Energy–momentum Relation Calculator

This calculator evaluates various equations relating to the energy-momentum relation.
This is done with the equations below.
General Energy-Momentum EquationThe general energy-momentum equation is as follows:
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E2=(pc)2+(m0c2)2, ∴ E=(pc)2+(m0c2)2E^2= (pc)^2+(m_0c^2)^2,\ \therefore\ E = \sqrt{(pc)^2+(m_0c^2)^2}E2=(pc)2+(m0​c2)2, ∴ E=(pc)2+(m0​c2)2​
Here are the variables of the equation
Input﻿﻿Mass, m(0)
:0.50kg​
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﻿﻿Speed of light, c
:299,792,458.00m / s​
﻿
﻿﻿Momentum, p
:0.50kg*m/s​
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Output﻿﻿Energy, E
:44,937,758,936,840,880.00J​
﻿
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E=(pc)2+(m0c2)2E = \sqrt{(pc)^2+(m_0c^2)^2}E=(pc)2+(m0​c2)2​
Special Case 1: Massless ParticleWhen a particle is massless, like, for example, a photon, the energy-momentum relation can be simplified. In the massless particle case, the equation is denoted as below.
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E = pcE\ =\ pcE = pc
Input﻿﻿Particle momentum, p
:0.01kg*m/s​
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﻿﻿Speed of light, c
:299,792,458.00m / s​
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Output﻿﻿Particle energy, E
:2,997,924.58J​
﻿
﻿
E = pcE\ =\ pcE = pc
Special Case 2: Correspondence PrincipleThe  energy-momentum equation, according to the correspondence principle, is as follows:
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E=12m0v2+m0c2E= \frac{1}{2}m_0v^2+m_0c^2E=21​m0​v2+m0​c2
Here are the variables of the equation
E = the energy.
c = the speed of light.
m = the mass, i.e. m(0) is the mass when the object is at rest.
p = the momentum.
Input﻿﻿Rest mass, m(0)
:30.00kg​
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﻿﻿Speed of light, c
:299,792,458.00​
﻿
﻿﻿Velocity, v
:0.50m / s​
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Output﻿﻿Case 2 Energy, E
:2,696,265,536,210,453,000.00J​
﻿
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E=12m0v2+m0c2E= \frac{1}{2}m_0v^2+m_0c^2E=21​m0​v2+m0​c2
Special Case 3: Centre of Momentum FrameWhen a particle, or body, is in its rest frame, the centre of momentum frame, the energy-momentum relation equation can be simplified to the equation below. This is a result of the velocity equalling zero.
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E0=m0c2E_0 = m_0c^2E0​=m0​c2
Input﻿﻿Mass of particle, m(0)
:0.50kg​
﻿
﻿﻿Speed of light, c
:299,792,458.00​
﻿
Output﻿﻿Energy, E(0)
:44,937,758,936,840,880.00J​
﻿
﻿
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E0=m0c2E_0 = m_0c^2E0​=m0​c2
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