E = mc² Calculator: Mass-Energy Equivalence
Solve energy or mass with E = mc². Use joules, kWh, eV or tonnes of TNT for energy and kg, g or atomic mass units for mass, with c fixed at 299,792,458 m/s. Free and private in your browser.
The speed of light is fixed at c = 299,792,458 m/s (exact), so only energy and mass are fields.
Fill in all but one field: the empty field is the one you solve for.
About the E = mc² Calculator
The E = mc² Calculator solves Einstein's mass-energy equivalence. Enter a mass and it returns the rest energy that mass is equivalent to. Enter an energy and it returns the mass. The speed of light is built in as the exact value 299,792,458 m/s, so there is nothing else to type. The page shows the equation with the solved symbol highlighted and a one-line substitution such as 1 kg × (299,792,458 m/s)² = 8.98755 × 10¹⁶ J.
The result is the rest energy of an object: the energy locked in its mass when it is not moving. It is not the kinetic energy of an everyday moving object. For that, use the Kinetic Energy Calculator.
How to use the E = mc² calculator
Steps
- Enter a mass to find the energy, or an energy to find the mass. Leave the one you want to find empty.
- Pick units. Energy offers J, kJ, MJ, kWh, TWh, eV and tonnes of TNT. Mass offers kg, g, mg, u (the atomic mass unit) and lb.
- Read the answer under the equation, together with the same value in every other energy or mass unit.
Energy and mass must be zero or more. A negative value is flagged next to its field. The tonne of TNT is the standard convention of 4.184 gigajoules, and 1 u is 1.66053906892 × 10⁻²⁷ kg.
Formula
E is energy in joules, m is mass in kilograms and c is the speed of light in a vacuum. Because c² is about 9 × 10¹⁶ m²/s², a very small mass is equivalent to a very large amount of energy. The speed of light is exact because the metre is defined from it.
Worked examples
Example 1: one kilogram
E = 1 kg × (299,792,458 m/s)² = 8.98755 × 10¹⁶ J. That is about 24.97 TWh, roughly 21.5 million tonnes of TNT.
Example 2: one gram
E = 0.001 kg × c² = 8.98755 × 10¹³ J, or about 24.97 million kWh. Converting a single gram of matter completely into energy would release about 21.5 thousand tonnes of TNT.
Example 3: an atomic mass unit
For m = 1 u, choose eV as the energy unit. E = 931.494 MeV. This is why nuclear binding energies are quoted in MeV.
Example 4: the mass of a kilowatt-hour
Enter 1 kWh as the energy. The mass is 4.0 × 10⁻¹¹ kg, about 40 nanograms. A household's electricity bill corresponds to a mass far too small to weigh.
Good to know
- Chemical reactions release energy too, but the mass change is so small that it cannot be measured on a balance. Nuclear reactions convert a visible fraction, such as the mass defect behind fission and fusion.
- The Sun radiates about 3.8 × 10²⁶ W, which by this equation is a loss of roughly four million tonnes of mass every second.
- The full relation for a moving body is E² = (pc)² + (mc²)². This page gives the rest-energy term, which is the whole energy when the momentum p is zero. For momentum, see the Momentum Calculator.
Privacy
Nothing is uploaded; every calculation runs in your browser and never leaves your device.
Related tools
Use the Kinetic Energy Calculator for the energy of motion, the Mass Converter to prepare a mass in another unit, and the Speed Converter to compare a speed with the speed of light.
Frequently asked questions
What does E = mc² mean?
It says that mass and energy are two forms of the same thing. An object of mass m at rest has an energy E equal to m times the speed of light squared. The huge size of c² means a tiny mass is equivalent to a very large amount of energy.
How do I calculate energy from mass?
Multiply the mass in kilograms by the square of the speed of light, 299,792,458 m/s. One kilogram gives 8.98755 × 10¹⁶ joules. Enter the mass, leave the energy empty and choose the unit you want the answer in.
What value of the speed of light does it use?
The exact value 299,792,458 m/s. The metre is defined from the speed of light, so this is not a measured approximation. It is fixed in the formula, so you never need to type it.
How much energy is in one gram of matter?
About 8.99 × 10¹³ joules, which is roughly 25 million kilowatt-hours or 21,500 tonnes of TNT. Real reactions only convert a small fraction of the mass, so this is an upper limit, not what a power plant gets.
What is a tonne of TNT as an energy unit?
By convention one tonne of TNT is 4.184 gigajoules (4.184 × 10⁹ J). The calculator uses that value, which is why one kilogram converts to about 21.5 million tonnes of TNT.
Why use electronvolts and atomic mass units?
They suit atoms and particles. One atomic mass unit (u) is equivalent to 931.494 MeV, and an electron's rest mass is about 0.511 MeV. Choose u for mass and eV for energy to see these directly.
Does E = mc² give kinetic energy?
No. It gives the rest energy, the energy a mass has even when it is not moving. For the energy of motion at everyday speeds, use KE = ½mv² in the Kinetic Energy Calculator.
Does it send my numbers anywhere?
No. The mass or energy you enter is converted and solved locally in your browser using the speed of light, and nothing is uploaded, stored or shared with a server.