E = mc² Calculator - Mass-Energy Equivalence
Enter a mass to find its equivalent rest energy, or flip the calculation and enter an energy to find the equivalent mass. Results appear in multiple units simultaneously so you can relate the number to familiar real-world scales. Switch between forward (mass to energy) and reverse (energy to mass) mode, choose your preferred units for both inputs and outputs, and see the step-by-step arithmetic with the actual values you entered.
Formula
Worked example
For 1 kg of mass: E = 1 kg x (299,792,458 m/s)^2 = 8.988 x 10^16 J = 24,966,000 kWh = 21.48 megatons of TNT. To reverse, find the mass equivalent of 1 kWh = 3,600,000 J: m = 3,600,000 / 8.988e16 = 4.006 x 10^-11 kg = 40.1 nanograms.
What is E = mc²?
E = mc² is the most famous equation in physics. Proposed by Albert Einstein in his 1905 paper on special relativity, it states that rest energy (E) equals rest mass (m) multiplied by the square of the speed of light (c = 299,792,458 m/s). The equation reveals that mass and energy are two forms of the same thing: a small amount of mass corresponds to an enormous amount of energy, because c² is roughly 9 x 10^16 joules per kilogram. This is the theoretical maximum energy that could be extracted from a given mass if it were completely converted - a process that never happens in full in practice, but that underlies nuclear fission, fusion, and annihilation reactions.
How to use this calculator
Choose your mode at the top. In the default forward mode (E from m), enter the mass and select its unit - kilograms, grams, pounds, ounces, or atomic mass units. Pick your preferred energy output unit (joules, kilowatt-hours, megatons of TNT, electronvolts, and more). The calculator shows the rest energy in your chosen unit, plus parallel results in joules, kWh, and megatons of TNT so you can relate the number to familiar scales. In reverse mode (m from E), enter an energy value and its unit, and the calculator returns the equivalent mass in kilograms and atomic mass units. The "Show your work" panel walks through each arithmetic step with your actual values.
Forward vs reverse calculation
The same equation works in two directions. Forward (E = mc²) answers: "If I had this much matter and could convert it entirely, how much energy would I get?" Reverse (m = E / c²) answers: "If I want to produce this much energy from matter, how much mass would I need to annihilate?" The reverse direction is especially useful in particle physics: the mass of a particle is routinely quoted as its rest energy in MeV (megaelectronvolts) - the proton is "938 MeV", meaning 938 MeV is the energy equivalent of its mass. Nuclear binding energies, which show up as the mass deficit between a nucleus and its constituent nucleons, are also often given in MeV.
Real-world applications and context
Complete mass-energy conversion does not happen in ordinary nuclear reactions. A fission reactor converts less than 0.1% of fuel mass into energy; a fusion reaction about 0.3 to 0.7%; matter-antimatter annihilation would convert 100%, but we cannot yet produce antimatter at meaningful scale. Still, even 0.1% of a kilogram is roughly 90 terajoules - enough to power a large city for a day. The equivalence also means that any time a system gains or loses energy it gains or loses mass: a hot object is literally heavier than a cold one, a fully charged battery is heavier than a flat one, but the differences are far too small to measure outside laboratory settings. These mass changes are, however, central to atomic clock precision and GPS satellite timing corrections.
Notable mass-energy equivalences
| Object / Particle | Mass | Rest energy (joules) | Real-world comparison |
|---|---|---|---|
| Electron | 9.109 x 10^-31 kg | 8.187 x 10^-14 J (0.511 MeV) | Less than a photon of visible light |
| Proton | 1.673 x 10^-27 kg | 1.503 x 10^-10 J (938 MeV) | About 1836 electron rest energies |
| 1 gram | 0.001 kg | 8.988 x 10^13 J (89.9 TJ) | About 21.5 kilotons of TNT |
| 1 kilogram | 1 kg | 8.988 x 10^16 J (89.9 PJ) | About 21.5 megatons of TNT |
| Hiroshima bomb (full release) | ~0.7 g mass deficit | ~6.3 x 10^13 J | ~63 TJ (actual yield) |
| Annual US electricity use | equivalent ~3.9 kg | ~3.5 x 10^17 J | ~3.5 x 10^11 kWh / year |
| Sun (per second of output) | ~4.3 x 10^9 kg/s | ~3.8 x 10^26 J/s | 3.828 x 10^26 watts (luminosity) |
Rest energies for well-known objects and particles, calculated with E = mc². These are theoretical values; real reactions convert only a small fraction.
Frequently asked questions
What does c stand for in E = mc²?
c is the speed of light in a vacuum, exactly 299,792,458 metres per second (about 300,000 km/s or 186,000 miles per second). It is a defined constant in the International System of Units. Because it is squared in the formula, even a small mass corresponds to an enormous energy.
Does E = mc² mean all matter could be turned into energy?
In principle yes, but in practice no process converts 100% of matter into energy outside of matter-antimatter annihilation. Nuclear fission converts about 0.09% of mass, fusion about 0.3-0.7%. Still, even those fractions are enormous compared with chemical reactions, which convert zero mass (the mass change is too tiny to measure).
Why is the energy so large for such a small mass?
Because c² is approximately 8.988 x 10^16 joules per kilogram. That is nearly 90 quadrillion joules per kilogram - a consequence of the enormous speed of light. Even 1 gram of matter is equivalent to about 90 terajoules, roughly 21.5 kilotons of TNT.
What is the difference between rest energy and kinetic energy?
Rest energy (E = mc²) is the energy stored in mass itself when the object is stationary. Kinetic energy is additional energy an object carries due to its motion. At everyday speeds kinetic energy is tiny relative to rest energy. Near the speed of light, relativistic kinetic energy grows rapidly and the full energy becomes E = gamma * mc², where gamma (the Lorentz factor) is much greater than 1.
Why do physicists measure particle masses in MeV?
Particle masses are so small in kilograms that the numbers are unwieldy. It is more convenient to quote the rest energy in megaelectronvolts (MeV) or gigaelectronvolts (GeV) using m = E/c². The electron is 0.511 MeV, the proton is 938.3 MeV. The c² is often absorbed into the unit, written as MeV/c².
Can I use this formula for moving objects?
E = mc² gives the rest energy of a stationary object. For a moving object the total energy is E = gamma * mc², where gamma = 1/sqrt(1 - v²/c²). At ordinary speeds the correction is negligible: at 10% of c, gamma is only 1.005. You need a relativistic kinetic energy calculator for the moving case.