Mass–Energy Equivalence Calculator
The energy equivalent of a mass by E = mc², expressed in joules, kilowatt-hours, tonnes of TNT and years of a household’s electricity.
Einstein’s equation says mass and energy are the same thing in different units, and the exchange rate is c² — about 9 × 10¹⁶ joules per kilogram.
How the mass–energy equivalence calculator works
Einstein’s equation says mass and energy are the same thing in different units, and the exchange rate is c² — about 9 × 10¹⁶ joules per kilogram. A single gram is 25 million kilowatt-hours. Nuclear reactions release a fraction of a percent of a fuel’s mass as energy; chemical reactions release a billionth as much, which is why the mass change in burning is unmeasurable.
Formula: E = m × c², c = 299,792,458 m/s
Worked examples
| Inputs | Energy (J) | Note |
|---|---|---|
| One gram | 8.988e13 J | 8.988 × 10¹³ J, 21,480 t TNT |
| One kilogram | 8.988e16 J | 8.988 × 10¹⁶ J |
| A milligram | 8.988e10 J | 8.988 × 10¹⁰ J — 25 MWh |
FAQFrequently asked questions
Can we actually release all that energy?
Only matter–antimatter annihilation converts the whole mass. Fission releases about 0.1% of the fuel’s mass and fusion under 1%; chemical fuels release around a billionth, which is still 40 MJ per kilogram of petrol.
Why is c squared?
Dimensionally, energy is mass times a speed squared (like ½mv²), and the speed that appears is the one built into spacetime. It is also why the number is so large: c² is 9 × 10¹⁶ m²/s².
How much is a tonne of TNT?
Defined as 4.184 gigajoules. The 1945 Hiroshima bomb was about 15,000 tonnes of TNT, which corresponds to the conversion of roughly 0.7 g of mass.
Does this mean mass is not conserved?
Mass–energy together is conserved. A hot object weighs very slightly more than a cold one, and the products of a nuclear reaction weigh less than the reactants by exactly the energy released divided by c².
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Physical Laboratory — the UK's national measurement institute
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.