. Unlike a punch, a kick, or most other types of attacks, a lift is a slow sustained motion which allows for many more muscles fibers to be recruited into the movement more easily, generating much more energy than a fast movement used in combat. Lifting movements also allow the body's tendons to help out by storing the energy, then releasing it in a sudden burst, acting like a spring. If we use real world ratios, when the world's heaviest deadlift is compared to the world's most powerful punch, the deadlift has nearly 5 times more energy, demonstrating the disparity between the two types of movements. Similarly, if telekinesis (or any other ability of a similar nature) is used, the lifting must be performed in a timeframe capable of being used as an attack.

In cases close to the ground

In cases where an object is lifted or falls relatively close to the surface of the earth the difference in gravitational potential energy can be calculated using the simple formula

E_p = M*g*h

where

• M = mass of the object in kg
• g = the gravitational acceleration. For earth this is about 9.81 m/s²
• h = how high the object was lifted / how far down the object fell in meter
• E_p = gravitational potential energy difference in joules.

In cases far away from the ground

In cases where an object is lifted very high or falls from very high up the upper formula can not be used any more. Instead the following formula should be used:

E_p = |(G*M*m)/r₁ - (G*M*m)/r₂|

Where

• G is the gravitational constant, which is 6.674*10^-11 N*m²/kg²
• M is the mass of the planet in kg, in case of earth 5.972*10²⁴kg
• m is the mass of the object falling in kg
• r₂ is the distance between the center of mass of the planet and the center of mass of the object after the fall / before being lifted (in meters). So usually it is radius of the planet (in case of earth 6371000 m) + how far the object is away from the ground after the fall / before being lifted.
• r₁ is the distance between the center of mass of the planet and the center of mass of the object before the fall / after being lifted (in meters). So usually it is radius of the planet (in case of earth 6371000 m) + how far the object is away from the ground before the fall / after being lifted.
• E_p is the gravitational potential energy difference in joules.
  

Terminal velocity

Air resistance is mostly relevant for the case of falling objects and even then can be ignored for most heavy objects like meteors or big constructs.
However for lightweight objects, like for example humans, it becomes relevant.
The air resistance opposes gravity in pulling the object down and due to that slows down the fall of the object, reducing the kinetic energy it gains while dropping.
If an object falls long enough it will reach its terminal velocity and not get any faster than that (provided it wasn't faster to begin with or influenced by other forces than gravity).
Because of that the kinetic energy an object has at terminal velocity often forms a limit to how much energy an object can gain through falling, which means that if our calculated change in potential energy is greater than that we have to consider it as a too high estimate for the energy when reaching the ground.
The terminal velocity of an object can be calculated like described here, but, for example due to the drag coefficient being depended on the fall speed of the object, it is in practice often difficult to calculate. For a human terminal velocity is approximately 53 m/s close to the ground.
An example of terminal velocity being relevant for the result of a calculation can be found here.

Change in Temperature and Vaporization or Melting Energy

This would be one way of determining attacks that make use of fire, ice, etc. If something is melted, ignited, or frozen we can determine destructive capacity for one or two steps:

First:

• We determine the energy given or taken in changing the temperature, the equation for this is E=m*c*ΔT
• E is the energy
• m is mass
• c is specific heat capacity, this varies between materials and is based on how much energy is required to get that material to a certain heat (if you put stone and steel over the same fire they will receive energy at the same rate but the steel will heat up faster)
• ΔT is the change in temperature; the starting temperature will usually be a reasonable room temperature unless there is a reason why the temperature would begin hot or cold in the calculation, the final temperature will usually be either melting point, freezing point, boiling point, or (if a burnable material is present) the auto-ignition temperature or burning material; this is measured in kelvin.

Second:

• We determine the energy given or taken in changing the state of matter (if the feat we are calculating did not involve a state change i.e. something being set on fire does not include a change of state, then we do simply perform this second step).
• If the feat involved a change between solid and liquid (in either direction) we must multiply the mass of the material with the material's "heat of fusion".
• If the feat involved a change between liquid and gas (in either direction) we must multiply the mass of the material with the material's "enthalpy of vaporisation", this varies based on atmospheric pressure.

This type of feat will most often involve water:

Specific heat capacity of water is 4181 J/kg°K

Heat of fusion for water is 334000 J/kg

Here a few pre-calculated example values (starting with the materials at 20°C):

• Melting Granite: 4358.9475 J/cm^3
• Melting Cement: 12.232.65 J/cm^3
• Melting Glass: 2494 J/cm^3
• Freezing Water: 418 J/cm^3
• Vaporization of water: 2575 J/cm^3
• Vaporization of titanium: 49079.7 J/cc

(Values taken from here and here)

Specific Heat Capacity/Latent Heat of Fusion and Vaporization

	Specific Heat Capacity	Latent Heat (Fusion)	Latent Heat (Vaporization)	Melting Point	Boiling Point
Silver	230	104726.6	5327260	962	1950
Iron	460	247112.54	6213627	1538	2861
Aluminum	870	396567.46	10859277	660.32	2519
Tin	240	58972	2442928	231.93	2602
Copper	390	206137	4720692	1084.62	2927
Zinc	380	112420	1820128	419.53	907
Silicon	710	1787113	12780350	1414	2900
Gold	130	63463	1675127	1064.18	2856
Calcium	630	213000	3867458	842	1484
Water	4186	334000	2264705.7	0	100
Granite	821.46	947657.98	6077872	1215	?
Titanium	470	390666	8878768	1668	3287
Oxygen	919	13875	213125	-218.3	-182.9
Nitrogen	1040	25702	199190	-210.1	-195.8

• Specific heat capacity = Joules/Kg*K (K and °C are in this case interchangeable for most calculations)
• Latent heat = J/Kg
• Boiling/Melting point = (°C)

Plasma

Plasma is one of the four fundamental states of matter, together with solid, liquid and gas.

A Plasma is an ionised gaseous substance, which is highly electrically conductive, to the point that long range electric and magnetic fields dominate the behavior of the matter.

The energy imbued into a plasma is highly variable. For example a candle flame is a form of plasma with very few energy and the matter that the core of the sun is made of is a plasma with very much energy.

As such the energy within a plasma or the energy necessary to create it can, in general, not be estimated without having further information.

Should the mass of the plasma, the material it is made of and the degree of ionisation be known, one can estimate the energy as follows:

1. Use the molar mass of the material the plasma is made of together with the mass to figure out the number of atoms in the plasma. So if you have 50 g of plasma, with your substance having a molar mass of 1.007 g/mol, then you have (50 g) / (1.007 g/mol) = 49.6524 mol of atoms = 6.022*10²³ * 49.6524 atoms = 2.990067528*10²⁵ atoms. Be careful: the molar mass of a non-atomic substance, like water, gives the amount of mass per molecules, not atoms.
2. Next we want to calculate the amount of ionised atoms within the substance. If the degree of ionisation of the substance is x, then this is simply done by multiplying x with the amount of atoms calculated in the first step.
3. Now we can calculate the energy to turn it into plasma: For that we just have to multiply the amount of ionised atoms, with the Ionisation energy of the atoms in question.

Consider that the energy that was used to turn the material into the state before it was made into a plasma is not considered here. So if for example rock is turned into plasma, the energy to vaporize it can be put on top of this calculation result.

If there are other specific statements those can possibly be used to get results in an easier way.

For example plasma, for which high energy density physics applies, is defined to have at least an energy density of 10¹⁰ J/m³.

Heat, Radiation and Nuclear-like Explosions

When dealing with a feat that is heat related only, we can still manage to find Destructive capacity, by finding the given temperature of the object in question, estimate or calculate its surface area and emissivity, and apply the values to the following Calculator:

http://www.endmemo.com/physics/radenergy.php

While it does calculate joule/second, it is still reliable enough for us, though it should be noted that if the values inserted aren't extremely high, the results would likely be underwhelming. It is usually assumed that only 1 second of the calculated Joules per second value contributes to the attack potency, or less if the object only had that heat for less than one second.

When dealing with an explosion that doesn't leave a crater behind, we can use the following Calculator:

http://www.stardestroyer.net/Empire/Science/Nuke.html

Although it is tricky to use, we need to find the radius of the explosion in question, and insert the megaton value into the calculator until we get the same value for the "Air Blast radius (near total fatalities)" as the radius that we have scaled.

Volume, Mass, Destruction Values and TNT table

Many feats cause visible destruction after they are preformed (such as leaving a crater, destroying a mountain/meteor). To measure these feats we need to know the Volume of the matter that was destroyed in the attack.

Volume is a space composed of three perpendicular dimensions, if its a mountain, it has length, width, and height. If it is a crater, it has length, width, and depth.

Here is a page with classic formulas of classic geometrical shapes that maybe useful when calculating volume:

http://www.basic-mathematics.com/volume-formulas.html

For example, sometimes, when trying to find the volume of a mountain, we may use the formula of a cone to give us a rough estimation of its size.

Usually after we have found the volume, we may get the final measurement to be in cubic meters (m^3) or sometimes in cubic Kilometers (Km^3). At this point, in order to get the Energy measurement for the feat, we need to convert the volume from whatever unit we are using, into cubic Centimeters (Cm^3 or cc).

Here are some terms that will make said conversion easier:

1 km^3 = 1000000000 m^3

1 m^3 = 1000000 cm^3

Destruction Values

According to the method used within the Naruto Forums, there are different methods of Destruction (for lack of a better term) that require different levels of energy for every cubic centimeter of the volume that was destroyed during the feat:

Fragmentation: Applied when the matter that was destroyed was turned into fairly large and distinguishable pieces. The value is 8 joules per Cubic centimeter (j/cc).

Violent Fragmentation: Applied when the matter that was destroyed was turned into small but still distinguishable pieces. The value is 69 (j/cc).

Pulverization: Applied when the matter that was destroyed was turned to dust. We usually use this value when we see no remains of the matter that was destroyed in the aftermath of the attack. The value is 214.35 (j/cc).

Vaporisation: Applied when the matter that was destroyed was vaporised during the attack. Much like for Pulverization, we usually use this value when we see no remains of the matter that was destroyed in the attack, but in addition there has to be a considerable amount of visible vapor and/or character statements that imply vaporization, usually the latter. The value is 25700 (j/cc).

Atomization: Applied only if clearly stated. It describes the energy to separate all atoms in a chemical substance. The value is 30852.2 (j/cc).

Subatomic Destruction: Applied only if clearly stated. It describes the energy necessary to destroy all atoms in a substance, by separating the particles in their nucleus. Note that Protons and Neutrons still stay intact. Value is 5.403E13 (j/cc).

These values are only relevant for solid objects like rocks, buildings and mountains.

After we have determined both the method of destruction and the volume (in cubic centimeters), we multiply both Values to get the value of energy that was exerted for the feat, and thus we have the destructive capacity.

Table of Destruction Values

	Fragmentation	Violent Fragmentation	Pulverization	Vaporization	Atomization	Subatomic Destruction
Concrete	6 j/cc	17-20 j/cc	40 j/cc	5304 j/cc		4.168E12 j/cc
Cement	6 j/cc	17-20 j/cc	40 j/cc	5304 j/cc		4.168E12 j/cc
Soil	0.15 j/cc	0.2 j/cc	0.4-1 j/cc
Steel	208 j/cc	568.5 j/cc	310-1000 j/cc		59526.65 j/cc	6.7034E12 j/cc
Iron	20 j/cc	42.43 j/cc	90 j/cc	60915.7 j/cc	58401 j/cc	6.6965E12 j/cc
Glass			1000 j/cc
Ice	0.5271 j/cc	0.825 j/cc	4.3919 j/cc		51384.16 j/cc	8.9363E12 j/cc
Human body	4.4 j/cc	7.533 j/cc	12.9 j/cc	4638.75 j/cc	72416.33 j/cc	1.09729000691E10 j/cc
Silver	65 j/cc	204 j/cc	300 j/cc	97794.79 j/cc	27669.25 j/cc	8.983E12 j/cc
Aluminium	48.75 j/cc	234 j/cc	280 j/cc	35190.2 j/cc	32241.5 j/cc	2.172E12 j/cc
Tin	5.5 j/cc	10.8 j/cc	11 j/cc	22317.22 j/cc	18693.24 j/cc	6.058E12 j/cc
Copper	172.37 j/cc	217.1 j/cc	330 j/cc	52455.62 j/cc	47784.97 j/cc	7.11E12 j/cc
Zinc	45 j/cc	120 j/cc	160 j/cc	15402.32 j/cc	13758.07 j/cc	5.982E12 j/cc
Silicon	56.5 j/cc	67.8 j/cc	120 j/cc	34542.6 j/cc	36484.37 j/cc	1.895E12 j/cc
Carbon					156545 j/cc	1.9414E12 j/cc
Tungsten	400 j/cc	1412.5 j/cc	2425 j/cc		88098.07 j/cc
Gold	50 j/cc	132 j/cc	205 j/cc	39486.35 j/cc	36058.28 j/cc	1.474E13 j/cc
Calcium					7116.124 j/cc	1.276E12 j/cc
Water				2575 j/cc	51384.16 j/cc	8.9363E12 j/cc
Diamond			110000 j/cc		210081 j/cc
Rock	8 j/cc	69 j/cc	214 j/cc	25700 j/cc	30852.2 j/cc	5.403E13 j/cc
Bronze	297 j/cc	538 j/cc	641 j/cc
Grey cast iron	400 j/cc	613.5 j/cc	827 j/cc
Damascus steel	814.5 j/cc
Reinforced concrete	10 j/cc	61.2 j/cc	610 j/cc
Wrought iron	194.22 j/cc	308.76 j/cc	699 j/cc
Stainless steel	358 j/cc	597 j/cc	1631 j/cc
Granite	14 j/cc	103.42-175 j/cc	203.25 j/cc	27050 j/cc
Marble	9 j/cc	62.1-103.42 j/cc	154.95 j/cc
Limestone	10 j/cc	50-140 j/cc	250 j/cc
Sandstone	8 j/cc	55.16-95 j/cc	144.7 j/cc
Slate	15 j/cc	103.42-150 j/cc	172.5 j/cc
Basalt	20 j/cc	60-200 j/cc	224 j/cc
Titanium	550 j/cc	760 j/cc	970 j/cc	49097.7 j/cc
Ballistic glass	32.41 j/cc	38.89 j/cc
Ceramic	3.4 j/cc	4.53 j/cc	2393.33 j/cc

Values taken from here, here, here, here, here, here and here.

We are aware that these values don't capture the complex topic of destruction of materials in real life, which involve many factors like toughness, surface area, force (pressure), area of effect, etcetera. However, since they are widely established, and fit our simplified attack potency system better (as it is based on an easier to follow linear energy system), it is not possible to switch to a more accurate system at this point, as we concluded in a discussion here.

Destruction values of wood

Below are detailed tables of destruction values of wood. In most cases, it should be fine to assume that the wood destroyed is white oak, which has a fragmentation value of 7.3774 j/cc, a violent fragmentation value of 13.7895 j/cc and a pulverization value of 51.297 j/cc.

Table of Destruction Values - Hard Wood

	Fragmentation	Violent Fragmentation	Pulverization
Ash, White	7.9979 J/cc	13.1690 J/cc	48.8149 J/cc
Ash, Black	5.2400 J/cc	10.8248 J/cc	41.1617 J/cc
Birch, Paper	4.1369 J/cc	8.3427 J/cc	39.2312 J/cc
Cherry, Black	4.7574 J/cc	11.72108739 J/cc	49.02172433 J/cc
Cottonwood, Balsam Poplar	2.0684 J/cc	5.4469 J/cc	27.7169 J/cc
Elm, Rock	8.4806 J/cc	13.2379 J/cc	48.6080 J/cc
Maple, Black	7.0327 J/cc	12.5485 J/cc	46.0570 J/cc
Maple, Red	6.8948 J/cc	12.7553 J/cc	45.0917 J/cc
Maple, Sugar	10.1353 J/cc	16.0648 J/cc	53.9859 J/cc
Oak, Black	6.4121 J/cc	13.1690 J/cc	44.9538 J/cc
Oak, Chestnut	5.7916 J/cc	10.2732 J/cc	47.0912 J/cc
Oak, Live	18.3401 J/cc	19.5811 J/cc	61.3633 J/cc
Oak, Post	9.8595 J/cc	12.6864 J/cc	45.5054 J/cc
Oak, Northern Red	6.9637 J/cc	12.2727 J/cc	46.6086 J/cc
Oak, White	7.3774 J/cc	13.7895 J/cc	51.2970 J/cc
Sycamore, American	4.8263 J/cc	10.1353 J/cc	37.0938 J/cc
Walnut, Black	6.9637 J/cc	9.4458 J/cc	52.2623 J/cc
Willow, Black	2.9647 J/cc	8.6184 J/cc	28.2685 J/cc
Yellow Poplar	3.4474 J/cc	8.2048 J/cc	38.1970 J/cc

Table of Destruction Values - Soft Wood

	Fragmentation	Violent Fragmentation	Pulverization
Cedar, Northern White	2.1374 J/cc	5.8605 J/cc	27.3032 J/cc
Douglas-fir, Coast	5.5158 J/cc	7.7911 J/cc	49.8491 J/cc
Fir, White	3.6542 J/cc	7.5842 J/cc	39.9896 J/cc
Hemlock, Mountain	5.9295 J/cc	10.6179 J/cc	44.4022 J/cc
Pine, Eastern white	3.0337 J/cc	6.2053 J/cc	33.0948 J/cc
Pine, Red	4.1369 J/cc	8.3427 J/cc	41.8512 J/cc
Redwood, Young-growth	3.5853 J/cc	7.6532 J/cc	35.9906 J/cc
Spruce, White	2.9647 J/cc	6.6879 J/cc	35.7148 J/cc

TNT Measurements

Most of the time, when calculating Destructive capacity, we end up with extremely large values of energy that are very long to write, also, even if using Orders of magnitude to "shorten" the number, for most people, these large values of energy mean nothing and they cannot rank them easily. That is why we need to convert the numbers we get to TNT measurements, as it is a measuring system that is easier to understand for a wider diversity of people.

To understand the TNT measuring system, we must first explain how it works: 1 gram of TNT contains about 4184 joules of energy. Therefore we can say that every 4184 joules equals 1 gram of TNT, and from here we establish a measuring system:

• 1 gram of TNT = 4184 (j) = 4.184 * 10^3 (j)
• 1 kg of TNT = 1000 gram of TNT = 4184000 (j) = 4.184 * 10^6 (j)
• 1 ton TNT = 1000 kg of TNT = 4184000000 (j) = 4.184 * 10^9 (j)
• 1 kiloton of TNT = 1000 tons of TNT = 4.184 * 10^12 (j)
• 1 Megaton of TNT = 1000 Kilotons of TNT = 4.184 * 10^15 (j)
• 1 Gigaton of TNT = 1000 Megatons of TNT= 4.184 * 10^18 (j)
• 1 Teraton of TNT = 1000 Gigatons of TNT= 4.184 * 10^21 (j)
• 1 Petaton of TNT = 1000 Teratons of TNT= 4.184 * 10^24 (j)
• 1 Exaton of TNT = 1000 Petatons of TNT= 4.184 * 10^27 (j)
• 1 Zetaton of TNT = 1000 Exatons of TNT= 4.184 * 10^30 (j)
• 1 Yottaton of TNT = 1000 Zetatons of TNT= 4.184 * 10^33 (j)

Now, to convert the Energy value to a TNT measurement, we need to divide the energy value by 4.184, and then divide the result of that division by the highest order of magnitude (that is divisible by 3) that is lower/equal to the order of magnitude that was received after the first division, and that will tell you the TNT measurement. For example:

Where does 2*10^24 (j) register on the TNT Measurement system?

(2*10^24) / 4.184 = 4.78*10^23

(4.78*10^23) / 10^21= 478

This was divided by 10^21 because it was the highest order of magnitude that was both divisible by 3 and lower than the order of magnitude of the number that was received after dividing by 4.184, and since the value was divided by 10^21, the TNT measurement is in teratons, according to the chart above:

2 * 10^24 (j) = 478 Teratons.

Mass

When you need to determine the mass of an object, you must first find its volume. Then you must estimate from what type of substance that the object is made out of, as every substance has its own density:

Mass = Volume * Density.

Here is a chart of densities of common materials:

• Continental crust, stone and earth: 2700 Kg/m^3

• Meteors: 3000-3700 Kg/m^3

• Concrete: 2400 Kg/M^3

• Water: 1000 kg/m^3

• Clouds: 1.003 Kg/m^3

Speed Calculations

To calculate the speed of a character or object the basic formula used is v = d/t, where v is the speed of the object, d is the distance the object moved and t is the amount of time it took the character/object to move that much.
Usually the time it took for an object to move the distance is calculate by dividing the distance another object moved during that time, through the speed of that object. That requires knowing the speed of the other object, of course.

More details, such as more in depth explanations on how to figure out the distance and the time as well as examples on how to calculate speed, can be found on the following pages:

Slow Motion Calculations

Sometimes when calculating speed one might encounter scenes where time seems to move slowly from the perspective of a fast moving character. Fundamentally speed calculations can be performed in the same way as normal in such cases.

In other words one just has to figure out a timeframe through the movement of a reference object with known speed, measure how far the character moved during that timeframe and divide the distance through the length of the timeframe (v = d/t).

However, sometimes the time is not just slowed down, but appears outright frozen.

In this case, if a reference object with known speed can be visually confirmed to not have moved even 1 pixel (which requires the feat to happen in a visual media like a comic, movie or animation) one can figure out the timeframe, by saying that it must have been less than the timeframe that the object would have taken to move 1 pixel.

If that can not be confirmed different upper limits, with similar argumentation, can usually be confirmed. In cases with a moving camera/point of view it can be useful to compare the movement to an object that can be assumed to be static.

Especially for written feats another method can be relevant. In that one first wants to figure out how many times slower the time is from the real time and then figure out how fast a movement in that time really is, based on how fast it looks in the slowed down time.

So the formula would be (real speed of reference object / apparent speed of reference object) * apparent speed of object of interest = real speed of object of interest

For example: If an object that really is 1000 m/s fast seems to move with only 10 m/s in slowed down time a character that seems to move with a human walking speed of 1.4 m/s in slowed time would move with (1000 m/s / 10 m/s) * 1.4 m/s = 140 m/s.

Useful values for the apparent speed of movement would be:

• Human walking speed: 1.4 m/s
• Human jogging speed: 3.71 m/s
• Human running speed: 5-7.7 m/s

Sometimes even something like "time seems frozen" or that nothing moves is stated. Often this kind of statements are hyperboles. However, should that not be the case one may assume that the apparent speed of the reference object is less than or equal to 0.001 m/s.

Mind rule 7 regarding Cinematic Time, whenever calculating feats involving slowed time.

Do not assume that a character viewing the world in slow motion is caused by time dilation. The depiction usually doesn't match the real life phenomena and the effect is commonly caused by the character being able to process events very fast, so that they seem to happen in slow motion to them, instead.

Calculators and other utilities

Calculators

• Elipsoid calculator

• Projectile motion calculator

• Planetary parameter calculator

• Relativity calculator

• Asteroid destruction calculator

• Asteroid/Comet calculator

• Multipurpose calculator

• A calculator which can calculate figures up to thousands of digits of precision

• A calculator which can handle and calculate numbers up to ¹⁰¹⁰10 (10 raised to the power of itself 10¹⁰ times)

• Optical lens calculator

• Tsunami speed calculator

• General advanced scientific calculator

• Integral calculator

• Derivative calculator

• Freefall calculator w/air resistance

• Another nuke calculator

Other utilities

Planck units, they come up often enough in VS debating

• List of scientific constants

• Debunking of common misconceptions regarding heat

• Explanation of explosives

• Various lists of notable constants, etc

Starting Out

Calculations may seem intimidating, but there is a very real and easy way to start getting into them. While being swamped with information may seem overwhelming, taking things piece-by-piece will go miles to easing your newfound endeavor. Though this is a hefty read, it is designed for an individual with almost no mathematical background to learn how to calc from scratch, with most of the resources needed all in one place.

In order to make a calculation, you must first determine what you want to calculate. Once you have a feat in mind, you must begin gaining the necessary information to the calc. Whatever you will need will vary from calc to calc, but keep this in mind: All calculations need to start with at least one value! Finding that value is the first step to completing any calculation. Do not feel like a calculation is impossible due to the amount of variables. After you find one value, it may be much easier to determine the next. I will now go over what needs to be done in order to make a calculation in a very rough outline, from start to finish.

Speed Calcs

Basic Speed Calc

1. For speed, you need two things: Distance and Time. You will need to obtain both of these in order to determine a speed, but focus on one of these two first.

2. In order to determine time frame, look to the media itself. If the feat is in video format, you can easily determine exactly how long it takes for the feat to be completed. For videos, determining what Frames per second the video runs at and counting the frames can be an extremely accurate way to dictate time. The tool Watchframebyframe can help with this process. Looking at the timestamp from feat start to feat end can be acceptable as well for longer feats. If the media is not video based, see if there is any indication of a time. Does a character speak of how long it took? If so use this. If not and there is no other way to determine speed, you will need to assume a time frame. If it was a very quick feat, assume 1 second. If it was longer, 1 minute to upwards to 10 minutes can work. Go with whatever makes the most sense in the context of the feat. Once you have this time, convert whatever value you have into seconds.

3. Now that you have time frame, you need a distance. This can be gathered a variety of ways. If a something within the feat gives you a distance (e.g. Flash stating he just ran around the city), take this and convert whatever distance covered into meters; this conversion to meters applies for pixel scaling and angsizing. Whatever your result is, it must be in meters, The next option is pixel scaling, which will be most commonly used. In order to pixel scale, you will need a program capable of both capturing images and altering them. Two separate programs can be used to achieve this, or a single program if applicable. Gyazo and Paint.net can be used for image capture and alteration, respectively. If you are capturing a YouTube video, try to include the full screen for reference, which is 854x480 pixels when capturing with Gyazo. Once you are able to begin pixel scaling, bring up the full image and begin working. If the distance you want to measure isn't easily found, put it into perspective with another object/character in the shot. You will not always be graced with knowing the distance or height of what you want, so get creative. If there is an adult man in the shot, measure him in pixels and take the average height for men, which is approximately 177 centimeters, and find out how many centimeters/meters each pixel is worth. Once you have this, you can work from there. Sometimes you may need to scale an object to something of known height (X) to an unknown height object (Y) and apply the now found object (Y) height to a new object (Z) that wasn't previously scale-able, due to the lack of a known distance object on screen. Once you have determined how many meters/centimeters a pixel is worth, measure the distance in question to determine the real distance covered. To angsize, follow the guide on our. Remember to convert to meters if you were using any other measurement.

• Note! If the distance is not perfectly angled (not 0, 90, 180, 270, or 360 degrees), you will need to take the height and length, originating for the starting position, and find the hypotenuse to get an accurate distance. Feel free to use Google's hypotenuse calculator or input the formula yourself (c=a^2+b^2, where a^2+b^2 is under the square root symbol). If the distance can be determined by a 90 degree angle, do so to save yourself the time. Paint.net has a built-in angular indicator for the line function.

4. With both distance and time, divide distance covered in meters by time in seconds. S= D/T when S is speed in meters per second, D is distance in meters, and T is time in seconds. This is your result and the calculation is completed!

Speed Calc by Comparison

Oftentimes a distance will not be ascertainable, or it will not be accurate compared to what truly happened. Media oftentimes depicts extremely fast characters moving at moderate speeds for the audience's enjoyment; no one wants a fight to end in half a second. In order to determine the speed of such characters, you will need to compare the speed of a known object to that of the unknown. This is primarily done for bullet and lightning dodges.

1. Determine the true speed of the known object. If there is an arrow fired at the character, determine the speed of the arrow. For example, the average speed of a compound bow arrow is about 100 m/s. If you find a speed that isn't in meters per second, covert it to meters per second. If a gun was used, determine what gun it is and the speed of the gun. Google is your friend! Try to use the most scientifically based and accurate source as possible. Remember, if the fact you are looking up isn't common knowledge, you NEED to cite your sources. To put something as a link in source editor, use one backet containing the link and words; use two for in-wiki articles/sources (e.g. [.[Amon (StarCraft)]] without the period in between the brackets; (https://www.outdoorlife.com/features/chasing-speed-fastest-compound-bow/ 100 m/s) replacing the parenthesis with a single bracket). For lightning this Wiki uses 4.4x10^5 meters per second as the average lightning speed. Once you have your speed, it is time to compare it to the unknown speed object/character.

2. Determine the distance the known object moved. Follow the previous Step 3 of pixel scaling to do this. Once you have the distance for the known object, you need to determine how "fast" it was moving.

3. Find a time frame for the known object. Follow the previous Step 2 in order to do this. Once you have this you can determine the "speed" of your known object.

4. Divide distance over time as done in the previous Step 4. You will now have the speed at which the object appeared to move at, as well as the true speed of the object. Remember, you must get both of these in meters per second. For lightning, take the value of 4.4x10^5 and divide it by the amount you found. This is your multiplier for the unknown character's speed. For example, if the lightning appears to be moving at 63.8349 m/s, you know the scene is moving at 6892.781x faster than normal. For more info see these calcs.

5. Repeat the current Steps 2 to 4 for the unknown object's speed. Once you have that speed you can finish the calc.

6. Multiply your previously determined multiplier by the unknown character's found value to determine the unknown character's true speed. Calculation completed!

There are more advanced ways to find Speed, such as Rotational speed, but most of the less obvious forms of calcing can be learned as you progress.

Attack Potency Calculations

AP can be used to get a variety of stats. For example, AP can lead to finding Durability, Striking Strength, and even uses what you would need to find Lifting Strength, so long as the method you are using needs Mass. With that said, AP is far more variable and can be harder to find than speed. Common forms of AP can usually be seen in Destruction, Explosions, and Kinetic Energy, although there are many more ways to get AP than these (Latent Heat, Gravitational Binding Energy, and more). First you need to determine which method to use before proceeding. Did something get destroyed, cracked, broken, or even vaporized? Use Destruction. If an explosion was set off, use Explosions. If something moved at high speeds, use Kinetic Energy.

• Do note if using Kinetic Energy, do NOT Calc Stack! Calc Stacking occurs when you use a value as determined by another calculation from another scene and use it on your calc (e.g. Using another calc's Speed as a value for your Kinetic Energy).

While this will not be as in-depth as the Speed section, this will briefly overlook what needs to be done in order to find AP results for these three common methods.

Destruction

1. For Destruction, you need to determine volume in cubic centimeters. First, choose the most accurate formula for the object destroyed. See here for geometric formulas.

2. Next, you need to measure the object with either pixel scaling, as shown in the first Step 3, or a statement. Find all the values needed for your formula to be completed. For cubes and spheres, all you will need is a single value. For others you will need more. Remember, if you can't find the object's real size, get creative and look for objects around your target to get a comparison to use. For destruction volume, measure in centimeters.

3. Now that you have the inputs for the formula in centimeters, input in the values in order to get your result in cubic centimeters.

Explosions 1

1. For explosions, all you will need is radius. Get this value in any way you can, and enter the radius into this calculator. Change the megaton yield until your radius value appears. Use the airburst radius (either widespread destruction or near-total fatalities) as your radius.

2. Now take the value you found and divide it by 2. Calculation completed!

Explosions 2

You also have the ability to manually calculate the yield with a formula. This is a bit trickier, but it will help accuracy. If you are interested in using this formula, please view the section below under "Near Total Fatalities". See this blog for more information.

Kinetic Energy

1. Kinetic Energy, or KE, is the energy an object holds while moving. The formula is KE = 0.5xMxV^2, where KE is Kinetic Energy in joules, M is mass in kilograms, and V is speed in meters per second. As it would appear, you need to find speed and mass. Find mass. To do this, measure the volume of the object as listed in the Destruction Steps 1 and 2. Sometimes the mass will already be known, such as the mass of a car or human. If this is available to you, use this mass.

2. Now find the density of what is moving. Densities vary by object, so make sure you cite where you have found this density unless it is common knowledge. For example, the density of clouds is 1.003 kg per cubic meter.

• Warning! The value I just gave is in cubic meters. Make sure you use your value appropriately or suffer vastly skewed results.

3. Once you have density and volume, multiply the values to get mass. If everything was done properly, the value you have should now be the mass of the object being moved/moving in kilograms.

4. Obtain speed. See Speed Calcs above for more information on how to obtain speed.

5. Input your obtained speed value in meters per second and your obtained mass value in kilograms. When put into the formula, the result will be your energy in joules. Calculation completed!

Other

There are many other ways to calculate AP, but three notable others are Mass-Energy Conversion, Shearing Force, and Gravitational Binding Energy. The former may only be used if such a method is explicitly stated. If this type of conversion is stated, however, you can use the formula E=Mc^2, where E is energy in joules, M is mass in kilograms, and c is the speed of light in meters per second. Shearing Force is what is used for cutting or slicing feats. If you are interested when and how to perform such feats, these blogs will be useful. Gravitational Binding Energy is the energy needed to bind a planet together, as the name implies, if the planet is destroyed, you will be able to use this formula as a minimum, as its GBE has been overcome. This calculator can find GBE for you, as long as you can provide the values.

Practicing and Tips

You can either try to dive headfirst into original calculations of your own, or you can try to calculate an already accepted calculation from a Calculation Group member without looking at how they did it or the results in order to test your skills! If you choose to do this, try to work through the feat and calculate it. If you choose the same option that the original user did, you can see what their results were. If you got the same or a close result, you know you are on the right track. If your version is wildly different, try to find out what went wrong or what value changed the result.

Practicing can be a vital tool to hone your calcing skills before submitting a formatted blog post to get an original calculation evaluated. There are plenty of calculations out there, so you can practice nearly anything you wish before getting into making official, accepted calculations. Also, if you are having trouble in deciding where to go with a calculation, existing calculations can help you with unusual formulas or applications of anything mentioned here or elsewhere.

Common Calculation Examples

1. Speed Without Pixel Scaling: Interplanetary Travel

2. Speed With Pixel Scaling: Projectile Speed

3. Speed by Comparison: Lightning Dodges

4. Lifting Strength: Large Object Lifting

5. Attack Potency via Explosion: Standard Large Explosion

6. Attack Potency via Destruction: Destroying a "Mountain"

• Note! The above calculation is a perfect example as to why all "mountain busting" feats are not always Mountain level or higher. Don't take statements at face value if the feat is calcable.

7. Attack Potency via Storm Energy: Near-Planetary Storm Creation

8. Attack Potency via Kinetic Energy: Kinetic Energy of Storm Rotation

9. Attack Potency via Vaporization of Organics: Vaporization of Large Animals

• Note! Organic beings are made up of many different materials. This explains what goes into vaporizing a human or similarly sized organic lifeforms.

Formulas and References

Convertanyunit. Can convert Joules into Ton of Energy equivalents up to Yottatons. Very useful for quick conversion. Doesn't have values for FOE or Ergs.

You can also use Google's online converter.

Basic Formulas Kinetic Energy M * 0.5 * V^2

M = Mass in Kilograms

V = Velocity in m/s

Example:

The fastest car in the world (Hennessey Venom GT) has a top speed of 270 mph, or 120.701 m/s and a weight of 2,743 lbs, or 1244.204 kg

1244.204 * 0.5 * 120.701^2 = 9,063,236.94202 Joules. This is the kinetic energy of the Hennessey Venom GT at top speed.

Potential Energy MGH

M = Mass in Kilograms

G = Gravity in m/s^2 (almost always 9.8)

H = Height as in elevation in meters above ground level.

No real life example, but let's assume that you suspend the aforementioned Hennessey Venom GT in the air by 1 kilometer, or 1000 meters.

1244.204 * 9.8 * 1000 = 12,193,199.2 Joules

Near Total Fatalities

R = Y^(1/3)*0.28

R = Radius in Kilometers

Y = Yield in Kilotons

This one is a bit trickier to explain; it took me awhile to figure out so use an example from Antoniofer's blog regarding the formula.

Let's say you generate an explosion 45.5 kilometers in Radius. Plug that into the equation and solve for Y. I use this calculator to solve for Y.

So plugging the following into that calculator:

45.5 = Y^(1/3)*0.28

According to the calculation, that means Y = 4,291,015.625

Remember, that's the yield in Kilotons

Now to double check, remove the "R =" from the equation and plug the yield into it as such:

4,291,015.625^(1/3)*0.28 = 45.5

Reference Compendium

Latent Heat Values for Common Elements and Molecules

Conversion Table for Prefixes and Units

Algebraic Calculator

Converter for energy values

Destruction Values Table and Explanations

Gravitational Binding Energy Calculator

Units and Values

This section will give a brief overview of what commonly used values are, and what they mean and are used for.

Distance:

Centimeter: 1/100th of a meter.

Inch: A small imperial measurement. Equal to 2.54 centimeters.

Meter: A standard measurement of distance. Equal to 3.28 feet.

Kilometer: 1000 meters.

Mile: A large imperial measurement. Equal to 1.61 kilometers or 5280 feet.

Light Year: The distance light will travel in one year. Equal to 9.46x10^15 meters, 9.46x10^12 kilometers, or 5.879x10^12 miles.

• Note! Despite the name "light year", this is not a measurement of time. It is purely a measurement of distance. This value is found by taking the speed of light, 299,792,458 meters per second, and multiplying by the number of seconds in a year (31,536,000 seconds).

Energy:

Erg: A very small unit of energy measurement. Equal to 10^-7 joules.

Joule: The SI unit for work or energy.

Watt: Persistent energy measurement. Equal to 1 joule per second, and is equal to a joule in most scenarios.

Ton of TNT: Energy equal to the explosive release of 1 metric ton of TNT. Equal to 4.184x10^9 joules.

FOE: Energy equal to that of a standard supernova. Equal to 10^44 joules.

Formatting an Official Calculation

To make an official, acceptable calculation, make sure to put it in your Blog post. Provide it with a relevant title, feat description, context, and any media used in the calculation (if you uses a manga panel, provide the panel; if you pixel scaled a picture or image, profile the edited picture). Explain your work; attempt to make it as easy as possible to read and understand. Preferably, someone who has no experience with calculations should know what you are doing and why you are doing it.

If you feel so inclined you can organize the post further by dividing up the post with two equals signs (==insert section here==) that will divide the post into manageable and quickly comprehensible chunks, and use three apostrophes (insert important text here) to bold important information, such as significant values, formulas, and results.

Once you are done, end the blog post by giving the found values as well as the result in an energy rating/speed as well as our corresponding ratings (e.g. 7.369x10^13 joules, 7-C, Town level). Now upload it to your Blog.

Large Size Calculations

In fiction, there are many characters of Large Size. When it comes to tiering them their size alone can be an indicator of their statistics. This page explains which statistics can and can't be calculated from size alone.

Attack Potency

The physical attack potency, and with it the durability, can be estimated from the size of a character alone.

That follows a simple conservative estimation: Any character can at least just fall unto someone. In other words, their potential energy can be used to attack. The only prerequisite to this method is that the character should be at least Type 0 Size on the Large Size scale.

In order to perform the calculation one will need the mass of the character and its center of mass.

The center of mass of a human-shaped character is about 10 cm below the navel, albeit this varies from individual to individual. Generally one can estimate that it is around 50% of the body height up.

In order to find the mass of the character upscaling methods are helpful. If the character is x-times larger than its normal-sized counterpart, and made of roughly the same materials, then its mass would be about x^3-times larger.

With this information, the energy can be calculated via the usual GPE methods.

Except for very large characters that is simply "Potential energy = mass*9.81*height of center of gravity". Mass should be in kilogram and height in meter. The result is in joule.

An alternative method to calculate Attack Potency from size is from Kinetic Energy. There one takes the mass of the character and uses its running speed to get Kinetic Energy via "Kinetic Energy = 0.5*Mass*(Running speed)^2". Here mass should be in kilogram and running speed in meter per second. The result is in joule.

The best practice is to measure the speed directly from the source material. Should that not be possible, but it is known that the character moves relative to its size as fast or faster than its normal-sized counterpart, upscaled speed can be used. To confirm that they are that fast, it must be clear that they, for instance, take steps within the same timeframe or less than a normal human would. If that is the case, then their speed should be x-times higher than that of their normal-sized counterpart, if they are x-times larger.

Lifting Strength

Lifting Strength should not be calculated from size. While characters have to lift more bodyweight, lifting strength is the weight they can lift in addition to that. There is no way of telling how much more that is.

Speed

As mentioned in the AP section speed can under circumstances be taken from size. An x-times larger character should also be x-times faster. However, strict confirmation is necessary.

Cloud Calculations

Due to being virtually always present clouds are one of the most common objects affected by the attacks or powers of characters. As such how to calculate feats involving the creation, destruction or movement of clouds is of common interest.

Cloud Volume

The first step necessary for any cloud calculation is determining how much of a certain cloud was affected (created, destroyed or moved). Pixel scaling is the most reliable way to do so and the first thing one should try to do. However, in case of clouds there often is nothing one could scale from. Hence other practices are often relevant.

Viewing Distance

If all clouds visible in the sky are affected and the view to the horizon is not obstructed by obstacles, through for example buildings or trees, one can use the maximum viewing distance to figure out the radius in which the clouds are affected. There are two things that limit how far one can see. One is the curvature of earth, that is the horizon, and the other is the visibility, that is how much fog, air pollution and similar limit the maximum viewing distance.

In practice the limit is almost always determined by the visibility, as clouds, due to being high up in the sky, are usually in the line of sight for over a hundred kilometers beyond the horizon.

On clear days (no rain, fog or snow) the visibility is about 20km. On very clear days it can be around 50km and on exceptionally clear days even 280km. On slightly hazy days it can also just be 10km.

The standard value to use is hence 20km. Higher or lower values can be used if there is a reason for it.

Characteristic Cloud Thickness

Different types of clouds have a characteristic thickness to them. The thickness is the distance from the lower border to the upper border of the clouds. If clouds can't be directly scaled this is usually the only way to figure out the height to use for the calculation of the affected cloud volume.

Cloud Type	Description	Characteristic Thickness	Appearance
cirrus	Generally characterized by thin, wispy strands. They are usually white or light gray in colour. Since cirrus clouds arrive in advance of the frontal system or tropical cyclone, it indicates that weather conditions may soon deteriorate. While it indicates the arrival of rain, cirrus clouds only produce fall streaks (falling ice crystals that evaporate before landing on the ground).	100m to 8000m, with 1500m on average.
stratus	Low-level clouds characterized by horizontal layering with a uniform base. They vary from dark gray to nearly white. Stratus clouds may produce a light drizzle or a small amount of snow. These clouds are essentially above-ground fog formed either through the lifting of morning fog or through cold air moving at low altitudes over a region.	Less than 1000 meters
cumulus	Clouds which have flat bases and are often described as "puffy", "cotton-like" or "fluffy" in appearance. Cumulus clouds are often precursors of other types of clouds, such as cumulonimbus. Normally, cumulus clouds produce little or no precipitation.	600m to 2000m
stratocumulus	Clouds characterized by large dark, rounded masses, usually in groups, lines, or waves. They look much like cumulus clouds, except lumped together and bigger.	Less than 1000 meters, of the order of 100m
Nimbostratus	A cloud with a diffuse cloud base. Although usually dark at its base, it often appears illuminated from within to a surface observer. Typical rain clouds.	2000m to 4000m
cumulonimbus	Dense, towering vertical clouds. They are the clouds that usually accompany heavy rain, storms and thunderstorms.	Usually between 8000m to 11800m. Sometimes as few as 2000m in polar air.

Volume

Using the two values from above one can approximate the volume of the clouds. A simple acceptable approximation is given by pi*(viewing distance)^2*(cloud thickness). There are better, but more complicated, formula model the clouds as the intersection of a spherical shell and a spherical sector. However, usage of those usually isn't necessary with the normal distances.

Cloud Mass

In order to determine the cloud mass from its volume one simply has to multiply it with the clouds density. However, what a clouds density is can be defined in two different ways

1. The density of the water in the cloud.
2. The density of the water and air in the cloud together.

Which to use depends on which way the cloud was affected. Chemical changes, like vaporization or condensation of water use the first density, while movement changes like the creation of instabilities or changing the clouds position or shape use the second density.

The density of the water and air in the cloud together is approximately 1.003 kg/m³.

The density of just the water in the cloud is the liquid water content. The liquid water content depends on the cloud type. Following values can be used as orientation:

Cloud Type	Liquid Water Content (g/m3)
cirrus	0.03
fog	0.05
stratus	0.25 to 0.3
cumulus	0.25 to 0.3
stratocumulus	0.45
Nimbostratus	nearly 1
cumulonimbus	1 to 3

Energy

In order to get the final result you need to find out which method was used to affect the clouds. There are 3 methods that are typical:

1. Condensation, for creation, or vaporization, for destruction, of clouds. This should be used if clouds are created or destroyed, by condensing / vaporizing the water that makes up the cloud. If the cloud creation includes the creation of great amounts of natural winds, in other words storms, CAPE should be used instead.
2. Kinetic Energy for moving of clouds. Should only be used if clouds are moved from one place to another.
3. Convective available potential energy (CAPE) for creation of storms. Should be used if clouds are created together with a lot of wind. If the CAPE value is lower than the condensation value, use condensation instead.

If it can not be said, within reasonable certainty, which of the three methods applies to the created clouds all three can be calculated and the lowest result used.

Condensation / Vaporization

To calculate the energy necessary to create/destroy the clouds via condensation/vaporisation simply take the mass of the clouds (water mass, without air), in kilogram, and multiply it by the latent heat of vaporization for water, which is 2264705 J/kg. An even better result can be reached if one estimates the temperature and uses the formula here to get the latent heat of condensation for water in clouds and multiplies that with the mass of the clouds (in gram).

Kinetic Energy

To calculate the energy via kinetic energy one needs to additionally know the speed at which the clouds were moved. Since speed is distance over time, one needs to somehow figure out these two values. If that it done it can simply be calculated through the formula "kinetic energy = 0.5 * cloud mass * (Speed of cloud movement)²". The cloud mass is here the mass with the air.

One should keep in mind that not all clouds in a cloud movement feat necessarily move with the same speed. In such cases one has to calculate the kinetic energy with the different speeds of the different parts in mind. An example of this would be creating clouds and spreading them omnidirectionally around a center point. In that case the speed with which the clouds move may increase the further from the center they are. In the case of such an omnidirectional expansion one could use the formula "kinetic energy = 0.25 * cloud mass * (Speed of cloud movement)²" to account for the different speeds involved.

For pulling in clouds omnidirectional towards a center point, or dispersing them from a center point, the formula "kinetic energy = 1/12 * cloud mass * (Speed of cloud movement)²" can be used.

CAPE

C.A.P.E is an indicator of atmospheric instability and hence associated with storms and their strength. In order to calculate the energy to create a storm we approximate the C.A.P.E. using some simple indicators and from that the necessary energy.

The main variable for the calculation is the value for instability.

Using this thread as a reference, our alternatives for instability will be as follows:

• 1 Kj/kg, - "weak instability"
• 2.5 Kj/kg - "moderate instability"
• 4 Kj/kg - "strong instability"
• 5.89 Kj/kg - 1999 Oklahoma Tornado Outbreak
• 8 Kj/kg - 1990 Plainfield Tornado

In order to make use of the value we chose, we need to calculate the mass of the clouds.

First we need the volume. That can be calculated as described here. That cloud type to assume for that is cumulonimbus.

Then we get the mass by multiplying the volume with 1.003 kg/m^3.

Multiplying that with the instability value gives us the energy in Kj.

For short the formula is: Volume (in m^3) * 1.003 kg/m^3 * Instability.

Standard results

In the following a table of the most common results will be given. For that the following assumptions will remain steady throughout all of the results:

• The storm is cylindrical in shape
• The clear day viewing distance is the radius the clouds cover (20km).

The variables that will change:

• The thickness of the clouds: The clouds of the storms are assumed to be cumulonimbus clouds and hence about 8000m to 11800m tall
• Assumed Instability in Kilojoules

	8000m	11800m
1 Kj/Kg	1*1016 J	1.48*1016 J
2.5 Kj/Kg	2.5*1016 J	3.71*1016 J
4 Kj/Kg	4*1016 J	5.94*1016 J
5.89 Kj/Kg	5.93*1016 J	8.76*1016 J
8 Kj/Kg	8*1016 J	1.18*1017 J

Table of Results using CAPE and Different Real-Life Examples

The values of this table are obtained form using the areas of different countries, continents, oceans, etc., multiplying it by 8000 to 11800 meters to get the volume, using cloud density to find the mass and using CAPE multipliers to get AP values from the storm cloud's mass.

Assumptions:

• The storm covers the entirety of the country/continent/island/ocean/etc. or an area equivalent to its total area and nothing else.

That's about it.

The following formula is used:

(Area of country in m^2 * (8000m or 11800m)) * 1.003 * CAPE

CAPE will be switched out for 1000 j/kg, 2500 j/kg, 4000 j/kg, 5890 j/kg, and 8000 j/kg for different ends.

Vatican City - 440,000 m^2

	1000 j/kg	2500 j/kg	4000 j/kg	5890 j/kg	8000 j/kg
8000 m	3.53056e+12 J	8.8264e+12 J	1.412224e+13 J	2.0794998e+13 J	2.824448e+13 J
11800 m	5.207576e+12 J	1.301894e+13 J	2.0830304e+13 J	3.0672623e+13 J	4.1660608e+13 J

Malta - 316,000,000 m^2

	1000 j/kg	2500 j/kg	4000 j/kg	5890 j/kg	8000 j/kg
8000 m	2.535584e+15 J	6.33896e+15 J	1.0142336e+16 J	1.493459e+16 J	2.0284672e+16 J
11800 m	3.7399864e+15 J	9.349966e+15 J	1.4959946e+16 J	2.202852e+16 J	2.9919891e+16 J

New York City - 783,800,000 m^2

	1000 j/kg	2500 j/kg	4000 j/kg	5890 j/kg	8000 j/kg
8000 m	6.2892112e+15 J	1.5723028e+16 J	2.5156845e+16 J	3.7043454e+16 J	5.031369e+16 J
11800 m	9.2765865e+15 J	2.3191466e+16 J	3.7106346e+16 J	5.4639095e+16 J	7.4212692e+16 J

Rhode Island - 4,002,000,000 m^2

	1000 j/kg	2500 j/kg	4000 j/kg	5890 j/kg	8000 j/kg
8000 m	3.2112048e+16 J	8.028012e+16 J	6.4032e+13 J	1.2844819e+17 J	2.5689638e+17 J
11800 m	4.7365271e+16 J	1.1841318e+17 J	1.8946108e+17 J	2.7898144e+17 J	3.7892217e+17 J

Hawaii - 28,311,000,000 m^2

	1000 j/kg	2500 j/kg	4000 j/kg	5890 j/kg	8000 j/kg
8000 m	2.2716746e+17 J	5.6791866e+17 J	9.0866986e+17 J	1.3380164e+18 J	1.8173397e+18 J
11800 m	3.3507201e+17 J	8.3768002e+17 J	1.340288e+18 J	1.9735741e+18 J	2.6805761e+18 J

Japan - 377,930,000,000 m^2

	1000 j/kg	2500 j/kg	4000 j/kg	5890 j/kg	8000 j/kg
8000 m	3.0325103e+18 J	7.5812758e+18 J	1.2130041e+19 J	1.7861486e+19 J	2.4260083e+19 J
11800 m	4.4729527e+18 J	1.1182382e+19 J	1.7891811e+19 J	2.6345691e+19 J	3.5783622e+19 J

California - 423,970,694,000 m^2

	1000 j/kg	2500 j/kg	4000 j/kg	5890 j/kg	8000 j/kg
8000 m	3.4019409e+18 J	8.504852e+18 J	1.3607763e+19 J	2.003743e+19 J	2.7215522e+19 J
11800 m	5.0178628e+18 J	1.2544657e+19 J	2.0071434e+19 J	2.95552e+19 J	4.0142888e+19 J

Texas - 695,621,000,000 m^2

	1000 j/kg	2500 j/kg	4000 j/kg	5890 j/kg	8000 j/kg
8000 m	5.5816629e+18 J	1.3954157e+19 J	2.2326652e+19 J	3.2875995e+19 J	4.4653303e+19 J
11800 m	8.232951e+18 J	2.0582382e+19 J	3.2931812e+19 J	4.8492091e+19 J	6.5863622e+19 J

Alaska - 1,717,854,000,000 m^2

	1000 j/kg	2500 j/kg	4000 j/kg	5890 j/kg	8000 j/kg
8000 m	1.378406e+19 J	3.4460151e+19 J	5.5136242e+19 J	8.1188116e+19 J	1.1027248e+20 J
11800 m	2.0331472e+19 J	5.082871e+19 J	8.1325956e+19 J	1.1975247e+20 J	1.6265191e+20 J

Brazil - 8,515,767,000,000 m^2

	1000 j/kg	2500 j/kg	4000 j/kg	5890 j/kg	8000 j/kg
8000 m	6.8330514e+19 J	1.7082629e+20 J	2.7332205e+20 J	4.0246673e+20 J	5.4664403e+20 J
11800 m	1.0078751e+20 J	2.5196865e+20 J	4.0315003e+20 J	5.9363843e+20 J	8.0630007e+20 J

Arctic Ocean - 13,985,935,800,000 m^2

	1000 j/kg	2500 j/kg	4000 j/kg	5890 j/kg	8000 j/kg
8000 m	1.1222314e+20 J	2.8055788e+20 J	4.4889259e+20 J	6.6099435e+20 J	8.977851e+20 J
11800 m	1.6552914e+20 J	4.1382286e+20 J	6.6211657e+20 J	9.7496665e+20 J	1.324233e+21 J

India Ocean - 70,551,276,126,000 m^2

	1000 j/kg	2500 j/kg	4000 j/kg	5890 j/kg	8000 j/kg
8000 m	5.6610343e+20 J	1.4152586e+21 J	2.2644137e+21 J	3.3343491e+21 J	4.5288274e+21 J
11800 m	8.3500251e+20 J	2.0875064e+21 J	3.3400103e+21 J	4.9181644e+21 J	6.6800205e+21 J

Pacific Ocean - 152,809,298,510,000 m^2

	1000 j/kg	2500 j/kg	4000 j/kg	5890 j/kg	8000 j/kg
8000 m	1.2261418e+21 J	3.0653546e+21 J	4.9045673e+21 J	7.2219751e+21 J	9.8091346e+21 J
11800 m	1.8085592e+21 J	4.5213976e+21 J	7.2342366e+21 J	1.0652414e+22 J	1.4468473e+22 J

All of the earth's oceans - 360,000,000,000,000 m^2

	1000 j/kg	2500 j/kg	4000 j/kg	5890 j/kg	8000 j/kg
8000 m	2.88864e+21 J	7.2216e+21 J	1.155456e+22 J	1.701409e+22 J	2.310912e+22 J
11800 m	4.260744e+21 J	1.065186e+22 J	1.7042976e+22 J	2.5095782e+22 J	3.4085952e+22 J

Surface area of the entire Earth - 509,968,658,925,000 m^2

	1000 j/kg	2500 j/kg	4000 j/kg	5890 j/kg	8000 j/kg
8000 m	4.0919892e+21 J	1.0229971e+22 J	1.6367954e+22 J	2.4101809e+22 J	3.2735908e+22 J
11800 m	6.0356831e+21 J	1.5089208e+22 J	2.4142732e+22 J	3.5550172e+22 J	4.8285465e+22 J

Creating a real-life hurricane

If a character creates a real-life hurricane, or its winds, the following calculation can be used. What is important is that one is reasonably certain that the hurricane in question covers the same gigantic area as a real one typically does. Usually, characters with the ability to manipulate the weather don't necessarily create one of this size, instead of more local phenomena. Hence a convincing argument regarding the size needs to be made. The following calculation was originally made here by Chris Landsea:

Hurricanes can be thought of, to a first approximation, as a heat engine; obtaining its heat input from the warm, humid air over the tropical ocean, and releasing this heat through the condensation of water vapor into water droplets in deep thunderstorms of the eyewall and rainbands, then giving off a cold exhaust in the upper levels of the troposphere (~12 km/8 mi up).

One can look at the energetics of a hurricane in two ways:

1. the total amount of energy released by the condensation of water droplets or ...
2. the amount of kinetic energy generated to maintain the strong swirling winds of the hurricane.

It turns out that the vast majority of the heat released in the condensation process is used to cause rising motions in the thunderstorms and only a small portion drives the storm's horizontal winds.

Method 1) - Total energy released through cloud/rain formation: An average hurricane produces 1.5 cm/day (0.6 inches/day) of rain inside a circle of radius 665 km (360 n.mi). (More rain falls in the inner portion of hurricane around the eyewall, less in the outer rainbands.) Converting this to a volume of rain gives 2.1 x 1016 cm3/day. A cubic cm of rain weighs 1 gm. Using the latent heat of condensation, this amount of rain produced gives 5.2 x 10^19 Joules/day or 6.0 x 10^14 Watts.

Method 2) - Total kinetic energy (wind energy) generated: For a mature hurricane, the amount of kinetic energy generated is equal to that being dissipated due to friction. The dissipation rate per unit area is air density times the drag coefficient times the windspeed cubed. One could either integrate a typical wind profile over a range of radii from the hurricane's center to the outer radius encompassing the storm, or assume an average windspeed for the inner core of the hurricane. Doing the latter and using 40 m/s (90 mph) winds on a scale of radius 60 km (40 n.mi.), one gets a wind dissipation rate (wind generation rate) of 1.3 x 10^17 Joules/day or 1.5 x 10^12 Watts.

Conclusion:

1. Energy to create Hurricane Force winds: 1.5e+12 J / 358.508604207 Tons of TNT, Multi-City Block level
2. Energy to create a full Hurricane: 6.01e+14 J / 143.642447418938 Kilotons of TNT, Large Town level

Common Results

The following values assume that the clouds in question cover a radius of 20km and are cumulonimbus clouds and hence 8000m thick and have a liquid water content of at least 1 g/m^3. For the kinetic energy values it is assumed that the storms are pulled from 20km so that in the end the sky is completely covered within 1 minute. That means this values should not be used, if the timeframe might be longer, the viewing distance is limited to below 20km or the clouds in question are not cumulonimbus clouds.

	Energy	Attack Potency
Condensation	2.277e+16 J	Small City level
Kinetic Energy	9.336+16 J	City level

Step 1: Find the Size of the Explosion

First, you have to find the exact page, or scene where an explosion is shown as a feat. Depending on the environment where the explosion occurred, you may have to scale the size of a smaller object that is shown in the map. Let's do an example...

Example 1: An Explosion Occurs

An explosion of unknown size occurs in this picture, engulfing the object. Find the size of the explosion. The explosion is shown in the below scene.

• The first thing that notice is that you do not know the exact size of the object shown in the picture.
• However, you are allowed to find the size of the object by comparing it with an another object, such as the one shown beside the object.

Step 2: Finding the Radius of the Explosion

From example 1, there is a scene that shows the object in relation to the object shown from the first picture. This is located below. We will use the height of the door as a reference in this case.

• Given that the door size of the door is 7 feet, or 2.13 metres tall, you can now find the size of the object.
• Log down the size of the object.
• After you have found the size of the object, you compare the size of the object to the diameter of the explosion shown in the first picture.
• Divide the diameter by two to get the radius of the explosion.

Step 3: Finding the Yield of said Explosion

Here is a sample calculator that you can use in order to find the yield of an explosion, provided that you have found the exact diameter of it. Keep note that if the explosion is against a surface it is preferred, but not required, that you use the surface detonation setting on this calculator.

• Generally, you take the near-total fatalities section from the list of calculated values/calculator above.
• As for why it is used, the definition of near-total fatalities means states that: all large above-ground structures are destroyed within that radius, as well as causing 100% fatalities to anyone that is affected within the radius due to sheer pressure alone.
• When you get the result of said explosion, you multiply the value by 0.5. This is because only 40 to 50 percent of the total energy of the explosion is actually from the blast.
• Keep in mind that if the explosion is an actual nuclear explosion, you can disregard the point above.

If you are having a hard time using the nuclear calculator, this equation can be used to find the yield of said explosion.

• Air blast radius (near-total fatalities) Yield: Y = ((x/0.28)^3)/1000 with Y in megatons of TNT and x the radius in km.

However, the rules above are for explosions happening in mid-air. For explosions that happen on the ground, we use this formula:

• W = R^3*((27136*P+8649)^(1/2)/13568-93/13568)^2, where W is the yield in tons of TNT, R is the radius in meters, and P is the shockwave pressure in bars, where we generally use 1.37895 bars or 20 psi of pressure.

Durability From Tanking an explosion

Let's say an explosion occurs and a character endures the explosion. If that explosion doesn't occur close to the character the amount of energy that hits it will be significantly lower than the full energy of the explosion. To find the actual amount of the energy from the explosion that he/she tanks one first applies the inverse square law.

Credit to Wikipedia

What does the inverse square law state?

• The further you are away from an explosion, the less damage you will take from it. That is, because the power of said explosion is distributed over a larger and larger surface area as the distance from the epicenter increases.
• The surface area of a sphere is A = 4πr^2. This is relevant because when an explosion occurs, the energy of said explosion radiates outwards as a sphere, unless obstructed. If it happens on the ground the explosion is restricted in the downwards direction and hence only expands in half a sphere, meaning A = (4πr^2)/2. Other surface areas are imaginable as well.
• The intensity of said explosion at a distance of r is I = P/A, where I = Joules of energy, A is as above and P=Power/Yield of explosion, in Tons of TNT.
  • I is a measure of Energy per Area (J/m^2 in SI units).

How does that relate to the durability needed to survive an explosion?

• The amount of energy that hits a target if r meters away from an explosion is E=I*CA, where I is calculated as described above and E is the energy the target is hit by. CA is the crossectional area of the target. That is the area of the largest cross section of the target that is orthogonal to the direction the explosion expands into. That is not half the surface area of the target, but less than that. For a sphere for instance this would not be 4*pi*r^2 / 2, but instead pi*r^2 as that is the area of the largest cross-section which, in this case, is a circle with the same radius as the sphere laid through its center (in such a way that it is orthogonal to the expansion of the explosion).
  • It should be noted that the above idea of calculating it via the crosssectional area is strictly speaking a simplification that work well when the size of the target is small when compared to that of the explosion at the point it hits it. If one imagines the source of the explosion as a lightsource and the shockwave of radius r as a sphere or dome, then the area of the shadow that the object throws on the sphere/dome is the precise area to be used. This is, in general, considerably more difficult to calculate, though. The crossectional area as explained above will generally provide an underestimation of the area in question.
• CA is approximately 0.68 m^2 for a grown human. It can also be estimated as half of the bodies surface area calculated using this, but that is a slight overestimation.

Let's do an example.

Example

An omnidirectional explosion of 7 kilotons of TNT occurs, and a human 30 meters away from the epicenter endures the explosion. How high is the durability of the human?

• First, we set P = 7000 Tons of TNT, as that is the yield of said explosion.
• Second, we set the radius, or r = 30m
• Third, we find the value of I, or the intensity of the explosion at a specific distance.
• I = (7000 Tons of TNT) / (4π((30m)^2))
• This means at 30 metres away from the epicenter of the explosion, the shockwave is hitting with an intensity of I = 0.619 Tons of TNT per m^2.
• CA = 0.68 m^2 for a human.
• So I*CA = 0.619 Tons of TNT per m^2 * 0.68 m^2 = 0.42092 Tons of TNT = E.
• The character can withstand a 0.42092 Tons of TNT blast, meaning Building level durability.

Explosion Radius

The aim of this page is to find the area (near-total fatalities) that an explosion should cover to reach certain AP tier.

Using the formula from, R = Y^(1/3)*0.28, where Y is the yield in kilotons and R the radius in km, so that:

• Yield*2 ==> Radius*2^(1/3) = Radius*1.26
• Yield*5 ==> Radius*5^(1/3) = Radius*1.71
• Yield*10 ==> Radius*10^(1/3) = Radius*2.1544

Since the calculator didn't give results below 1 kiloton, the above would be useful; using these lists we will find the required area.

Nuclear Explosions

These values can only be used when the detonation has a nuclear origin.

• Room level (4.8 - 17.7 m) = The size of a Tennis court, the size of a Volleyball court, the area of a typical three-bedroom house
• Building level (17.7 - 35.3 m) = The surface of a Olympic-size swimming pool
• Large Building level (35.3 - 62.3 m) = An American football field area, a Soccer field area, a Baseball field area (including outfield), Hagia Sophia
• City Block level (62.3 - 130 m) = A cricket field area, a common city block from Manhattan, the Pyramid of the Sun area
• Multi City Block level (130 - 280 m) = Great Pyramid of Giza area (min)
• Small Town level (280 - 500 m) = The Vatican City, The Pentagon
• Town level (0.5 - 1.3 km) = The City of London
• Large Town level (1.3 - 2.7 km) = The Smallest Oceania islands (min), Machu Picchu
• Small City level (2.7 - 5 km) = Nauru (min), Manhattan Island
• City level ( 5 - 12.5 km) = Teotihucan (min), Taipei City, Disney World, Paris (inner city), Washington D.C., Hollywood, Brooklyn
• Mountain level (12.5 - 28 km) = wikipedia:es:Andorra:Andorra (min), Los Angeles, Hong Kong, Tokyo
• Large Mountain level (28 - 45.5 km) = Luxembourg (min), Trinidad Island
• Island level (45.5 - 130 km) = Jamaica, Belgium, Puerto Rico, Israel, Netherland, Yellowstone National Park
• Large Island level (130 - 280 km) = Austria, South Korea, North Korea, Greece, Great Britain, Cuba, Benelux
• Small Country level (280 - 535.6 km) = Philippines, Japan, Spain, Turkey, Germany, France
• Country level (535.6 - 1300 km) = Egypt, Alaska State, Mexico, Greenland, Argentina, India
• Large Country level (1300 - 2555 km) = Australia, Brazil, China, United States of America, Antarctica, the area of Pluto, Russia, Canada, South America, Europe
• Continent level (2555 - 4600 km) = Africa, the area of the Moon, The Americas, Asia
• Multi-Continent level (4600 - 86614.1 km) = The Area of Mars, the area of Earth, the area of Neptune

Non-Nuclear Explosions

• Small Building level (6 - 22.2 m)
• Building level (22.2 - 44.4 m)
• Large Building level (44.4 - 78.5 m)
• City Block level (78.5 - 163.7 m)
• Multi-City Block level (163.7 - 352.8 m)
• Small Town level (352.8 - 633.8 m)
• Town level (633.8 - 1637.4 m)
• Large Town level (1.67 - 3.53 km)
• Small City level (3.53 - 6.5 km)
• City level (6.5 - 16.4 km)
• Mountain level (16.4 - 35.3 km)
• Large Mountain level (35.3 - 57.4 km)
• Island level (57.4 - 163.7 km)
• Large Island level (163.7 - 352.8 km)
• Small Country level (352.8 - 674.8 km)
• Country level (674.8 - 1637.4 km)
• Large Country level (1637.4 - 3220 km)
• Continent level (3220 - 5800 km)
• Multi-Continent level (5800 - 86650 km)

Calc Stacking

Calc stacking refers to the practice of using results from one calculation in order to calculate other feats. Calc stacking is flawed in nature and any calculations that use it will be disregarded almost always. This is due to the level of inconsistency it gives along with inflated results. Through the method any long running franchises could also scale their stats infinitely upwards without actually ever showing any feats in the range they are listed.

Only parameters that can't change between calculations can be re-purposed. To provide a few examples:

• Pixel scaling over several steps is permitted, as long as the size of the scaled objects usually stays constant.
• Using the calculated speed of a projectile to calculate the speed of a character dodging said projectile on the very same occasion is usually permitted, as long as the projectile wouldn't have changed its speed mid flight.
• Using a reliable stated timeframe and reliably stated speed something travels during that timeframe one can calculate the distance travelled. Said distance can then usually be used for calculations.
• Multipliers can be used under the conditions lined out on the multiplier page.
• Using speed of characters or attacks calculated at other instances can't be used, as characters and attacks can vary in speed. This is the case regardless of whether the character is seriously trying to do his best or anything similar.

However, even for these parameters calc stacking is avoided as much as possible. That means that results taking less such steps are usually taken over results that rely on more calc stacking.

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