Calculations

## What is a calculation?

A calculation (referred to as calc for short) is a method of determining a statistic (referred to as stat for short) of a character (usually Attack Potency or Speed) in cases where it cannot be directly determined. It makes use of scientific formulae and mathematical equations to calculate any particular stat of the character.

## Benefits of a calculation

Since scientific formulae and mathematical equations are universally standard and objective (i.e. not subject to either opinions or individual perspectives), they are accepted as true and not subject to debate by either supporters or opponents of the fictional series. In simplified terms, a calc is the best and most objective method to either prove or disprove a statement, or end a debate as it were.

## Drawbacks of a calculation

Of course, not everything is that simple. Even calculations have their own drawbacks. For one, calculations generally involve pixel scaling (more of that later on) which is hard to measure and utilize. Calculations also make presumptions beforehand which are subject to much debate (and are hence not argument-proof). Last of all, calculations are tough. To not only calculate a stat, but to also convey the procedure step by step is tricky and often leads people confused if done incorrectly.

## Frequently Used Measuring Techniques

### Pixel Scaling

As we have discussed in the calculation methods page, we will most likely need to determine volumes of various objects in order to determine destructive capacity, and as we've also discussed, volume is composed of three perpendicular dimensions, and in order to find the lengths of those dimensions, we will use Pixel Scaling.

Pixel Scaling works much like the scales we have on maps, in fact its were the name of the term comes from. In maps you the scale that states how many Kilometers/meters one Centimeter on the map represents in the real world, in Pixel Scaling we try to find how many kilometers/meters/centimeters one pixel represents on a certain scan, and we will find said ratio by using measuring stick.

A measuring stick (not to be confused with the real life measuring sticks and rulers) is basically something that we already know the size of, and can measure how many pixels in the scan it takes to cover said size, for example; if a human whose height is 172 centimeters would be portrayed as 172 pixels high in a certain, the scale would be one centimeter per pixel in said scan.

However, there are some flaws in Pixel Scaling, such as the fact that we measure feats in 3 dimensions, while scans of comics and manga are 2 dimensional, that is why we need to make sure that every object we scale must be in close proximity to our measuring stick.

Angular size

If we need to find the size of something that is far away, or the distance from it to us or to a certain object, we will need to use the angular size formula which states that ; Retinal Size= Size of Object/ Distance of object.

Using you're measuring stick, you can find the retinal size, so in order to use this formula, you will need to know either the distance of the object or its original size, depending on what it is you are trying to calculate.

this method gives a solution to the problems that sometimes occur in pixel scaling, but it is important to remember that if both a direct pixel scaling measurement for a certain object in one scan, and an Angular size measurement for said from another scan are taken, and do not give a close results, pixel scaling takes precedent, and should be treated as more accurate.

## Starting a calculation

Start a calculation by first obtaining three things:

a) Presumptions: Every calculation needs a certain set of presumptions to justify the subsequent calc. List your presumptions clearly and state your reasons for the presumption.

b) Scans: If your calculation makes use of pictures (such as manga panels), it is imperative that you present it to the community for first-hand viewing.

c) Scientific guides/articles: If your calculation makes use of any scientific formula which is obscure, present a link to the formula in question.

Once all three are obtained, present your calculation.

## The calculation

Display every step of your calculation (equations and such), along with a sentence in order to explain the workings of your calc. Also try to explain the science behind your calc as you go along. Make sure to highlight important figures and equations which are to be utilized repeatedly. Also, highlight all end results for fast viewing.

## After the calculation

Once your calculation is done, invite community members to inspect your calc, who will do so. The community may point out any errors in the calc or in the presumptions before it. Try and explain your point if there is a misunderstanding. In case of any errors, correct them. In case of a discrepancy, members can ask Admins to present their opinions on the matter.

## Conclusion

At the end of a calculation, if it accepted by the community, link the relevant pages to the calculation in question. If otherwise, try to find out the reasons for discarding your calc and next time, make a calc keeping them in mind.

## 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 preform such a feat. Sometimes the destructive capacity of the feat can be determined easily with no need of a calculation, but most of the times 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, more information about the subject on the GBE page .

**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 earths 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 earths atmosphere.

Note: if the meteor in question wasn't ablated and didn't come from outer space, we will us Potential-Gravitational Energy, as it does not requires the use of speed:

Ep = M\*g\*h

M = mass

g = Gravity

h = height

That is unless we can mathematically find a speed for the meteor.

**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 recieve 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 4181J/kg°K

Heat of fusion for water is 334.16J/g

**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 findiing 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.

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 magaton 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 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

From here, 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 120 (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).

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.

**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

**Others**

Elipsoid calculator

Projectile motion calculator

Planetary parameter calculator

Relativity calculator

Asteroid destruction calculator

Asteroid/Comet calculator