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E = mc² Calculator

See how much energy a given mass is worth, or how much mass an amount of energy equals, with Einstein's mass–energy relation E = mc².

Level: Grades 8–9

  • Common Core standard 8.EE.A.4Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology
Printable worksheet

E = mc² Calculator

Know the answer you need? Pick an input to work backward.

Inputs
Convert

Result

Equivalent energy

89,875,517,873,681.77 J

1 g of mass is equivalent to 89,875,517,873,681.77 J.

Energy in joules
89,875,517,873,681.77 J
Energy in kilowatt-hours
24,965,421.6316 kWh
TNT equivalent
21.4808 kt TNTBy convention, 1 kiloton of TNT = 4.184 × 10¹² J.
Energy in megaelectronvolts
5.6096e+26 MeV

See the step-by-step solution ↓

Step-by-step solution

  1. Change mass to kg, the standard unit the formula uses (1 g = 0.001 kg)

    1 g×0.001=0.001 kg

  2. Square the speed of light (c), multiplying 299,792,458 m/s by itself

    299,792,4582=8.987552e+16 m²/s²

  3. Multiply the mass in kilograms by c² to get the energy in joules

    0.001×8.987552e+16=89,875,517,873,681.77 J

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

What this calculator does

See how much energy is locked up in a bit of mass, or how much mass a given energy adds up to. Einstein's E = mc² says mass and energy are two forms of the same thing. E is energy, m is mass and c is the speed of light. Any mass m has a rest energy E equal to the mass times the speed of light squared. Any change in an object's energy changes its mass by E ÷ c². c² is a huge number, about 9 × 10¹⁶ m²/s². So a tiny amount of mass matches an enormous amount of energy.

This calculator converts both ways. Enter a mass, from daltons up to tonnes, to see its rest energy. You can show it in joules, kilowatt-hours, electronvolts or tons of TNT equivalent. Or enter an energy to find the mass it matches. The working shows every conversion, and the squaring of c too.

Where it's used

Why this math matters outside the classroom:

  • Nuclear energy. Turning just 1 gram of mass into energy releases 0.001 × (3 × 10⁸)² = 9 × 10¹³ J.
  • The Sun's output. Astronomers estimate the Sun converts about 4 million tonnes of mass into energy every second to supply its light.
  • Particle masses. Physicists quote particle masses in energy units, so an electron's 9.11 × 10⁻³¹ kg is listed as about 0.511 MeV.
  • Chemical vs nuclear. Students compare chemical and nuclear energy and see that burning fuel changes its mass far too little to measure on a scale.

Grade level and standards: Grades 8–9; Common Core State Standards for Mathematics 8.EE.A.4. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Choose mass → energy or energy → mass.
  2. Enter the value and its unit.
  3. Pick the unit for the answer.
  4. Read the result. You'll also see the same energy in joules, kilowatt-hours, megaelectronvolts and kilotons of TNT.

What the inputs mean

Mass (m)
A dalton (Da), also called the unified atomic mass unit, is one twelfth of the mass of a carbon-12 atom. That's about 1.66 × 10⁻²⁷ kg. It's handy for atoms and particles.
Energy (E)
For particle physics, use eV, MeV or GeV (electronvolts and their millions and billions). For explosions, use kilotons or megatons of TNT. For everyday power use, use kilowatt-hours.

Formula and method

E = m × c²
m = E ÷ c²
c = 299,792,458 m/s (exact)
c² = 89,875,517,873,681,764 m²/s²

E is the energy, m is the mass and c is the speed of light. With m in kilograms and c in meters per second, E comes out in joules. The speed of light is exact by definition in the metric (SI) system, because the meter is defined from it. So the only uncertainty in the result comes from your input.

The formula gives the rest energy. That's the energy an object has just by having mass, measured while it sits still. A moving object also has kinetic energy, the energy of motion. Its total energy is then γmc². Here γ (gamma) is the Lorentz factor, a number that grows as the speed nears the speed of light.

Unit conversions use exact or agreed-on factors. 1 eV = 1.602176634 × 10⁻¹⁹ J exactly, and 1 kWh = 3.6 × 10⁶ J. By convention, 1 kiloton of TNT = 4.184 × 10¹² J.

Worked example

How much energy is equivalent to one gram of mass?

  1. Convert to kilograms: 1 g × 0.001 = 0.001 kg.
  2. Square the speed of light: (299,792,458)² = 8.98755 × 10¹⁶ m²/s².
  3. E = 0.001 × 8.98755 × 10¹⁶ = 8.98755 × 10¹³ J.
  4. In other units: about 24.97 million kWh, or about 21.48 kilotons of TNT.

Result: One gram of mass matches about 8.988 × 10¹³ J. That's roughly the energy released by a 21-kiloton explosion.

Understanding the result

Everyday energy changes come with almost no measurable change in mass. Burning a liter of petrol releases about 3 × 10⁷ J. That matches only about a third of a microgram (a millionth of a gram).

Nuclear reactions convert a bigger share. When uranium-235 splits (fission), about 0.1% of the fuel's mass becomes energy. When the Sun fuses hydrogen into helium, it's about 0.7%.

In particle physics, masses are often given directly as energies. An electron's rest energy is about 0.511 MeV, and a proton's about 938 MeV.

Assumptions and limitations

  • The result is the rest energy (or rest mass). The object is treated as standing still.
  • All of the mass is counted as convertible, which gives the most energy possible in theory.
  • No practical process turns ordinary matter completely into energy. Only matter–antimatter annihilation, where matter meets its opposite, does. Real reactions release a small share of the rest energy.
  • The calculator doesn't work out kinetic energy at speeds near light speed. That needs the Lorentz factor.
  • TNT equivalent is a standard unit for comparison, not a statement about any real event.

Frequently asked questions

Why is the speed of light squared?

It's what the units and the physics call for. Energy has units of mass times speed squared. In special relativity, Einstein's theory of motion near light speed, the speed of light is the natural link between mass and energy. The square is why so little mass gives so much energy.

Does a hot object weigh more than a cold one?

In principle, yes. Adding heat energy E raises the mass by E ÷ c². Heating a kilogram of water by 100 °C adds about 4.2 × 10⁵ J. That raises its mass by only about 5 × 10⁻¹² kg, far too little to measure on a scale.

What is a dalton in energy terms?

One dalton matches about 931.494 MeV. Nuclear physicists use this figure to turn the small mass differences between nuclei into the energies released in nuclear reactions.

Is E = mc² only about nuclear energy?

No. It applies to every form of energy, including chemical and heat energy. Nuclear reactions just convert a much bigger share of mass, which makes the effect easy to see.

How this calculator is checked

Method: Mass–energy equivalence E = mc² with c = 299,792,458 m/s (exact SI); 1 eV = 1.602176634 × 10⁻¹⁹ J (exact); 1 Da = 1.66053906892 × 10⁻²⁷ kg (CODATA 2022); 1 kt TNT = 4.184 × 10¹² J (convention). The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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