About the E=mc² Calculator
Einstein's mass–energy equivalence, E = mc², says that mass and energy are two forms of the same thing, linked by the square of the speed of light. Because c is so large (exactly 299,792,458 m/s), a tiny amount of mass corresponds to an enormous amount of energy. This E=mc² calculator converts a mass into its rest energy, or works backwards from an energy to the mass it is equivalent to.
Results are shown in joules plus the units that make the numbers meaningful: kilowatt-hours for electricity, mega-electronvolts for particle and nuclear physics, and tonnes of TNT for explosions. Students use it for modern-physics homework, and it is a quick way to see why nuclear reactions, which convert about 0.1% of their fuel's mass, release millions of times more energy than chemical burning.
The energy shown is the total rest-mass energy — what you would get if the mass were converted completely, as happens when matter meets antimatter. Real fission or fusion converts only the small mass difference between reactants and products, so enter that mass defect to estimate the energy released. The calculator uses the exact SI values of c and the electronvolt.
How to use the e=mc² calculator
- 1Choose mass → energy or energy → mass.
- 2Enter the amount and pick its unit.
- 3Read the result in joules, kWh, MeV and tonnes of TNT, or as a mass.
- 4For nuclear reactions, enter the mass defect rather than the total fuel mass.
Formula and method
Rest energy equals mass times the speed of light squared. With mass in kilograms and c in metres per second, the energy comes out in joules; c² is about 8.988 × 10¹⁶ J/kg, so one kilogram is equivalent to roughly 90 petajoules. Dividing an energy by c² gives the equivalent mass.
Conversions use exact or standard factors: 1 kWh = 3.6 MJ, 1 eV = 1.602176634 × 10⁻¹⁹ J (exact since the 2019 SI redefinition), 1 tonne of TNT = 4.184 × 10⁹ J by convention, and 1 atomic mass unit = 1.66053906660 × 10⁻²⁷ kg, which corresponds to about 931.494 MeV.
- E
- Rest energy (J)
- m
- Mass (kg)
- c
- Speed of light in vacuum, exactly 299,792,458 m/s
Worked examples
Energy in one gram of matter
E = 0.001 kg × (299,792,458 m/s)² = 8.988 × 10¹³ J, or about 25 million kWh. That is roughly 21.5 kilotonnes of TNT, similar to the yield of the 1945 Nagasaki bomb.
Rest energy of one atomic mass unit
One dalton is 1.66054 × 10⁻²⁷ kg. Multiplying by c² gives 1.4924 × 10⁻¹⁰ J, which divided by 1.602 × 10⁻¹³ J/MeV is 931.494 MeV, the conversion factor used throughout nuclear physics.
Mass converted in a 1-megaton explosion
One megaton of TNT is 4.184 × 10¹⁵ J. Dividing by c² gives about 0.0466 kg — only 46.6 g of mass turned into energy.
Mass equivalent of one kilowatt-hour
1 kWh is 3.6 × 10⁶ J, and 3.6 × 10⁶ ÷ 8.988 × 10¹⁶ = 4.006 × 10⁻¹¹ kg — about 40 nanograms. A charged battery really is that tiny bit heavier than a flat one.
Frequently asked questions
What does E = mc² mean?+
It means mass and energy are equivalent: an object's rest energy E equals its mass m times the speed of light squared. Because c² is about 9 × 10¹⁶ m²/s², a small mass corresponds to a huge amount of energy.
How much energy is in 1 kg of mass?+
About 8.988 × 10¹⁶ joules, or roughly 25 billion kilowatt-hours — around 21 megatonnes of TNT. That is the energy released if the mass were converted completely, as in matter–antimatter annihilation.
How much mass is converted in a nuclear reactor?+
Fission of uranium-235 converts only about 0.09% of the fuel's mass into energy; about 200 MeV is released per fission. A reactor producing 1 GW of electricity (about 3 GW of heat) converts roughly 1 kg of mass per year.
Does E = mc² apply to chemical reactions?+
Yes, but the mass change is far too small to weigh. Burning fuel releases energy that corresponds to a mass loss of only about one part in a few billion, so chemists treat mass as conserved.
What is the speed of light used in the calculation?+
Exactly 299,792,458 metres per second. Since 1983 the metre has been defined from this value, so it has no measurement uncertainty.