Mass-Energy Equivalence Calculator

By Calxy · Calculation methodology

Enter a mass to find its rest energy, or an energy to find the equivalent mass, using Einstein's mass-energy equivalence and exact SI constants.

Printed from Calxy · https://www.calxy.net/other/mass-energy-calculator

Energy89,875,517,873,681.7700 J

1e-40 – 1e+40

Energy

89,875,517,873,681.7700 J

  • Kilowatt-hours24,965,421.6316 kWh
  • Mega-electronvolts5.609589e+26 MeV
  • TNT equivalent (1 kt = 4.184 × 10¹² J)21.4808 kt

E = mc² gives the rest energy of a mass. Converting it fully to usable energy requires matter–antimatter annihilation; fission and fusion release well under 1% of the mass. c = 299,792,458 m/s and 1 eV = 1.602176634 × 10⁻¹⁹ J are exact.

How this was calculated

m = 1 g = 0.001 kg.

E = mc² = 0.001 kg × (299,792,458 m/s)² = 8.987552e+13 J.

The formula

Rest energy equals mass times the speed of light squared: E = mc². With c = 299,792,458 m/s exactly, c² is about 8.9876 × 10¹⁶ m²/s², so 1 kg of mass corresponds to about 9 × 10¹⁶ J.

Rearranged, m = E ÷ c². Particle physicists quote masses in MeV/c² using 1 eV = 1.602176634 × 10⁻¹⁹ J, which is exact.

Worked examples

One gram: E = 0.001 × 299,792,458² = 8.99 × 10¹³ J, about 25 million kWh or 21.5 kilotons of TNT (at the conventional 4.184 × 10¹² J per kiloton).

A proton's rest energy of 938.272 MeV converts to 938.272 × 10⁶ × 1.602176634 × 10⁻¹⁹ ÷ c² = 1.6726 × 10⁻²⁷ kg, matching its measured mass.

What the number means

E = mc² is the total rest energy, not what a reactor or engine can extract. Fission of uranium converts under 0.1% of the fuel's mass to energy and hydrogen fusion about 0.7%; only matter–antimatter annihilation converts all of it.

References

Frequently asked questions

How much energy is in 1 kg of mass?

About 8.98755 × 10¹⁶ joules, or roughly 25 billion kilowatt-hours.

Is the speed of light exact?

Yes. Since 1983 the meter is defined so that c is exactly 299,792,458 m/s, so there is no uncertainty in c².

Does chemical energy change mass?

In principle yes, but by a tiny amount. Burning fuel releases so little energy relative to mc² that the mass change is far too small to weigh.

Last updated . Results are estimates for informational purposes only.