Miscellaneous Calculations

This page is to talk about and show calculations that are of different measurements besides kinetic and potential energy.

## Bekenstein Limit

This is to calculate how much maximum amount of information there is in a certain space before becoming a black hole. With this, can you find how much mass and/or energy there is for stat for intelligence or information processing. Here are some of the components for the formulas:

* I = Information (bits)
* R = Radius (meters)
* m = Mass (kilograms)
* *ħ* = reduced Planck constant (1.054571800e-34 J/s)
* c = speed of light (299792458 m/s)
* *ħc* = reduced Planck constant (3.16152649e-26 J/m)
* ln = natural logarithm (log)
* E = energy (Joules)

For Mass formula:

(2\*pi\*299792458\*R\*m/1.054571800e-34\*log(2))

For Energy formula:

(2\*pi\*R\*E/3.16152649e-26\*log(2))

Or to find Energy from Information:

I/(2\*pi\*R/3.16152649e-26log(2))

## Bending Strength/Energy

For this section, we will be finding the energy and force needed to bend certain objects, which the former would apply to the Lifting/Striking Strength calcing.

In reference to this calc for Force of a rectangular object (for a long tubular bar, calc here):

1. you would need to find the the dimensions (in) of the material that is being bent
	1. The thickness
	2. the length of material
	3. and the die opening (which is the distance between a welding point)
2. Then you would need to find the Ultimate Tensile Strength of the material (psi)
3. Set the Safety Factor, which is usually 1
4. Then you get your results in Tons

To calc for Energy:

1. you would need the convert Tons or Pounds to Newtons
2. And then multiply N with the distance (meters) of how much the material bends to get joules (J)
	1. Note if the distance is greater than the material's ability to bend, it would fragment

## Lifting Strength Formula

With this section, we will find the lifting strength which is force from the pressure and area:

1. Area is cm^2
2. Pressure is MPa
3. Multiply the two to get Newton-metre (Nm)
	1. To convert from Newton-metre to Newtons: you would need to have (4 \* Nm / height of initial distance m) = Newtons
	2. For Work done, multiply Newtons above by how much distance the material used in the lifting strength bends (meters) to get Joules (j)

## Black Hole Creation

The good thing is that there is an easy formula that lets us approximate the mass of black holes based on the radius of the event horizon. It is:

r
s

=
2
∗
g
∗
m

/

c
2

{\displaystyle r^s=2\*g\*m/c^2}

where:

*r*s is the Schwarzschild radius (radius of the event horizon);
G is the gravitational constant;
M is the mass of the object;
c is the speed of light in vacuum.
Another way is mass to energy conversion. A more comfortable way may be calculators for the mass and size of a black hole such as this one or this one. Usually besides measuring from the radius of a black hole is if we can find out what the mass would be in general.

In order for it to be considered a true black hole, it must follow most or all of the following:

* Black holes cannot be destroyed with brute force, because they will simply absorb all energy/matter thrown at them, and grow larger, nor can they be physically interacted.
* Black Holes are formed from a collapse of spacetime compacted mass/information, they do not have physical boundaries.
	+ Black Holes do demonstrate warping of time or being close to a Black hole affect's one's perception of time.
* They are capable of easily destroying planets and stars (although with small black holes, it might take a while)
* Black Holes are described as an infinite Gravity Well.
* Approaching Black Holes stretch matter in a spaghetti like fashion.
* When passed the Event Horizon, the Matter crushed down and sucked in to their smallest components.
* Black holes do decay over time due to Hawking Radiation, so if you leave a black hole alone and don't feed it anything, it will eventually grow smaller and explode (this type of detonation is a 100% efficient mass - to - energy conversion, with more potential power than a nuke or antimatter explosive)
* Tiny black holes with masses less than a few trillion tons would evaporate nearly instantly. Black holes with higher masses last much longer - a black hole with the mass of the sun, for example, would last for billions or trillions of years before evaporating.
* If creating a Black Hole you do not move it around as it would make the character scale to the mass and lifting strength (*Unless the character scales to other characters who are as strong or stronger, disregard this*)
* Black Holes can absorb anything slower than FTL objects pass it's Event Horizon.
	+ At it's singularity, it would logically be infinite speed as it is of infinite density and stretches spacetime infinitely.
* If there is a description of how powerful said Black Hole is and matches the Calced energy, It can have a qualification.
	+ And like the Light-Laser qualification, if there are higher tier characters or similar in stats from other feats, this could be applicable as well

The only way for Black Holes to be theoretically destroyed or avoid being caught in it are for the following, Exhausting all it’s mass in Hawking Radiation, Reality Warping or Extreme hax, or moving faster than light to not get caught in it’s gravity. Otherwise considered pseudo-black holes and it’s stats are labeled as **Unknown**.

With this article, while outside Black holes themselves, matter is still drawn in at 30% the speed of light around it's accretion.

Here is a Calc that give more detail than usual.

Here are more equations for other methods of Black Holes: Page 155

This equation below is the the way to find the Kerr Metric (dimensionless spin parameter) this way you can find the angular velocity or the angular momentum for spinning black holes.

* a = dimensionless spin parameter
* c = constant light speed (299792458 m/s)
* J = Angular Momentum (kg m2 s−1)
* G = Gravitational Constant (6.67408 × 10-11 m3 kg-1 s-2)
* M = Mass (kg)

### Angular Velocity

You can also use the above to find the Angular velocity and then the velocity from the Angular Momentum.

## C.A.P.E. (Conventional Available Potential Energy)

This calc page is for feats that are to find the energy of storms created.

### Variables

First are the variables that would remain constant and would not change in any formula.

* he storm is cylindrical in shape
* Independent of how high it floats off the ground, the storm mass itself 30,000 ft tall, going by this. And with Cumulonimbus which have a thickness of about 8000m to 11800m
* The distance to the horizon is the radius of the storm

And some variables that would change depending on the feats.

* Observer Height, and thus, distance to the horizon (here is a link for that)
* Assumed Instability in Kilojoules
* Here is the density of r clouds (1.003 kg/m^3)

Here are some set of values to finding the storms AP (via Kilojoules) in different settings: "Weak Instability" refers to a CAPE value of less than **1 kj/kg**, "Moderate Instability" means **1 to 2.5 kj/kg**, and "Strong Instability" yields **2.5 to 4 kj/kg**. Or some real life examples such as **5.89 Kj/kg** - 1999 Oklahoma Tornado Outbreak and **8 Kj/kg** - 1990 Plainfield Tornado.

Here is a list of Cloud Types by Thickness for calculating mass.

### Calculation of Cloud

here is the equation to find the volume of the clouds by applying the above.

V = (m^3) \* 1.003 kg/m^3 \* Instability

Or...

Volume = (Area in m^2 \* (8000m or 11800m)) \* 1.003 \* CAPE

pi =  **3.14**

### Sum It All Up

then apply the cloud density to the equation by multiplying the volume (m^3) result by 1.003 (kilograms per cubic meter), then multiply the total mass by the CAPE values. in joules per kilogram (change the Kj to J, 1 kj = 1000 j).

here is the other equation: ((pi \* Horizon distance (in meters)^2 \* 13,000 m) \* 1.003) \* CAPE (In j/kg).

## Center of Mass

This section is for calculating the center of mass for particular objects

### Hemisphere

This usually requires extensive calculus, but someone on a different wikia provided a simplified version, First you would have to find the volume of the Hemisphere, or sphere that is hollow, you can use this calc here and then divide by 2 (Or simple do this for the Volume of a hollow Hemisphere ***4/3\*π\*[(R2)^3 - (R1)^3]***).

When you find the **Ri** (*inside radius*) and the **Ro** (*Outside radius*), apply both to this calc below):

1. 3/8(***Ro***^4-***Ri***^4)/(***Ro***^3-***Ri***^3) = *z*cm
2. then multiple *z*cm by 2 = **ri**
# 3. Then follow this formula below: **W

∫

r
i

r
f

F
(
r
)

d
r

→

{\displaystyle W = \textstyle \int\limits\_{r\_i}^{r\_f} F(r)\vec{dr}}**
	* F(r) = Gravitational Force = G\*m^2/r^2
	* m = mass (kg)
	* G = Gravity = 6.67e-11  m3 kg-1 s-2
	* W = Watts
	* r = radius
	* d
	r

	→

	{\displaystyle \vec{dr}}

	 = Vector

# Or solve with this (*recommended*): ***W
G

m
2

(
1

/

r
i
−
1

/

r
f
)

{\displaystyle W=Gm^2(1/ri-1/rf)}***

* rf = ri + (distance separating both objects meters)
* ri = *z*cm from #2
* **Ex.** 6.67e-11\*4.9825e+21^2((1/1696418)-(1/1727418))

**NOTE:** You can follow this page here for more information. or here is a proper sample.

## Compression

This Calculation is for feats that involve compression of any scale. Here are a few things to find in order to get a reasonable formula:

* Area (m^2)
* thickness of the target (km)

Multiply them together to get the volume of said target, after that find the size of what the target is after compression or information for accuracy, once done that, do the following:

* Size \* Volume = volume after compression

Then you must find the compression value (minimum should be 69 MPa = 6.9e+7 N/m^2 = P)

Then we need to find the difference in the two volumes pre and after compression (∆V)

* Pre Volume - After Volume = Difference m^3

Now we need to multiply both of the compression value with the difference in volume.

* P\*∆V=Nm (Newton Metre)

Finally we find the the Energy value by converting the Newton to Joules (1N/m^2 = 1J).

Or

Find the volume (cm^3) of a given target, and then find what material is being used to cause compression (MPa) and then multiply both together.

Here are some other calcs revolving around compression calcing:

* http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/adiab.html
* https://www.omnicalculator.com/physics/thermodynamic-processes

## Cross-Section for Humans

This calc is to find the cross section of the surface area of the human body.

For Surface Area finding which can be explained here

* First would need to find the height of a person (meters) to (centimeters)
* Second find the weight of the person (pounds) to (kilograms)

* Then you do the following: Multiply mass and height, then divide by 3600, the square root the result to get the real result.
	+ You can use this website or this one to make things easier.

As for finding the cross section for the human body, you have to take the best estimate guess of how much percentage would an attack effect. Then multiply the percentage with the area to get the final result.

### (NOTE)

This can be applied to any other objects with calculated surface areas. the average cross-section for a fully grown human is 0.68 m^2.

For Explosions durability away from the epicenter, you can find it with the following:

* Intensity Tons of TNT per m^2 = ( **Tons of TNT**) / (4π((**distance m**)^2))
* I (Intensity) \* CA (Cross Section Area) = Tons (Durability)

## Decibel

This page is to talk about how to find the energy in the calculation of the Decibels for Intensity and Pressure (The later is what is used for AP). Here is a website to help understand sound intensity and this link converts decibel-milliwatts to watts. Intensity is the most common calc to use when finding decibel to watts for Stats. Here is a list of comparable decibel levels.

First is the Intensity:

* NdB = # of Decibels
* P2 = Intensity = (# of Watts or Joules / Area squared meters)
* P1 = threshold of human hearing (10^-12) lowest possible sound for human hearing
* Find the number of decibels/watts you wish to convert
* Once you found Watts, apply it to the following equation to (P2) to the right side.
* Then divide said watts by area

* Then divide P2 with P1 (10^-12)
* With the result, apply it to the log^10
* Then \* by 10 to get the final result for # of decibels
* You can apply this to find watts as well by doing the formula in reverse.

Now for the Pressure

* Find the number of decibels/pressure you wish to convert
* Once you found pressure (Pa), apply it to the following equation (*p*) to the right side
* Then divide *p* by *Pref* (2.0x10^5)
* With the result, apply it to the log^10
* Then \* by 20 to get the final result for # of decibels
* You can apply this to find the pressure by doing the equation in reverse
* you can then convert pressure to newtons which is equal to Joule m^2.

Here is a link to help find the sound intensity (W/m^2) for any sound intensity level (db).

Or a simplified version for conversion and calculation which would require finding shockwave radius and decibel numbers:

1. Find the Decibel number.
2. Conversion formula to W/m^2 (watts per squared meter) = **10\log \_(10)((x = Db)/(1\*10^(-12)))**
3. Required energy: x = 10^((**Db**/10)-12) = **W/m^2**
4. Shockwave area: π\*(**shockwave radius meters**)^2/2 = **m^2 (squared meter)**
5. Sound Energy - **m^2** \* **W/m^2** = **W (Watts)** = **J/S (Joules per Second)**

Here are a few more websites to help with this:

* bpastudio.csudh.edu/FAC/LPRESS/471/hout/wireless/db.htm
* https://www.isa.org/standards-publications/isa-publications/intech-magazine/2002/november/db-vs-dbm/
* http://www.decibelcar.com/menugeneric/87.html
* http://www.sengpielaudio.com/calculator-soundlevel.htm
* http://www.sengpielaudio.com/TableOfSoundPressureLevels.htm
* https://www.engineeringtoolbox.com/sound-power-level-d\_58.html

## Durability

This one can come in many different varieties such as explosions, here is an example for inverse law:

* 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 CA is the area of the cross section of the target (the cross section orthogonal to the direction the explosion expands into, to be specific) and E is the energy the target is hit by.
* 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.

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/(4π\*30^2)
* 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.
	+ NOTE: Any distance to explosion less than 1 meter would get weirdly higher results, for any on-screen durability feats less than 1 meter such just consider it full durability.

## Earthquake

### Overview

An earthquake (also known as a quake, tremor or temblor) is the perceptible shaking of the surface of the Earth. Earthquakes can be violent enough to toss people around and destroy whole cities. Such earthquakes being caused by characters are a method useable to determine Attack Potency.

One has to differentiate between different ways an earthquake was caused, if one wants to calculate the energy.

### Case 1: Meteor impact

This is the easiest method to determine the necessary energy to cause an earthquake, even though not the most commonly used one.

#### In which cases should it be used?

This method should be used if an earthquake is caused through the impact of a meteor or through an event very similar to that.

* It is important to note that not all Meteor feats are the same, if it is not from outer space and formed within the atmosphere and does not show any friction to catch fire, then it would not be the standard speed of 11 km/sec for KE calc, you should use 2 of the following:
	+ Potential Energy Calc
	+ Terminal Velocity Calc

#### How is it done?

##### **Step 1:**

First step is to determine the distance of a place, for which we know which effects the earthquake had on, to the epicenter. To clarify: The epicenter is the point on the Earth's surface that is directly above the hypocenter or focus, the point where an earthquake or underground explosion originates. From the rest this calculator will be used.

##### **Step 2:**

Input the distance from the epicenter, which was determined in Step 1, in the "Distance from Impact" field.

After that input the rest of the values, for now it doesn't matter what stands in the rest of the fields.

Press "calculate effects".

If the inputs were sufficiently high on the page that appears will be a section named "Seismic effects".

In that section descriptions are given which describe the effects of an earthquake, which was caused by a meteor with the properties described by the prior input. Specifically this are the effects at the input distance from the epicenter.

All possible descriptions are listed in Table 1. What one now wants to do is to change the input values, except the "Distance from Impact" value, so long until you have the lowest values, for which still the description best fitting for the effects at your chosen distance from the epicenter is shown.

##### **Step 3:**

If you have found this values take a look at the "Energy" section above the "Seismic Effects" section on the page. The value given for "Energy before atmospheric entry" is the energy of your (theoretical) meteor and with that also the energy of necessary to cause the earthquake.

Here are some values you can use for the calculator above in Step 1:

* Distance from impact = 4240 km (rounded off)
* Projectile diameter = 10 km
* Projectile density = 3000 kg/m^3
* Impact angle = 90 degrees
* Target type: Sedimentary rock
* Impact velocity: Play around with this till you get Mercalli intensity IV to V under "Seismic Effects". At 37 km/s is where we get those Mercalli intensities.

### Case 2: Natural Earthquakes

This method doesn't find much use, but is worth mentioning.

#### In which cases should it be used?

This method should only be used in case a natural earthquake occurs, as it takes into account the work necessary to overcome the friction between continent plates etc.

#### How is it done?

First perform step 1 and step 2 like described in "Case 1: Meteor Impacts".

Since here one does not wish to know the energy necessary for a meteor, but for a real earthquake this time the third step has to be different.

Instead of looking at the "Energy" section, one looks at the "Seismic Effects" section again. There a value named "Richter Scale Magnitude" will be listed. This is the magnitude an earthquake would need to have to cause the described effects at the distance from the epicenter we input. The value is independent from the method through which the earthquake was caused, so it also stays true for other natural earthquakes which aren't caused by meteor impacts.

One takes the Richter Scale Magnitude and inputs it in this calculator in the "Earthquake Magnitude" field. Then press the compute button.

The value for "Total "Seismic Moment Energy" (MO)" is the energy necessary to cause such an earthquake.

### Case 3: Other

This is the most common method to calculate earthquakes.

#### In which cases should it be used?

This should be used if the earthquake is not caused through something very similar to a meteor impact and is also not a natural earthquake.

#### How is it done?

The method is identical to that of "Case 2: Natural Earthquakes", just this time instead of the "Total Seismic Moment Energy" (MO)" value our end result is the "Seismic Energy in Waves Radiated from Earthquake Source" value.

The reason one uses that value in this case is that the big energy loss that comes through the movement of the continental plate or similar processes of natural earthquakes is not present here. Instead we can only use the amount of energy that actually takes part in the effects we observer. Hence only the energy radiated in form of seismic waves is relevant for this case.

Use this as a reference for Earthquake power chart.

Or this to get both the formula and Richter scale magnitude.

A description of magnitude's capabilities.

Or you can use this as an **Alternate Method to determine Richter Magnitude**.

## Frequencies

This section is where you find frequencies from distance and/or velocity.

* You can accomplish this but dividing Distance (d) from Velocity (v) to find Frequency.
* You can find find Frequency (f) with 1 divided by time.
* You can reverse this to find Velocity with v (m/m) = f (rpm) \* d (m).

Here is a list of converting values:

* 1 Hertz = 1 rotations per second (RPS)
* 1 Hertz = 60 rotation/revolutions per minute (RPM)
* ! Hertz = 60 Actions per Minute (APM)

## Alternative Method to determine Richter Magnitude

A more direct method to figuring out the result is the following.

### 1. Mercalli Intensity to Magnitude at distance

The first step is the figure out the (Richter) Magnitude the earthquake corresponds to at the distance from the epicenter (origin) it is felt at. To do that we look at Table 1 above and pick the appropriate Intensity. Then we use that intensity to pick the appropriate "Magnitude at distance" from the table below.

 2-3
 3-4
 4-5
 5-6
 6-7
 7-8
 8-9
 9+

### 2. Magnitude at distance to Magnitude at origin

To do this knowing how far away from the origin we measured the Magnitude at distance is necessary. We call that distance r (unit should be km). To figure out how much the actual magnitude of the earthquake is we differentiate between 3 cases.

1. **r < 60km:** In this case the formula is (Magnitude at distance) + 0.0238\*r = Richter Magnitude of Earthquake
2. **60 ≤ r < 700 km:** In this case the formula is (Magnitude at distance) + 1.1644 + 0.0048\*r = Richter Magnitude of Earthquake
3. **r ≥ 700 km:** In this case the formula is (Magnitude at distance) + 6.399 + 1.66\*log10((r/110)\*((2\*π)/360)) = Richter Magnitude of Earthquake

### 3. Richter Magnitude to Energy

To get the energy from the Richter Magnitude (*RM*) we differentiate between 3 cases on how the earthquake was created:

1. **Meteor Impact:** The formula is 10(Richter Magnitude + 5.87)/0.67 or 10^[(RM+5.87)/0.67] = Energy in Joules
2. **Real Earthquake:** Just use this or using this for a calculator. The Total Seismic Moment Energy is the result.
3. **Others:** Used for any artificially created earthquakes or earthquakes that aren't the former two. The formula is 101.5\*(Richter Magnitude)+4.8 or 10^[1.5\*(RM)+4.8]= Energy in Joules

### Simplify

Here is the calculation simplified: M = log10(mm)+3\*log10(8\*t)-2.92 (Using the Whitebeard's Calc)

* M = Richter Magnitude
* t = time difference (distance by miles divided by 5.7)
* mm = amplitude (It is amplified by x10 for each 1 magnitude increase using logarithmic (Or simple 10^#))
	+ 2.5 = 50 mm, you can use this for reference to multiply
	3.5 = 500mm
	4.5 = 5000mm
* Then You find the Energy by conversion M to Earthquake Power with this **link**.

Here is a handy List of Radiating Waves Energy and Total Seismic Energy.

**NOTE: Total Seismic Energy should only be used for real earthquake. It shouldn't be used for physical earthquakes or earthquakes caused through abilities.**

### Shaking the World: Radiating Waves & Total Seismic Energy

* We'll assume that it feels like a Magnitude 4 across the world, just standard noticeable shaking with no real damage.

To find how strong of an impact it truly was, you use this equation:

(Magnitude at distance) + 6.399 + 1.66×log((r/110)×((2×π)/360)) = Richter Magnitude of Earthquake, with r representing the distance away from it.

In our case, it would be, using half of the Circumference of earth,

(4)+6.399+1.66×log((20037.5÷110)×((2×π)÷360)) = Magnitude 11.2328648415393

Now, we take the magnitude and use the formula for a joule count from said magnitude listed in Earthquake Calculations

10^(1.5\*(11.2328648415393)+4.8) is 4.459613919339E21 Joules, 1.06587330768147 Teratons, Small Country level

* This method is only applied when you have proof you're causing it through manually moving the plates, as elaborated above. We'll use the same magnitude, 11.2328648415393, but, we'll use a different formula.

This time, we'll use 10^(1.5×11.2328648415393)×10^9.091 to get...

8.715599440089E25 Joules, 20.8307826005974 Petatons, Multi Continent level

## Field of View (Degrees/Distance/Size)

This section is for finding distance finding using different points of view (POV) using field of views (FOV) calculations, so this would be the standard formula to use:

(Focus Object) \* (Panel Height) /[0.2159\*2tan(70/2)]

make sure that when finding the object in question and the panel, they are the same units of measurement, you can do this by comparing them by pixel size as well.

* Now when you calc you need to find not only the pixel for size and distance, but the angular view.

Or you can use the following to find angsizing without the website when finding distance for the perspective point of view for the three fields:

* **Degrees:** 2 atan (tan (70deg/2) \* (px of object size/px height of the image "On the right side")) (***Primary Use of Calcs for Distance or Size***)
* **Distance:** (Size of object / 2) / (tan (Visual Angle deg from above/ 2)) or this one.
* **Size:** 2 \* distance \* (tan (Visual Angle deg / 2))

Make sure for measuring size or distance you match the units of measurement

As for finding the differences in distances between two points, you need to find two distance measurements and then subtract between the two.

As for finding the distance of a further away object, you can do the distance measurement from one of the known object sizes and then do a ratio to get the distance of the further object, you can then find the object size from the distance then.

When finding degrees with other units of measurement in comparison to one another

* Radian 1 = Degrees 57.2958
* Gradian 1 = Degrees 0.9
* Minute of Arc 1 = Degrees 0.0166667
* Seconds of Arc 1 = Degrees 0.000277778

Here is a link for example Astronomical bodies with Angular Sizes.

Here is the calcs for them:

* https://rechneronline.de/sehwinkel/angular-diameter.php
* http://www.1728.org/angsize.htm

For finding the distance of something from two sizes at different points, it is best to measure both and then do a difference in comparison to each other subtracting form one another.

Alternatively to using the calculator one can also directly plug the values into these formulas to solve everything in one step:

* Distance from point of view to object = object size \* panel height in pixels/[object height in pixels\*2\*tan(70deg/2)]
* Object size = 2\*tan(70deg/2) \* distance from point of view to object \* object height in pixels / panel height in pixels

In both formulas the unit of object size is the same as the unit of the distance from the point of view to the object. In these formulas as well make sure your calculator is calculating the tan in degrees, not radians.

For texts regarding an individual's visual description for distance, it is important to get the full context of the scene, but would can a distance if you know the size of the object and utilize the known degrees of field of vision with [1] at 120 degrees. vertical FOV 90 degrees].

### Relative Angsizing

This sub-section is for scaling pixels if they are close enough together to find the size of something,

* The best way to do that is with this (((**known size** km x **pixels of unknown size** px) /**pixels of first known size** px) x **1000 to convert to** meters)
* Or you can use the ratio calculator to find the odds to then divide or multiply the known size to find the unknown size of the object.
* Another method is by dividing the known size by it's pixel equivalence would give the distance # per pixel.

## Horizon Validity

This section is for if there are any feats that are being calculated the suggests they use the horizon as a base for size of distances. here is a calc for those who do use Horizon for either.

But there are a few things to look into to say that it is horizon:

* Make sure that the panels in question do show the feat does reach or passes the horizon itself
	+ Sometimes multiple scans with different locations would help out.
* Sometimes, if there is an official animated adaptation, that can be used to clarify if it does or doesn't
	+ Ex. a Beam travels a great distance, if it keeps going at same speed without slowing but stops abruptly at the horizon point, that would be a good indicator that it did reach the horizon or further. If it slows down before reaching a certain point, then it would not mean it did reach the horizon, because that it how eyesight works. You see a jet plane flying faster than the human eye to follow, that maybe the case if you just look straight and it just flies past you from left to right, but watching it fly away would appear slow.

The calc below is for any feats that use the *True Horizon*, which is at sea level:

* d(km) ≈ 3.57(km/m½)√h(metres)

When using the visible Horizon calculation, when finding the height of the person on the ground or higher above, add 840 meters which is the means above sea level, based on this link:

* https://www.reddit.com/r/askscience/comments/jxspj/what\_is\_the\_average\_height\_of\_land\_above\_the\_sea/
* Or use this link for calcing horizon above sea level.

## Luminosity Brightness

This will be about the **Apparent Brightness** Of any object, which is the distance brightness from any source, to find it you need this formula:

L = 4\*pi\*d2\*b

* b = apparent brightness of the star (in watts/meter2) Ex. The Sun's is 1370W/m^2, the moon's is 1367W/m^2
* L = luminosity of the star (in watts)
* d = distance to the star (in meters)
* pi = approximately 3.14159265 (but you knew that already)

## Map Size

This page is for working to find the size of the map or location that you are trying to make, these steps will help you to do so.

### First

find an app or program that is good with pixel measurement such as GIMP or photoshop, then find images that would connect to one another. It is good to start with what is small then work your way up on size comparison.

### Second

Find a reliable source for reference from said series, or use a reliable source for average size of for example a human male. then use that as a basis.

### Third

Then you use pixel lines to measure from smallest thing with reference then star working your way up with size comparison until you finally reach the area you want to find the size of.

### Sites

Here are a few sights to help your find the area of an area, facility, settlement, building, large vehicle or celestial body.

* https://www.freemaptools.com/area-calculator.htm
* http://www.1728.org/angsize.htm
* http://www.calculator.net/area-calculator.html
* https://anatomy4sculptors.com/hpc

## Freezing Energy

This page is to find the energy for feats that causes freezing or creations of large polar bodies, here are the following steps for that.

* First, find the the volume (m^3), density (kg/m^3), and then multiply both to find the mass (kg).
* Then find the mass of the atmospheric composition of area by dividing it by the percentage of each elemental compounds. Then multiply separately each compound percentage with the both the original volume and density to get the mass.
* Now things get more complicated as it requires you to find the following for each elemental compound to get the answer you seek.
	+ air temperature (Kelvin)
	+ specific heat (j/kgk)
	+ Boiling point (kelvin)

Then do the following equation with the values above with the specific compound (mass (kg) \* specific heat (j/kgk) \* ( air temperature (K) - boiling point (K)) = **Joules**

* use this website to help when you have gathered information on a compound: https://www.omnicalculator.com/physics/specific-heat
* repeat this process for each atmospheric compound

Now for each compound you must find the following:

* + Vaporization Heat j/kg
		- Then multiply that to original mass of the specific compound to get **Joules**
	+ Melting point Kelvin
		- use the first formula with the mass \* specific heat \* (air temperature - boiling point) except replace boiling point with melting temperature to get **Joules**.
	+ Fusion Heat j/kg
		- Multiply that with the mass of the specific compound to get **joules**

Now add all the four total number of joules together to get the total energy for that specific atmospheric compound, repeat the previous process for the remaining compounds

Finally once you have all the total energy for each atmospheric compound, add them all up together and you will have the total energy use seek.

## Height, Length, Depth, Volume, Angel Measurement

This is to talk about the measurement of the Depth of any DC feat which is using various factors such as length, width, height of any elevated geographic structure, angle of the shadows in the crater. This falls under certain steps in process such as the First Step.

1. First is finding the width and length (meters) of the end feat.
2. Then we measure the max height of the geographic elevation.

Step 2) Below is the way to look at how to measure the angle of the shadows.

So the basic of the calculations is this in order

1. Measure a triangular shape by first drawing a line from where the shadow is cast, then line down to the edge of the crater is (height) then connect the lines (Length) to form a type of Scalene Triangle. Here is a link for examples of shadow angles.
2. Length / Height = width of the shadow than convert to angular degree.
3. width (From first step) \* angle of the Shadow
4. Afterward add the height of the geographic elevation (height step 1) + total depth (or not for low end)

Step 3) Next is to find the closest volume for calculations (Use the most accurate prism for this case then add the depth):

1. Find the Width, Length then add the depth.
2. Then multiply all three to get the volume by m^3 (if measuring by meters)
3. then Multiply by method of destruction. Then you mad convert them to get the estimated result.

### Image Angle

If push comes to shove, you can use the following site for angle/distance and size

For any other means to find an object size or distance from certain points in a scene, first and foremost is to do pixel measurements and finding information to best determine the object's size or distance or an estimate for the average size of something that is related to it.

* First find the px number of both the height of the screen and the diameter of the object, then apply the info to the equation below
	+ 2atan(tan(70/2)\*(object size in pixels/screen height in pixels))
		- After that, convert the result from Radian to Degrees and you will get the result of degrees. use this "Radians \* 180°/π".
		- Then use the website above for angle/distance/size to find one of the following with the other two units of info.

### Square-cube Law

This method is to find the size of certain larger objects with comparing the length of something with either surface or volume, there are two ways of doing this.

Represented mathematically:

**A2 = A1 (l2/l1)^2**

where **A1** is the original surface area and **A2** is the new surface area:

**V2 = V1 (l2/l1)^3**

where **V1** is the original volume, **V2**  is the new volume, **l1** is the original length and **l2** is the new length.

### Diameter of a Circle/Planet

This is to help find the diameter of a circle, best for using to find curvature of planets (especially for pixel measurements).

This is the "Chord Length and Depth" with the formula below:

c^2/4h 1 + h 2

c = the length of the chord across the curve.

h1, h2 = height of chord from curve to center.

Once you find your answer, multiply by 2 to get the diameter.

Here is a calc or this one that could help simplify faster.

## Luminosity Energy

This is to help estimate the energy released from any body via Luminosity, To do that we need a few things:

Her is the equation to help move things along: (o\*t^4)\*(4\*pi\*r^2)=L:

* O is the Stefan Boltzmann constant (5.670373e-8 W m-2 K-4)
* t is the Temperature
* r is the radius of the body (meters)
* L is the Luminosity Total (watts=Joules)

You then convert the Joules per Second to Tons, and then multiply it by the area of the star to find the Energy of TNT to Tons per m^2 to get the **Intensity**.

The temperature of any given star, including a neutron star, is determined by using Wien's displacement law, which states that the wavelength is equal to the displacement constant (a value equal to 2900 *micro*meters per Kelvin, or about 2.897 7729(17)e-13 meters per Kelvin) divided by the temperature. So, in order to get the temperature, we need to do a quadratic equation; we divide the wavelength by the Wien constant.

**EX.** The maximum wavelength of a neutron star is 2.9 nanometers, or 0.0029 micrometers. The constant, as I said above, is 2900 micrometers per Kelvin.

* Tk = 2900Mm/0.0029 = 1,000,000 kelvins

## Perspective Calcing

This calc is for finding the speed of a character that moves at a speed in comparison to other speeds being slower, but this must be a known statement that would make use of this calc, now onto the values on how to do this.

First you would need to find what the speed of an object that the character will be matching or outpacing and considers it “Slow” by his/her perspective. We use the Snail speed of 1 mm/sec (.001 m/s and using the normal human speed (5-7.7 m/s)

Then you take the object‘s speed and you divide it by the snail’s speed, with the Result, you multiple by the human speed, for High, Mid and Low End, you use the following from the Normal Human Speed:

* Low: 5 m/s
* Mid: 6.35 m/s
* High: 7.7 m/s

## Radiation Energy

This is to help those who have temperature questions that wish to calculate that to actual feats or stats. the link below would help with finding the number for joules, this requires:

* Emissivity
* Surface Area
* Temperature

Here is the link for that simplified equation:

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

Here is the functions on how to find them

* Area: 2 π r^2 + 2 π r h
* emissivity: http://www.infrared-thermography.com/material.htm
* Temperature: what is being discussed

## Speed & Cinematic/Comic Time

This Page is for calculating the speed of characters, attacks and vehicles, through various means such as physical speed, teleportation speed, engine speed, speed via powers.

Usually, Time-frames determined via author statements, time-measuring devices of any form in the story work, or **calculations based on the in-verse depiction of the events** will take precedence over cinematic time.

The standard calculation of speed involves the classic Time/Speed/Distance formula.

For the speed of other means or for more details such as powered jumps, flight, swimming, etc. must require more factors such as strength of jumps, their height and landing, etc..

This can be calced for both, regular speed, combat speed or reaction speed.

For Speed from a video or comic/manga and not a map, if there is no accurate distance/time/speed labeled, go to the Image Angle above to find the size of any location on any screen/panel and the size of the object (km) via pixel measurements and measure how much time passed between both points of movement.

* after you find the distance between both points (km) before and after, You then take take those points and minus them.
* When you find how much time has past (seconds), find the frames per second on a video and how many seconds it takes and multiply them together to find the fps.
* For panels, this one is a bit tricky, you can use the Syllable counter or this link which is average speaking speed of 4-5 syllables per second. as for panels that have no dialogue, on this website, would count as **1 second**, If something was accomplished between two panels where there is no show of movement and it just happened, that would be at best .5 second (***don't confuse this with time lapse panels which show a change from one point in time to another, trying to determine time passed from multiple focus points, or fade in or out/black or white which obviously show an undefined amount of time that passed thus cannot be measured***) but that is a tricky scenario too.
* Otherwise, you would honestly have to use your best judgement, in other websites they say the average is between 10-30 seconds, but again, use your best judgement.
	+ So for doing Syllable counting, take the **# of syllables** / **4-5** = **# seconds**
* Once you find the time in either scenario, you then take the distance between the two points (km) and divide by time (seconds) to get the speed (m/s).
* For situations where there is no known time frame (*from one panel to the next without any panels showing movement or distance covered*), and yet has no form of transition to indicate that any undefined spans of time passed, it would indicate that it was a very brief period of time, so around **0.5 a second**.

Although such cases exist, cinematic time can be used to determine time-frames for calculations, such as this calc, or the Pumpkin speed calc here. Or simply use this (**Distance (m)/(FPS/Frames)**)

* Here is a website that can help with finding more precise timings in videos, Frame by Frame.

There are around 24-30 frames in a second.

* Distance (meters) / (# of frames / frames per second) = meters per second

NOTE: Sometimes in mangas, there are sound affects that may differ from one another.

## Surface Area of Beings

this is a page to calculate the surface area of any living being with certain requirements.

here is the site for making the calculation easier: halls.md/body-surface-area/bsa.htm

Another page to help here: https://www.uofmhealth.org/health-library/sig254759

Including the percentage of a human anatomy: https://wikem.org/wiki/Estimating\_body\_surface\_area

but the basic requirements are height (cm) and weight (kg) to find the surface area (m^2)

You can either use either of these methods to find the answer:

* 0.20247\*height in meters^0.725\*(weight in kilograms)^0.425 = surface area in m²

### Anatomy Proportion Measurement

Here is the website for anatomy proportion measurements

* Anatomy Calculator
* https://hpc.anatomy4sculptors.com

or

* Head height (1 h.u.) = h.u. is head unit
	+ Height (1 h.u.)
	+ Length (0.9 h.u.)
	+ Width (0.7 h.u.)
* Chin to Shoulder/length of neck (1/3 h.u.)
* thickness of neck (1/3 h.u.)
* Width of Shoulder (2 h.u.)
* Shoulder to nip (2/3 h.u.)
* Shoulder to navel (1.65 h.u.)
* Shoulder to crotch / main body (2.6 h.u.)
* Length of upper limb (3.5 h.u.) x 2
* Thickness of upper limb (0.5 h.u.) x 2
* Length of arm (1.7 h.u.) x 2
* Length of forearm & hand (1.8 h.u.) x 2
* Length of lower limb (4 h.u.) x 2
* Thickness of Thigh (1 h.u.) x 2
* Thickness of Calf (0.5 h.u.) x 2
* Crotch to bottom knee (2  h.u.) x 2
* Bottom knee to heels (2 h.u.) x 2
* Feet x 2
	+ Length (1.25 h.u.)
	+ Width (1/2 h.u.)
	+ Length of (f2) (1/4 h.u.)
* Hand x 2
	+ length (0.8 h.u.)
	+ length of (f3) (0.45 h.u.)
	+ thumb's radius (0.5 h.u.)
	+ width of palm (0.4 h.u.)

NOTE: When using this for Other feats such as measuring it with attacks to determine durability or so, You must find the cross section between both the humanoid surface area and the area of the attack, usually the difference is 50% or so, thus the area should be around ~40% of the humanoid surface area.

## Temperature Change/Heat Capacity

This page is to talk about found and calculating the change in temperatures and the heat capacity of certain substances.

### Temperature Change

First you need to find the standard temperature of the substance before you go for the changed temperature, then you find what the substance temperature changes to.

Then you take that and minus the original temp to find the change in temperature.

We use the room temperature for average which is 21.1-20 Celsius.

### Heat Capacity

* We determine the energy given or taken in changing the temperature, the equation for this is E=m\*c\*ΔT
* E is the energy (J)
* m is mass (kg)
* c is specific heat capacity (J/kgKorC), 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 (Kelvin or Celsius) which use take both the current temperature and the estimated new temperature and subtract the difference from each other to find the difference, then multiply it by the specific heat capacity of the substance/material.

You can use this to either find the energy or specific heat.

### Vaporization and Melting Energy

* 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.

here are a few examples for specific information

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

* Heat of fusion for water is 334.16J/g

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

Here are a few websites to help with that.

* thermodynamical energy constants for common substances
* Vaporization\_of\_Titanium\_Value
* Specific Heat Calculator
* search for Specific Heat in substances

## Water Body Creation

This page is for feats which creates bodies of water, here are the steps to accomplish this.

* first you need to find an accurate volume or size of the body of water in m^3
* Then find the density of the Water in kg/m^3
* Then multiply both to find the mass in kg
* Then convert Kg to moles (There are 55.6 moles in 1 kg)
* Then follow the enthalpy of the formation of water by multiplying the amount of moles form the previous step with 285800 J/mol.
* Then you will have your answer.

## Watt/Voltage/Ampere

This page is for the calculation of joules from watts/voltage/amperes, to do so, follow the Ohm's Law formula and these steps.

* voltage/resistors(Ohms)=amps
* Find the Voltage
* Find the resistors (1 M Ohm = 1000000.0 Ohm)

The result can be found in “Ohms Law”, According to Ohm's law I = U/R. So if we know the Electrical resistance of the object the electricity is flowing through we should be able to calculate the current through this.
Find the resistance material (Ohm/meter) and the distance said electric current travels (meters), then multiply both to get Ohm.

* then divide the voltage and Ohm to get amps
* then multiply the result with voltage to get watts which then becomes Joules.

## Technique Speed

Technique Speed is a way of measuring the speed of an attack that has either been initially cast, how fast it travels and/or how fast it takes effect.

* Water-cutting speed: ~1,020 m/s
* Ablation speed: 2000 m/s
* Meteor speed (Earth): 11,000 m/s
* Electrical discharge: 60,000 m/s
* Stepped Ladder Lightning: 150,000 m/s
* Light: 299 792 458 m/s (In a Vacuum)

This may be involved in the use of TimeFrame.

**NOTE**: For an so called "*Laser*" attack to be Lightspeed if it is Light Base must follow at a minimum, a few of these essential criteria:

* The beam refracts in a new material, such as a liquid or dense air, etc...
* The beam reflects/refracts off a/various materials/mediums that it can be expected to, such as a mirror or polished swords.
* the light diffracts in a prism or across the edge of an object that difracts.
* The beam is called lightspeed by credible scientific sources or credible source material from series (*Though it would need to be discussed)*.
* It is stated to be made of photons and/or light itself, again by a credible scientific source.
* It has its origin at a realistic source of light, such as a camera/sun/etc..

Here is a few criteria that would help support the feat for common features criteria:

* The beam is considered invisible until it hits a solid end point to be visible or traveling through some sort of medium and causes light to scatter (*if beyond visible light spectrum*).
* The Laser possesses qualities of light such as producing *flash* or *shining* affects, and even creates shadows.
* It travels at an infinite range as light travels as long as it doesn't interact with physical objects or medium.
* Light is described as being a particle and a wave and without mass or matter.
* If made of light, it does have some similar properties such as effects from being radiation and/or being just energy and momentum.
* Like the Black Hole feat, if there are speeds from other feats/characters that exceed the speed of light, this would be inconsequential.

Furthermore, there are criteria which show a beam is **NOT** real light:

* It is shown at different speeds in the same material
* Does not explode on contact
* It is tangible and can be interacted with physically by normal humans, and thus does have mass.
* They do not travel in straight lines (unless you can prove refraction/reflection with known real materials/elements, not pure fictional, see above).

NOTE: However, there maybe some exceptions to light bending if the light power in question comes from the same category of powers that are dubbed or proven as actual elements that would follow most of actual scientific criterias. Where the Laser may bend/curve depending on what type of medium it travels through (such as Atmospheric Refraction, Though you must prove that there is more than just air in the atmosphere to give it that excessive index refraction, for the air index refraction is 1.00029). In order to calc that though, there are a few ways to calc, such as the following:

1. Find the degrees of the angel in which the laser bends or curves.
2. Then apply it to this calc, sin(# of degrees) = answer.
3. divide 1 by the answer from #2 above.
4. Then divide the speed of light (m/s) by the answer from #3.
5. Then calc that in m/s to Light Speed to get results.

Or you can use the Snell's Law calculator to find the refractive Index 2 from refractive index 1 (Air) that light passes through and both angles of incidence and refraction, then do the following to find the speed of light in a medium.

* n (refractive index) = c (constant speed of light "m/s") / v (speed of light through a medium "m/s")

This part should be taken with extreme care and not be abused by simply saying this. If the atmosphere has any elements, they are quantifiable (*fictional is in question if they are unchangeable from nature*), if there is a curvature to the beam, then use the formula above, but only applicable if it meets the requirements above and/or doesn’t fall under the non-applicable criteria.

## Structure Calculation

This calculation is to help find the estimation of any structure to help further the calculation for DC or Dura.

You must follow this equation here Q = m\*c

* M = Mass (grams)
* c = Hollowness of a structure (estimated between High, Mid, Low Ends, which are 80%, 85%, 90%)

You can find the estimated mass of a structure by finding the volume first, which is finding all the proper dimensions, and then calculating it to cubic meters, Then multiply by the structure of which it is made of (kg/m^2), then convert the mass from kg to g.

This website should help with the process of finding the volume.

## Formula for Attack Dodging (Characters)

This can be used with the technique speed measurements above for dodging:

(Distance the character moved (m))
×
(Speed of attacks (m/s))

Distance the attack was away at the point character started moving (m)

=
Speed of character (m/s)

{\displaystyle \tfrac{\text{(Distance the character moved (m))} \times \text{(Speed of attacks (m/s))}}{ \text{Distance the attack was away at the point character started moving (m)}} = \text{Speed of character (m/s)}}

This would include various attack types such as lasers or lightning as well.

NOTE: If said formula does not show, it is simply this, (Distance the character moved (meters) times Speed of attack (m/s)), and then divide it by the attack's distance when the character started to move (meters) to get the answer of speed of character dodging (m/s)

## Stress-Strain Curve

This is to find the the Energy density of the material in question:

here is a website to help find that out: https://www.s-cool.co.uk/a-level/physics/stress-and-strain/revise-it/energy-in-stress-strain-graphs

to find it you would need to find the following:

Force = Newtons (can be found when applying Mass with force)

Young's Modulus = depends on the material (N/m^2)

area = m^2

Length = meters

Now we will find both of the Total Strain Energy and then the Energy Density:

Total Strain Energy Stored = (N\*meters)/(N/m^2\*m^2) = TSE J

Strain Energy Density = (Force\*J)/(2\*m^2\*meters) = Energy Density Jm^3

## Continental Drift

This calc is to determine the energy behind the continental drifts, for we need to find the surface area and then the volume, the surface area of each known continents are as follows:

* Australia = 7.692 million km^2
* North America = 24.71 million km^2
* South America = 17.84 million km^2
* Europe = 10.18 million km^2
* Asia = 44.58 million km^2
* Antartica = 14 million km^2

Then find the volume which is multiplied by the crust of the Earth which should be around 30-50 km thick and no more.

Then find the Mass which the density of the crust is around 2.7 g/cm^3, or 2.7e12 kg/m^3.

This is the mass of each Continent:

* Australia = (3.846e8 km^3) x 2.7e12 = 1.03842e21 kg
* North America = (1.2355e9 km^3) x 2.7e12 = 3.33585e21 kg
* South America = (8.92e8 km^3) x 2.7e12 = 2.4084e21 kg
* Europe = (5.09e8 km^3) x 2.7e12 = 1.3743e21 kg
* Asia = (2.229e9 km^3) x 2.7e12 = 6.0183e21 kg
* Antartica = (7e8 km^3) x 2.7e12 = 1.89e21 kg

The Shear strength of granite is 14 to 50 Mpa, or 14 J/cc to 50 J/cc, or Silicon which makes up most of the crust is around minimum of 14.68MPa.

Continents move approximately 2 centimeters a years or .02m.

So 0.02m in 1 year is like 6.342e-10 m/s

Then convert the Volume of each continent from Km^2 to cm^2 or cc, and then plug in the J/cc to find the energy in joules:

* Australia = (3.846e23 cc) x 14 = 5.3844e24 Joules
* North America = (1.2355e24 cc) x 14 = 1.73e25 Joules
* South America = (8.92e23 cc) x 14 = 1.2488e25 Joules
* Europe = (5.09e23 cc) x 14 = 7.126e24 Joules
* Asia = (2.229e24 cc) x 14 = 3.1206e25 Joules
* Antartica = (7e23 cc) x 14 = 9.8e24 Joules

Add all of that up and you get around 8.33044e25 Joules, or 19.91 Petatons just for detaching all the continents off the Earth's crust.

## Volcano Eruption Calc

This is to talk about the energy behind the eruptions of volcanoes, there are quite a few of them, but the most common one is the Kinetic Energy Calc

Here are a few, The Volcanic Explosivity Index (VEI) indicates how much volume the ejecta of the eruption takes up. One can estimate the energy release as a function of VEI class **M** as **E=10^[aM+c]** Joule where **a=0.79** and **c=14** (based on This Link). That was in turn based on estimates from Yokoyama (1957).

Another way of estimating is to look at seismic signals and calculate how much energy the eruption must have had to produce the measured waveforms. Seismologists have fairly decent models of the scaling of energy with shaking intensity, and one can estimate how much it attenuates with distance.

A third way is to consider how much the pressure in the magma chamber is reduced times the reduction in volume, **E=ΔP\*V**. A pressure drop of 5 MPa is apparently typical, and the volume reduction is proportional to the ejected volume (with some scaling factor from packed rock to ejecta).

Here is another method to calcing Volcanic eruptions based on the conversion between Mass and Energy based on Mega-joules per Kilograms (**1-1.2 MJ/kg**) which is based on the ejected material that is sent into space.

* Here is a link for the method, **Mason et al, 2004**.

## Time Dilation Formula

This calculation is for special relative events where one can calculate the time difference between two points. there is the basic formula for that:

Δt = the observer time, or two-position time (s)

Δt0 = the proper time, or one-position time (s)

v = velocity (m/s)

c = speed of light (3.0 x 108 m/s)

In the practical application it is to find the velosity in question.

* https://www.omnicalculator.com/physics/time-dilation

But in most fictional cases it is used to to differentiate the different flow of time between two places

Also, for understanding the amount of time that passes on other planets, that is the more tricky part, it all depends on the gravitational acceleration of the body/gravity well, however, you can find said day if you use earth's times of day for calculations.

* 1 minute = 60 seconds
* 1 hour = 60 minutes
* 1 day = 24 hours
* 1 week = 7 days
* 1 month = 4-4.34524 weeks
* 1 year = 12 months/52.1429 weeks/365 days/8760 hours/525600 minutes/3.154e+7 seconds
* 1 decade = 10 years
* 1 century = 10 decades
* 1 millennia = 10 centuries
* 1 Ma = 1000 millenia
* 1 Eon = 1000 Mas

### Example

The Demon King's Age is 1,576,800,000 years old, as he lived in Purgatory for 3000 years earth time, time there exists differently as one minute in earth time equals one year in Purgatory Time, so here is the formula example:

* **1** year = **525600** minutes
* after multiplying **3000** years by the **525600** minutes = **1,576,800,000** years

This link should help as well.

In the movie Interstellar, on the planet Miller, time moves differently as it is close to a black hole, 1 hour equals to 7 years, this example is to use multiple values to find the answer.

* 7 years = 61320 hours = 1 hour
* 3 hour passed on Miller = 183960 hours = 21 years

And here is the the example of time dilation in the Hyperbolic Time Chamber in *Dragon Ball Z*, always multiply up from the difference between two time flows from the slower time flow.

## Power Consumption

This calc method is for feats that involve the usage of energy usage either by individual people such as electric power, or a power generator of some kind that covers the area:

One can use the average energy consumption per person such between 909 - 10909 kWh per year.

And determine the size of certain group of people or population of the area, such as for cities that start at the size of 100,000 people or more.

## Size/Mass Change (Square Cube Law)

This section gives the estimated mass of a object through size change

Square Cube Law: Mass = (Changed Size (meters)/Normal Size(meters))^3\*Normal Weight (Kg) = Changed Weight (Kg)

## Ohm's Law

Here we are looking at we can find the energy of electrical currents.

Voltage = (V)

Amperes = (A)

* You can find Amperes from dividing Volts from Ohms
	+ Amps = Volts / Ohms

Ohms = (Ω)

* You can find the Ohms from the electrical resistances of materials from their Ohms Meters dividing the distance the current travels and the material's cross-section in meters squared by following this formula:
	+ Ohms = (Ohms Meters / meters) \* meters^2

Watts = (W) = Joules per second = Joules

* Watts = Volts \* Amps

## Atom count and power

here you can find out how to find the number and power of atoms in a given substance to achieve a state such as plasma.

which would require the known substance type for density, the volume in question and the molar mass for number of atoms

Number of atoms example:

6.022e+23 (Avogadro's Number) \* .1967 g/cm^3 (Deuterium Density in this example) \* 308 cm^3 (Volume) / 2.014 g/mol (Deuterium Molar Mass) = 1.8114918e+25 number of atoms

The degree of Ionization would be likely total in this case so will be 1.8114918e+25 ions

——

1 Atomic Number of Deuterium = 13.6 eV

here we will find the power by multiplying the electron volt by the number of atoms

1.8114918e+25\*13.6 = 2.4636288e+26 Watts

## Other Calcs

### Calories Calc

1 Calorie = 4.184 Joules

and you can find the amount of calories of something (Example Broccoli has average 30 kilocalories or 125 kJ per 3.1 oz (0.087 kg)) by finding the mass of the object, multiply by 125000 joules, then divide by per mass .087 kg.

#### Finding Calories through other means

you can find the calories of other objects by finding the water mass of the object, then multiply by the the specific heat of water, then multiply by the temperature change between starting temp to end temp.

### Tsunami Height

The formula currently being used to get the energy of an earthquake from the height of a tsunami is:

Mw1=1.5667∗Log(H)+7.0781

But this formula doesn't calculate the Richter Magnitude of an earthquake, but the moment magnitude.

* Example

### Ellipsoid Volume

Reverse angsize: distance (km) for the diameter of the explosion. According to this three studies, the depth is 0.18\*diameter.

### Dome Thickness

you would need to find the Volume of said dome with this calc (V = (2/3)πr3) V = Volume, r = radius)

And then you need to find the length of the dome object, and you will find the difference between it to get the estimated hollowness of the structure for the final volume.

### Stopping Power

you can find the stopping power of a target which is something before being incapacitated or immobilized by dividing Joules by seconds to get the watts.

## NOTEs

* It is important that when creating calculations, you use the visual original source material like the manga, however, if there is complications in trying to find the original source material, then you can use other reliable sources such as direct anime adaptations for reference.
* There is another calc for field of view which I still have to confirm the source (**2atan(804/(289/tan(70/2))) in degrees**)

## References

1. ↑ The Volcanic Explosivity Index (VEI)
2. ↑ One can estimate the energy release as a function of VEI class
3. ↑ de La Cruz-Reyna 1991 This Link
4. ↑ Another way of estimating is to look at seismic signals and calculate how much energy the eruption must have had to produce the measured waveforms
5. ↑ A third way is to consider how much the pressure in the magma chamber is reduced times the reduction in volume
6. ↑ Ma
7. ↑ Demon King's Age