E=mc2 calculator
This E=mc2 calculator applies Einstein’s mass–energy equivalence E = mc²: one kilogram corresponds to 8.987552 × 10¹⁶ joules, about 25 billion kilowatt hours or 21.48 megatons of TNT. It also works backwards from an energy to its mass.
Example: Calculate: Energy from mass (E = mc²) · Mass m 1 · Mass unit: kilograms (kg) → Result: E = 8.987552 × 10¹⁶ J. Source: NIST CODATA: speed of light in vacuum c = 299 792 458 m/s, exact (read 15.10.2026). Updated: .
How it is calculated
What E = mc² means
E = m · c²: the energy E in joules equals the mass m in kilograms times the speed of light squared. Because c = 299,792,458 m/s exactly, c² = 89,875,517,873,681,764 J per kilogram. A tiny mass therefore stands for a huge energy, and every energy has a mass: m = E ÷ c².
Examples
| Mass | Energy | Equivalent |
|---|---|---|
| 1 kg | 8.987552 × 10¹⁶ J | 21.48 megatons of TNT |
| 1 g | 8.987552 × 10¹³ J | 21.48 kilotons of TNT |
| 1 mg | 8.987552 × 10¹⁰ J | 24,965 kWh |
| 1 u (atomic mass unit) | 1.492418 × 10⁻¹⁰ J | 931.494 MeV |
| Electron, 9.109384 × 10⁻³¹ kg | 8.187106 × 10⁻¹⁴ J | 0.510999 MeV |
The last two rows match the CODATA values published by NIST: 931.494 103 72 MeV for the atomic mass unit and 0.510 998 950 69 MeV for the electron. A kilogram corresponds to 24,965,421,632 kWh, about 25 billion kilowatt hours.
Units in the calculator
- Electronvolts are the unit of particle physics: 1 MeV = 1.602176634 × 10⁻¹³ J.
- Kilowatt hours are the unit of your electricity bill: 1 kWh = 3.6 million joules. Everyday energies convert with the energy converter.
- Tons of TNT describe explosions: 1 ton = 4.184 × 10⁹ J by definition.
Why so much energy is not released
E = mc² gives the rest energy of the whole mass. Chemical and nuclear reactions release only the small mass difference between the starting and the end products. The Trinity test bomb released about 21 kilotons of TNT by the older estimate and about 25 kilotons by the 2021 re-evaluation – in mass terms only about one gram, since 1 g corresponds to 21.48 kilotons. Only when particles are destroyed completely, as when matter meets antimatter, is their whole rest energy turned into radiation. The same relativity theory explains slower moving clocks, which the time dilation calculator works out.
Frequently asked questions
How much energy is in 1 kg of mass?
8.987552 × 10¹⁶ joules, which is about 25 billion kWh or 21.48 megatons of TNT.
What is c² in E = mc²?
The speed of light squared: (299,792,458 m/s)² = 89,875,517,873,681,764 m²/s², so 1 kg ↔ 8.99 × 10¹⁶ J.
How do I calculate mass from energy?
Divide by c²: m = E ÷ c². 1 MeV corresponds to 1.782662 × 10⁻³⁰ kg.
What units does E = mc² use?
In SI units E is in joules, m in kilograms and c in meters per second. The calculator converts grams, pounds, atomic mass units, kWh, eV and TNT for you.
What is the rest energy of an electron?
0.510999 MeV, or 8.187106 × 10⁻¹⁴ J, from its mass of 9.109384 × 10⁻³¹ kg.
Sources and legal basis
- NIST CODATA: speed of light in vacuum c = 299 792 458 m/s, exact (read 15.10.2026)
- NIST CODATA: electron volt = 1.602 176 634 × 10⁻¹⁹ J, exact (read 15.10.2026)
- NIST CODATA: atomic mass constant 1.660 539 068 92 × 10⁻²⁷ kg; energy equivalent 931.494 103 72 MeV (read 15.10.2026)
- NIST CODATA: electron mass energy equivalent 0.510 998 950 69 MeV (read 15.10.2026)
- NIST Special Publication 811, Appendix B.8: kilowatt hour = 3.6 E+06 J, ton of TNT (energy equivalent) = 4.184 E+09 J (read 15.10.2026)
- Wikipedia, Mass–energy equivalence: c² = 89 875 517 873 681 764 J/kg, 1 kg ≈ 25.0 billion kWh ≈ 21.5 Mt TNT; Trinity/Nagasaki 21 kt (read 15.10.2026)
- Wikipedia, Trinity (nuclear test): yield 25 ± 2 kilotons of TNT (2021 re-evaluation; read 15.10.2026)
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