Mass-Energy Equivalence Calculator
Inputs
| Calculate | Mass → Energy |
|---|---|
| Mass | 1 g |
| Energy | 1 MJ |
Mass-Energy Equivalence Calculator
Calculate the energy equivalent of a mass or the mass equivalent of an energy using Einstein's E = mc². Enter a mass to find its energy content, or an energy to find the corresponding mass.
Inputs
Results
Enter a value to see results.
Mass-Energy Equivalence
Einstein's equation is one of the most famous results in physics. It states that the rest energy of an object is equal to its mass multiplied by the square of the speed of light . Because is an enormous number, even a tiny mass corresponds to a vast amount of energy.
This calculator works in both directions: enter a mass to find its energy equivalent, or enter an energy to find the corresponding mass.
What the equation means
does not mean that matter spontaneously converts to energy in everyday life. It sets the exchange rate between the two quantities. Mass and energy are not fundamentally different things — they are two aspects of the same conserved quantity. In nuclear reactions a small fraction of rest mass is converted to kinetic energy and radiation, and particle accelerators routinely create new particles from pure energy, demonstrating the equation in the opposite direction.
Formula
| Quantity | Symbol | Definition |
|---|---|---|
| Rest energy | Energy of the object at rest, | |
| Mass | Rest mass of the object, in kilograms | |
| Speed of light | (exact) | |
| Equivalent mass |
The speed of light is a defined constant, so is exact: (truncated to the digits used here).
Worked example — mass to energy
A nuclear warhead fission core contains roughly 1 kg of fissile material. Only about 0.1 % of the rest mass actually converts to energy in a fission reaction. What is the energy released?
E=mc2=0.001 kg×8.9876×1016 J/kg≈8.99×1013 JFor 1 g of matter completely converted (0.1% of 1 kg), the energy release is approximately — roughly 21 kilotons of TNT equivalent. Enter 1 g in the calculator to confirm this result.
Worked example — energy to mass
The Large Hadron Collider can deliver collision energies of around 13 TeV = . What is the equivalent mass?
m=c2E=8.9876×10162.08×10−6≈2.3×10−23 kgThis is less than 14 atomic mass units — showing that particle colliders create particles from energy with masses comparable to a few protons.
Nuclear energy in context
Fission reactors convert about 0.1% of fuel mass to energy; fusion reactions convert closer to 0.7%. Even at 0.1%, uranium fission releases roughly 2 million times more energy per kilogram than burning coal (), because the coal reaction rearranges electron bonds rather than converting rest mass. The difference between chemical and nuclear energy is entirely a consequence of .
Antimatter and complete annihilation
When a particle meets its antiparticle — for example, a proton and an antiproton — both are annihilated and their combined rest mass converts entirely to photons. One gram of matter plus one gram of antimatter would release , with 100% efficiency. This is the theoretical maximum energy extraction from matter. In practice, producing antimatter requires at least as much energy as it releases, so it is not currently a practical energy source.
Frequently Asked Questions (FAQ)
What is mass-energy equivalence?
Mass-energy equivalence is the principle, first stated by Albert Einstein in 1905 as part of special relativity, that mass and energy are two forms of the same physical quantity. They can be converted into each other through the relation E = mc², where c is the speed of light in a vacuum (approximately 3 × 10⁸ m/s). The implication is that even a small amount of matter contains an enormous amount of energy, because c² is about 9 × 10¹⁶ J/kg.
What does E = mc² actually mean?
E = mc² says that the rest energy E of an object at rest equals its mass m multiplied by the square of the speed of light c. It does not mean that matter is constantly converting into energy in everyday life; rather, it sets the exchange rate between the two quantities. Nuclear reactions — fission and fusion — release energy precisely because the total rest mass of the products is slightly less than the total rest mass of the reactants, and that mass difference appears as kinetic energy and radiation.
How much energy is in 1 gram of matter?
One gram of matter (0.001 kg) has a rest energy of E = 0.001 × (299 792 458)² ≈ 8.99 × 10¹³ J, or about 90 terajoules. For comparison, the atomic bomb dropped on Hiroshima released roughly 6 × 10¹³ J. Complete conversion of 1 g to energy is about 1.5 times that yield. In practice no process converts mass to energy with 100% efficiency; nuclear fission converts only about 0.1% of the fuel mass.
What is rest mass energy?
Rest mass energy is the energy a particle or object possesses solely because of its mass, when it is at rest (not moving). It equals E₀ = mc². This is distinct from kinetic energy, which a moving object gains on top of its rest energy. In particle physics, the rest mass energy of a proton is about 938 MeV. When a particle and its antiparticle annihilate, their combined rest mass energy converts entirely into photons (gamma rays), an example of Einstein's equation made concrete.