Comprehensive List of Formulas (Coming Soon in 2022)

**Notice**: As of right now, the Superpower List Project is currently being worked on this page here and the other page that can be found here, so come back around Early December 2021, to check out the finished list.

You may also check this page here to see how the progress of getting to each letter section of superpowers is currently going so far.

## Coulomb's Law Formula

Reminder:

* Coulomb Constant×Vacuum Permittivity = 1 / 4×Pi = 0.07957747154568913

Formula: Coulomb Constant = 1 / 4×Pi×Vacuum Permittivity

Here are the values for both Coulomb Constant and Coulomb:

* Coulomb Constant (ke, k or K): 8.987551792300001×109 kg×m3×s-2×C-2 or N×m2 / C2
* Vacuum Permittivity: 8.8541878127329801×10-12 C2 / N×m2

## Gravitational Force Equation (moving 2 celestial objects away from each other simultaneously) and Newton's Law of Gravitation Formula for Planetary & Stellar Fission (splitting it in half)

Reminders:

* The Gravitational Constant (G) is equal to 6.674299798307059×10-11m3kg-1s-2.
* The value of variable "R" could be either of these 2 things:
	+ Planetary/Stellar Fission: R = Radius of the Planet/Star
	+ Moving 2 celestial objects away from each other: R = Total Distance between the centers of the objects (2×R if both celestial objects have the same proportional sizes)
* The Mass (M) must be divided by 2 before it can be squared by the power of 2 when using the formula for Planetary/Stellar Fission, whereas the mass of the 2 celestial objects must be multiplied first before they can be squared.

In relation to the formula shown above, follow the steps in order below so you may be able to properly calculate the final result for splitting a Planet/Star:

* Step 1: Fg (Force of Gravity in Newtons) = G×((M/2)2)/R2 (in meters)
* Step 2: Final Result (in Joules) = Answer (in Newtons) × R2 (in meters)

So if you wanted to know the force of gravity that keeps the Earth from being separated into 2 hemispheres and the energy required to split the Earth in half (assuming that the total distance the planet is split apart isn't higher than its diameter), for example, then the Force of Gravity, in this case, would be **1.452914567425021×1025** Newtons and the energy required for Planetary Fusion of the Earth is exactly **5.87098074294631×1038** Joules (Substellar).

## Planck Unit Formulas

Reminder:

* Planck Temperature: Planck Mass×Speed of Light2 / Boltzmann Constant

I'm leaving this here just in case you're confused.

Here's the shortened list of Planck Unit values from the image above that you actually need to remember:

* Speed of Light (c) = 299,792,458 meters per second (m/s)
* Pi (π) = 3.1415926536
* Boltzmann Constant (k) = 1.380649×10-23 J×K-1
* Gravitational Constant (G) = 6.674299798307059×10-11m3kg-1s-2
* Planck Constant (h) = 6.62607015×10−34 J×Hz−1 or J×s
* Reduced Planck Constant (ħ) = 1.0545718176427302×10–34 J×Hz−1
* Planck Length (Lp) = 1.6162549999999994×10-35 meters
* Planck Time (tp) = 5.3912463668448889×10-44 seconds
* Planck Mass (Mp) = 2.1764343755995678×10-8 kilograms
* Planck Energy (Ep) = 1,956,081,666.250944 or 1.956081666250944×109 Joules
* Planck Power (Pp) = 3.628255014054753×1052 Watts
* Planck Force (Fp) = 1.210255600911332×1044 Newtons
* Planck Frequency (Wp) = 1.8548586578231786×1043 Hertz
* Planck Intensity (Ip) = 1.5453847968114563×10105 W/m2
* Planck Pressure (pp) = 4.632947067919372×10113 Pascals
* Planck Temperature (Tp) = 1.4167841835621825×1032 Kelvin
* Planck Mass Density (*P*p; the P is italicized, so don't get it confused with Planck Power) = 5.154848814813935×1096 kg/m3
* Planck Energy Density (pEp) = 4.6329470679193716×10113 J/m3
* Planck/Photon Momentum (p) = 6.524786111366897 kg×m/s
* Planck Charge (qp) = 1.8755460377725714×10-18 coulombs
	+ Elementary Charge (e) = 1.602176634×10-19 coulombs
	+ Fine-structure Constant/Sommerfeld's constant (a) = 7.297352569333272×103

## Space Travel Formula for Relativistic Speed

Also, you need to either click the "2nd" button or hold the Cosh or Sinh button until it changes to "acosh" and "asinh" respectively.
* T = Character's Timeframe (in seconds/minutes/days/years)
* t = Earth's Timeframe (in seconds/minutes/days/years)
* V = Character's Speed
* c = Speed of Light (299,792,458 m/s)
* D = The total distance that the character travelled
* a or g0 = Constant Acceleration (1 g (Earth's Gravity) = 9.80665 m/s2 = 32.1740485563 ft/s2)
* e = Base of natural logarithms (approximately 2.718281828459)
* R = Rocket's Mass Ratio (Dimensionless Number)
* Ve = Exhaust Velocity or Specific Impulse in m/s
* Isp = Specific Impulse in seconds
* sqrt [(x)]or(x) = Square root of x
* ln [(x)]or(x) = Natural logarithm of x
* sinh [(x)]or(x) = Hyperbolic Sine of x
* cosh [(x)]or(x) = Hyperbolic Cosine of x
* tanh [(x)]or(x) = Hyperbolic Tangent of x
* asinh [(x)]or(x) = Arc Hyperbolic Sine of x
* acosh [(x)]or(x) = Arc Hyperbolic Cosine of x

So anyway, here is a list of comparisons between the two I recently mentioned that will help show you what I'm referring about:
* Second (Time) and Light-Second (Length)
	+ Light-Second = Equals to the Distance when traveling at the Light for 1 second
* Minute (Time) and Light-Minute (Length)
	+ Light-Minute = Equals to the Distance when traveling at the Light for 1 minute
* Hour (Time) and Light-Hour (Length)
	+ Light-Hour = Equals to the Distance when traveling at the Light for 1 hour
* Day (Time) and Light-Day (Length)
	+ Light-Day = Equals to the Distance when traveling at the Light for 1 day
* Week (Time) and Light-Week (Length)
	+ Light-Week = Equals to the Distance when traveling at the Light for 1 week
* Month (Time) and Light-Month (Length)
	+ Light-Month = Equals to the Distance when traveling at the Speed of Light for 1 month
* Year (Time) and Light-Year (Length)
	+ Light-Year = Equals to the Distance when traveling at the Speed of Light for 1 year

Now that we got the first part covered, here are examples to get us started.
* Example 1: Let's say that a character travels 1 light-second distance away, this would be 1c = 299,792,458 m/s, correct? That's right and this is because a light-second represents the distance that the Speed of Light travels at 1 second.

After reviewing this example, you should now understand the relation between length and time regarding the Speed of Light and understand what the next example will explain to you next.
* Example 2: Let's say that a character travels 1 light-year distance away, this would be 31,536,000c, making it supposedly higher than 1c and is 31,536,000 m/s right? Sorry to say this but that's actually is incorrect and objectively wrong, so let me explain why.

The more distance the Speed of Light needs to cross through outer space in a short timeframe is actually slower than its top speed. This is because of the fact how it causes not only distance but also time to dilate, allowing the speed of light to take less time to arrive at the location, and that the microscopic particles of matter in outer space slow it down. So the correct answer would actually be 31,536,000c = 9454254955488000 m/y (year) since a light-year is equal to the distance that the Speed of Light travels at 1 year.
Lastly, if that doesn't convince you enough, according to the formula where the Speed of Light (meters) is equal to Planck Length (the distance that light travels in a perfect vacuum) divided by Planck Time (the timeframe that light takes to cross a Planck length) is the Universal Speed Limit since no measurable speed would be above this as it wouldn't be considered as legitimate or applicable for Speed since, after all, the same Speed of Light we currently know of is equivalent to the speed of the Big Bang and as for Planck time, this would represent the beginning of Time for our Universe.
The formula is shown for you below:
* Speed of Light = Planck Length / Planck Time
	+ Speed of Light = (1.6162549999999994×10-35)/(5.3912463668448889×10-44)

This would conclude that any "speed" measurements above 299,792,458 m/s (example: 400,000,000 m/s) would not be considered legitimate due to the Speed Formula being unable to be properly calculated algebraically since it ultimately decides whether its an actual Speed rating.
This is because the character is being transported to their location through a form of travel known as "Dimensional Travel," which works very similarly to teleportation since no physical movement is actually happening for the character due to T (Time) = 0 while traveling between dimensions.

	+ 1 Hour = 60 minutes = 3,600 seconds
	+ 1 Day = 24 hours = 1,440 minutes = 86,400 seconds
	+ 1 Week = 7 days = 168 hours = 10,080 minutes = 604,800 seconds
	+ 1 month:
		- 4 weeks, 2 days, 10 hours, 29 minutes, and 5 seconds
		- 30 days, 10 hours, 29 minutes, and 5 seconds
		- 730 hours, 29 minutes, and 5 seconds
		- 43,829 minutes and 5 seconds
		- 2,629,745.200416667 seconds
	+ 1 year:
		- 12 months
		- 52 weeks, 1 day, 5 hours, 49 minutes, and 2 seconds
		- 365 days, 5 hours, 49 minutes, and 2 seconds
		- 8,765 hours, 49 minutes, and 2 seconds
		- 525,949 minutes and 2 seconds
		- 31,556,942.405 seconds
* Distance Conversion:
	+ Light-Second = 299,792,458 meters
	+ Light-Minute = 17,987,547,480 meters
	+ Light-Hour = 1,079,252,848,800 meters
	+ Light-Day = 25,902,068,371,200 meters
	+ Light-Week = 181,314,478,598,400 meters
	+ Light-Month = 788,377,777,546,615.2 meters
	+ Light-Year = 9,460,533,330,559,382 meters

* Time Dilation Calculator (Main)
* Time Dilation Calculator (Alternative)
* In a Blaze of Brilliance — How Light’s Speed was Finally Clocked

**Reminder:** When calculating the Speed of Spacecrafts and the total distance that the spacecraft has traveled, you can only use the formulas that are applicable for Spacecrafts under the section labeled "For Spacecrafts only."
Also, 30 or 31 days is **not equal to the average number of days per month** and 365 days is **not a full year**, so keep that in mind.
Sources for the formulas can be found here, here and a better understanding of how these calculations work is explained here.
Here's a calculator that is available for you to use to plug in the values found at Web2.0calc here.

Step 1: Find either the Total Distance (D) that the character has traveled, Earth's Timeframe (t), or Character's/Spacecraft's Timeframe (T) by using the formulas below:
* Total Distance
	+ (Given Character/Spacecraft Timeframe only): D = (c2/a) × cosh([(a×T/c) - 1)
	+ (Given Earth Timeframe only): D = (c2/a) × sqrt([1 + (a×t/c)2] - 1)
* Earth's Timeframe (in seconds)
	+ (Given Distance only): t = sqrt[(D/c)2 + (2×D/a)]
	+ (Given Character/Spacecraft Timeframe only): t = (c/a) × sinh(a×T/c)
* Character's/Spacecraft's Timeframe (in seconds)
	+ (Given Distance only): T = (c/a) × acosh[(a×d / (c2)) + 1]
	+ (Given Earth's Timeframe only): T = (c/a) × asinh(a×t/c)

Step 2: Use either the Earth's, the character's/spacecraft's, or both timeframes to calculate the final result for the Character's Speed (V) by using either one of the formulas below:
* (Using the Character's/Spaceship's Timeframe only): V = c × tanh(a×T/c)
* (Using the Earth's Timeframe only): V = (a×t) / sqrt[1 + (a×t/c)2]

Time Dilation Feats only:
* (Using the Earth and the traveler's timeframes): V = c × sqrt[1 - (T/t)2]

For Spacecrafts only:
* R (Rocket's Mass Ratio) = e(a×T / c)
* Ve (Exhaust Velocity or Specific Impulse in m/s) = a / Isp
* Isp (Specific Impulse in seconds) = Ve / a
* Total Distance
	+ (Given Exhaust Velocity and Mass Ratio) D = (c2/a) × Cosh([(Ve / c) × ln(R)] - 1)
* Earth's Timeframe
	+ (Given Exhaust Velocity and Mass Ratio) t = (c/a) × sinh[(Ve / c) × ln(R)]
* Spacecraft's Speed
	+ (Given Exhaust Velocity and Mass Ratio) V = c × tanh[(Ve / c) × ln(R)]

Just in case this may be needed, here are the formulas to calculate the Time Dilation Factor (γ):
* γ (Gamma; Time Dilation Factor):
	+ (Given Character's Timeframe) γ = cosh(a×T/c)
	+ (Given Exhaust Velocity and Mass Ratio) γ = cosh[(Ve / c)×ln(R)]
	+ (Given Earth's Timeframe) γ = sqrt[1 + (a×t/c)2]
	+ (Given Distance only) γ = a×d / (c2)) + 1