E = mc² Calculator (mass–energy equivalence: joules, kWh, TNT)

Understanding the E = mc² calculator — concept and principle

This calculator turns a mass into its equivalent rest energy using Einstein's relation E = mc². It shows the energy in joules, kilowatt-hours, kilotonnes of TNT, days of output of a 1 GW power plant and electronvolts. Students use it to get a feel for how large c² is, and it helps when comparing nuclear, chemical and everyday energy scales.

Converting a whole gram would release about 21 kilotonnes of TNT; real reactions convert only a tiny fraction.

How it is calculated

E = m × c², with c = 299,792,458 m/s (exact)

The mass is first converted to kilograms (g × 10⁻³, mg × 10⁻⁶, µg × 10⁻⁹, t × 10³).
kWh = E ÷ 3.6 × 10⁶; kilotonnes of TNT = E ÷ 4.184 × 10¹²; days of a 1 GW plant = E ÷ 10⁹ ÷ 86,400; eV = E ÷ 1.602176634 × 10⁻¹⁹.

The principle

Special relativity shows that a body at rest still carries energy, its rest energy, and that energy and mass are two measures of the same thing. The conversion factor is c², about 8.988 × 10¹⁶ J per kilogram. Because c is so large, a tiny mass corresponds to a huge energy. The formula gives the energy if the whole mass were converted. Real processes release only part of it: fission releases about 0.1% of the fuel mass and hydrogen fusion about 0.7%, while chemical reactions change the mass by less than a part per billion.

Worked example

Default input: 1 gram.

m = 1 g = 0.001 kg.
E = 0.001 × 299,792,458² = 8.988 × 10¹³ J.
In kWh: 8.988 × 10¹³ ÷ 3.6 × 10⁶ = 2.497 × 10⁷ kWh.
TNT: 8.988 × 10¹³ ÷ 4.184 × 10¹² = 21.48 kilotonnes.
A 1 GW plant: 8.988 × 10¹³ ÷ 10⁹ ÷ 86,400 = 1.04 days.
In electronvolts: 5.610 × 10³² eV.

How to read the result

Read the result as an upper limit. One gram of mass is about the energy of a 21-kilotonne explosion, yet no practical process converts a whole gram of ordinary matter. Multiply by the fraction a real process converts to get a realistic figure: about 0.1% for fission gives around 9 × 10¹⁰ J per gram of fuel. The electronvolt value is handy for particle physics, where an electron's rest energy is about 0.511 MeV.

Common mistakes

Forgetting to convert grams to kilograms, which gives an answer 1,000 times too large.
Treating E = mc² as the energy any reaction releases. Only the mass difference between reactants and products is released.
Mixing up kilotonnes and megatonnes of TNT.

Keep in mind: The result is the full rest energy of the mass. It is a physics illustration, not a model of any real power source or weapon.

Frequently asked questions

Does a hot object weigh more than a cold one?

In principle yes, because added energy E adds mass E ÷ c², but the change is far too small to measure on a scale.

Why is the speed of light squared?

Energy has units of kg·m²/s², so a mass must be multiplied by a speed squared. The speed that appears in relativity is c.

Is mass destroyed in a nuclear reactor?

The products have slightly less rest mass than the fuel. That mass difference appears as kinetic energy of the fragments and then as heat.

What is 1 kilotonne of TNT in joules?

By convention 4.184 × 10¹² J.

Sources: OpenStax, University Physics Volume 3 (2016), section on relativistic energy · BIPM, The International System of Units (SI Brochure), 9th edition (2019) · NIST Special Publication 811 (2008), Appendix B

Checked 9 Nov 2026. OpenStax, University Physics Volume 3 (2016), §5.10 “Relativistic Energy” (total energy E = γmc², rest energy mc² for γ = 1); c and the electronvolt: BIPM SI Brochure, 9th edition (2019); ton of TNT = 4.184 × 10⁹ J: NIST Special Publication 811 (2008), Appendix B.

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