Mass-Energy Equivalence Calculator (E = mc²)
Calculate the energy equivalent of any mass using Einstein's E = mc².
Get joules, kWh, kilotons TNT, and comparisons to nuclear weapon and global energy scales.
The most famous formula in physics
Einstein’s 1905 paper on special relativity showed that mass and energy are not independent quantities. They are two aspects of the same thing, related by the speed of light squared:
E = m c²
Where m is the rest mass (the mass measured in the object’s own rest frame), c is the speed of light in vacuum (exactly 299,792,458 m/s by definition since 1983), and E is the energy equivalent of that mass. Because c² is enormous (about 9 × 10^16 m²/s²), even tiny amounts of mass contain stupendous quantities of energy when fully converted.
What “equivalent” means
E = mc² does NOT mean that every gram of every object is automatically convertible to energy. It means that, if you could somehow convert that mass entirely to energy, this is how much you would get. In practice, mass-to-energy conversion happens in three regimes:
In chemical reactions, the mass converted is essentially zero. Burning a liter of gasoline releases about 35 megajoules, which corresponds to a mass loss of around 3.9 × 10^−10 grams. This is far below any practical measurement precision, which is why chemistry treats mass as conserved.
In nuclear reactions (fission and fusion), about 0.1 to 0.7 percent of the mass is converted to energy. Hiroshima’s bomb converted roughly 0.6 grams of mass to energy and released about 15 kilotons of TNT equivalent. Hydrogen fusion in the Sun converts about 4.3 million tons of mass to energy every second.
Matter-antimatter annihilation converts 100 percent of the rest mass of both particles to energy (mostly gamma photons). One gram of antimatter combined with one gram of matter would release approximately 1.8 × 10^14 joules, or about 43 kilotons of TNT, comparable to a moderate nuclear weapon. This is why antimatter is the energetically densest fuel imaginable, and also why it is so hard to produce and store.
Reference energies for context
| Energy scale | Approximate value |
|---|---|
| Match burning | ~1 kilojoule |
| Stick of dynamite | ~1 megajoule |
| Hand grenade (TNT) | ~4 megajoules |
| Gallon of gasoline burned | ~120 megajoules |
| Average US home, daily | ~30 kWh = 108 MJ |
| Lightning bolt | ~1 gigajoule |
| Ton of TNT | 4.184 gigajoules |
| Hiroshima bomb | 15 kt TNT ≈ 63 terajoules |
| Tsar Bomba (largest H-bomb) | 50 Mt TNT ≈ 210 petajoules |
| Krakatoa eruption (1883) | ~200 megatons TNT ≈ 0.84 exajoules |
| Chicxulub impactor (dinosaur extinction) | ~100 million Mt TNT |
| Earth annual primary energy use | ~600 exajoules |
| Solar luminosity (per second) | 3.83 × 10^26 W |
A single gram of pure mass-energy equivalent equals 9 × 10^13 joules, or about 21.5 kilotons of TNT, roughly 1.4 Hiroshima bombs. A kilogram is 21.5 megatons, comparable to the largest Cold War hydrogen weapons. Earth’s annual energy consumption (around 600 exajoules) corresponds to roughly 7 tons of fully-converted mass.
Why the speed of light squared?
The factor c² is not arbitrary. It falls out of the relativistic invariance of energy-momentum. The full equation, valid for moving objects, is E² = (m c²)² + (p c)², where p is momentum. At rest (p = 0), this reduces to E = m c². The fact that the conversion factor is c² rather than c or some other power is a direct geometric consequence of the spacetime structure described by special relativity.
You can think of c² as the “energy per unit mass” intrinsic to the universe. It is enormous because c, our coordinate measure of speed, treats space and time as separate things measured with very different scales (meters and seconds). In natural units where c = 1, the formula reads simply E = m, and the deep meaning becomes clearer: energy and mass are the same quantity, measured in different units.
Practical takeaways
When you calculate E = mc² for an everyday mass, you are computing a number that has more energy than any chemical reaction could ever release from that mass. The energy stored as mass dwarfs the chemical bond energy by a factor of about 10^9 to 10^10. This is exactly why nuclear reactions, which tap mass directly, are so much more energy-dense than chemical reactions, which only rearrange atoms.
For a 70 kg human, E = mc² gives about 6.3 × 10^18 joules, or roughly 1.5 gigatons of TNT, or 100 thousand Hiroshima bombs. Fortunately, the strong nuclear force keeps the protons and neutrons in your atomic nuclei tightly bound, so this energy stays locked up. Only nuclear reactions or matter-antimatter annihilation can release a meaningful fraction of it.
Related quantities and concepts
For a moving object, the total energy is E_total = γ m c², where γ = 1/√(1 − v²/c²) is the Lorentz factor. The relativistic kinetic energy is the difference E_total − m c² = (γ − 1) m c². At zero velocity, the kinetic part vanishes and you are left with the rest energy E = m c². For massless particles like photons, there is no rest frame and the formula becomes E = p c, since m = 0.
The atomic mass unit u, used for atomic and nuclear masses, has an energy equivalent of approximately 931.494 MeV. This is why nuclear binding energies are typically reported in MeV per nucleon: it is the natural energy scale set by E = mc² applied to atomic-mass-scale objects.