Relativistic Energy Calculator
relativistic energy calculator. Get instant, accurate results. Enter values for instant results with step-by-step formulas.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator
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Formula: E = γmc² | KE = (γ-1)mc² | E₀ = mc²
Worked example — 1.173 MeV total
E = γmc² | KE = (γ-1)mc² | E₀ = mc²
Total energy includes rest mass energy plus kinetic energy at relativistic speeds.
Problem:mₑ=9.109×10⁻³¹ kg, v=0.9c
Solution:γ=2.294, E=2.294×0.511=1.173 MeV
Result:1.173 MeV total
At relativistic speeds, total energy is E = γmc², where γ = 1/√(1 − v²/c²). Rest energy is E₀ = mc² and kinetic energy is KE = (γ − 1)mc². Classical KE = ½mv² is only accurate when v ≪ c (less than ~10% of c).
Compute γ = 1/√(1 − v²/c²), then E = γmc² (total energy) and KE = E − mc² = (γ−1)mc². For an electron (m = 9.109×10⁻³¹ kg) at 0.9c: γ ≈ 2.294, E ≈ 1.173 MeV, KE ≈ 0.662 MeV vs. the classical estimate of 0.209 MeV.
Mass m is in kilograms (kg). Velocity v can be in m/s or as a fraction of c (e.g. 0.9c). Energy is expressed in Joules (J) or mega-electron-volts (MeV; 1 MeV = 1.602×10⁻¹³ J). The speed of light c = 2.998×10⁸ m/s and the Lorentz factor γ is dimensionless.
The law of conservation of energy states that energy cannot be created or destroyed, only transformed. In a closed system, total energy remains constant. For example, a falling object converts potential energy (mgh) to kinetic energy (0.5mv^2). At any point, KE + PE = total mechanical energy.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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