E = mc² says that mass and energy are two measures of the same thing, linked by the square of the speed of light. Because c² is such a large number, a few grams of matter correspond to an energy you would normally see from a power station. This calculator converts a mass into its rest energy, or an amount of energy into its mass equivalent, and expresses the result in units that make the scale tangible: kilowatt-hours, gigawatt-hours, kilotons of TNT, electronvolts and atomic mass units.
How to use the E = mc² calculator
- Under Solve for, pick Energy (from a mass) or Mass (from an energy).
- Enter the Mass (m) in kg, g, mg, µg, lb, oz, metric tons or atomic mass units (u), or the Energy (E) in J, kJ, MJ, GJ, TJ, kWh, GWh, kilotons or megatons of TNT, eV, keV, MeV, GeV, cal, kcal or BTU. Both must be greater than zero.
- Use Show the result in to choose the unit of the answer.
- Read the result with conversions, the equivalent number of atomic mass units, and how long a 100-W bulb could run on that energy. “Show the work” spells out c² and each substitution.
The mass–energy formula
Here c = 299,792,458 m/s exactly, as fixed by the SI definition of the meter, so c² = 8.98755178737 × 10¹⁶ m²/s². With mass in kilograms the energy comes out in joules. For atoms and particles it is easier to work in atomic mass units and electronvolts:
The calculator uses the CODATA 2022 value of the dalton, 1.66053906892 × 10⁻²⁷ kg. An electron (0.000549 u) works out to 0.511 MeV, the familiar electron rest energy.
Worked example: one gram
The rest energy of 1 g of anything
E = 0.001 kg × (299,792,458 m/s)² = 8.988 × 10¹³ J
That is 89.88 TJ, 24.97 GWh, or 21.48 kilotons of TNT (1 kt is defined as 4.184 × 10¹² J). Spread over time, it would keep a 100-W bulb lit for about 28,480 years. The same gram is 6.022 × 10²³ u, matching the Avogadro constant to the digits shown.
Going the other way, one kilowatt-hour corresponds to only 4.0 × 10⁻¹¹ kg, about 40 nanograms. A 1-gigawatt power plant running for a full year delivers 3.16 × 10¹⁶ J, the mass equivalent of about 351 g. The Sun radiates about 3.828 × 10²⁶ W (the IAU nominal solar luminosity), which means it sheds roughly 4.26 × 10⁹ kg, more than four million tonnes, every second.
Mass defect and nuclear binding energy
A nucleus weighs less than the protons and neutrons that make it up. That missing mass, the mass defect, is the binding energy that would be needed to pull the nucleus apart. Helium-4 is the classic case:
- Two hydrogen-1 atoms plus two neutrons: about 4.032980 u
- One helium-4 atom: about 4.002603 u
- Mass defect: 0.030377 u
Enter 0.0303766 u and choose MeV, and the calculator returns about 28.30 MeV, or 7.07 MeV per nucleon. Binding energy per nucleon peaks near iron and nickel at close to 8.8 MeV. Splitting very heavy nuclei and fusing very light ones both move toward that peak, and the mass that disappears along the way is the energy released.
How much mass actually turns into energy?
E = mc² gives the total rest energy, but ordinary processes release only a sliver of it. Orders of magnitude, consistent with the calculator’s note:
| Process | Share of mass converted | Typical energy release |
|---|---|---|
| Burning fuel (chemical) | about 1 part in a billion or less | ~46 MJ per kg of gasoline |
| Fission of uranium-235 | about 0.1% | ~200 MeV per fission |
| Deuterium–tritium fusion | about 0.4% | 17.6 MeV per reaction |
| Hydrogen to helium (stellar fusion) | about 0.7% | 26.7 MeV per helium nucleus |
| Matter–antimatter annihilation | 100% | 2 × 0.511 MeV per electron–positron pair |
So the energy a reactor or the Sun actually delivers is the result for the converted fraction, not for the whole fuel mass. To compare these energies with everyday ones, the energy converter handles joules, BTU and kWh, and the wavelength calculator turns photon frequencies into electronvolts.
Frequently asked questions
How much energy is in 1 gram of mass?
E = 0.001 kg × (299,792,458 m/s)² ≈ 8.988 × 10¹³ J. That is about 89.9 terajoules, 24.97 gigawatt-hours or 21.5 kilotons of TNT, enough to run a 100-W bulb for roughly 28,000 years.
Why is the speed of light exact?
Since 1983 the meter has been defined from the distance light travels in 1/299,792,458 of a second, so c is fixed at exactly 299,792,458 m/s by the SI. Its square, 8.98755178737 × 10¹⁶ m²/s², is what links kilograms to joules.
What is 1 atomic mass unit in MeV?
One unified atomic mass unit (dalton), about 1.66054 × 10⁻²⁷ kg, has a rest energy of about 931.494 MeV. Choose u as the mass unit and MeV as the result unit to convert nuclear and particle masses directly.
Does burning fuel convert mass into energy?
Strictly yes, but the amount is tiny. Burning 1 kg of gasoline releases about 46 MJ, which corresponds to roughly half a microgram, a few parts in ten billion of the fuel's mass and far too little to weigh. Nuclear reactions convert about a million times larger fraction.
Is E = mc² the energy of a moving object?
No. It is the rest energy, the energy a mass has while stationary. A moving object has extra kinetic energy on top, and its total energy is γmc², where the Lorentz factor γ grows without limit as the speed approaches c.