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Relativistic Energy Calculator

Calculate total, rest and kinetic energy of a particle at relativistic speed.

About Relativistic Energy Calculator

The Lorentz factor grows without bound as speed approaches c, so kinetic energy diverges — which is why massive particles cannot reach light speed. At 0.9c the classical formula understates kinetic energy by more than a factor of two. Particle accelerators are rated in energy rather than speed precisely because speed saturates near c while energy keeps rising.

Formula

Relativistic Energy

E = γ m₀ c², with γ = 1 ÷ √(1 − v²/c²)

γ
Lorentz factor, 1 at rest and rising without bound as v approaches c
kinetic energy
Total energy less rest energy

Worked example

With the default values below, Relativistic Energy Calculator returns Total Energy of 0.00000000034495349250. Change any input above and every figure here is recalculated in your browser.

Inputs used

Rest massminimum 0 kg
0 kg
Speed as a fraction of light speedaccepts 0–1
0.9

Results

Total Energy
0.00000000034495349250 J
Lorentz Factor
2.29416
Rest Energy
938.4842 MeV
Relativistic Kinetic Energy
1,214.5462 MeV
Classical Kinetic Energy for Comparison
380.0861 MeV

Step by step

  1. 1Values used
  2. 2Relativistic Energy
  3. 3Total Energy= 0.00000000034495349250 J
  4. 4Lorentz Factor= 2.29416
  5. 5Rest Energy= 938.4842 MeV
  6. 6Relativistic Kinetic Energy= 1,214.5462 MeV
  7. 7Classical Kinetic Energy for Comparison= 380.0861 MeV

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 20 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Relativistic Energy calculated?

E = γ m₀ c², with γ = 1 ÷ √(1 − v²/c²) The Lorentz factor grows without bound as speed approaches c, so kinetic energy diverges — which is why massive particles cannot reach light speed. At 0.9c the classical formula understates kinetic energy by more than a factor of two.

Why does Relativistic Energy matter?

Particle accelerators are rated in energy rather than speed precisely because speed saturates near c while energy keeps rising.

What values do I need to enter?

This calculator takes 2 inputs: Rest mass, Speed as a fraction of light speed. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.

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