Mass Energy Equivalence Calculator

Turn mass into energy and energy back into mass with E = mc squared, shown in joules, kilowatt hours, BTU and tons of TNT.

What it does

Einstein's mass energy relation is the shortest equation with the biggest consequences. Mass and energy are the same thing measured in different units, and the conversion factor is the square of the speed of light. The NIST page on the fundamental constants puts it plainly: in Einstein's theories of relativity, mass and energy are equivalent, with the energy being directly proportional to the mass and the constant of proportionality being the velocity of light squared.

The numbers look impossible at first because everyday masses are tiny next to the factor. One kilogram multiplied by 299792458 squared gives 8.9876e16 joules, which is the energy released by roughly 21 million tons of TNT. There is nothing wrong with the arithmetic. A kilogram of matter is being compared with a bomb, and that bomb is what the same mass would give if all of it were turned into energy.

The relation is not only a curiosity for physics students. It is the reason nuclear power stations release so much energy from so little mass, and the reason particle accelerators need so much energy to make new particles. It also runs backwards, which is the part people forget: any joule of energy has a mass, and 8.9876e16 joules weighs a kilogram.

This page does both directions. Give it a mass and it returns the energy in joules, in kilowatt hours, in BTU and in tons of TNT. Switch to the other direction and give it an energy and it returns the mass that carries it. Metric and imperial units are supported, so a mass in pounds and an energy in BTU work as well.

One caution belongs with the numbers. Converting mass into energy by multiplication tells you how much energy a mass would release in a perfect, complete conversion, and it says nothing about whether such a reaction is possible. Most of the mass of ordinary matter converts to energy through nuclear processes only under extreme conditions. The equation is exact; the practical part is the chemistry and the physics around it.

How to use

1. Choose metric or imperial units for the mass and the energy.
2. Pick whether you want the energy of a mass or the mass of an energy.
3. Enter the mass in kilograms or pounds, or the energy in joules.
4. Read the energy in the unit of your choice and the equivalent in kilowatt hours and tons of TNT.
5. Switch the direction to check the number the other way, since the two answers have to agree.
6. Remember what the figure means: it is the energy a perfect conversion would release, not a claim that the conversion is easy.

Formula

E

Energy in joules.

m

Rest mass in kilograms.

c

Speed of light in a vacuum, exactly 299792458 m per second.

1 kWh

3.6 million joules.

1 ton of TNT

4.184 billion joules, the conventional definition of the ton of TNT.

The speed of light is exact by definition, so every digit in the answer comes from the mass you typed. The ton of TNT is a unit of energy rather than a substance: it is defined as the energy released by one ton of TNT detonated, and the 4.184 gigajoule figure is the convention used here. This is the rest mass relation, so it applies to a body at rest, not to a moving one, where relativistic momentum also carries energy.

Worked example

Reference table

Limits

• The page covers the rest mass relation only. A body that is moving carries extra energy from its motion, and that part is not included.
• The figure is what a complete conversion would release. It does not describe whether any particular reaction can happen.
• The mass that energy carries is far too small to weigh in a laboratory, so this is a calculation rather than a measurement.
• Ordinary chemical reactions change mass by only a few parts in ten to the power of 10 to the 12, which is why calories and food energy look so different from the table above.

Common mistakes

• Writing c as 300 million m per second instead of 299792458. The speed of light is exact, and rounding it introduces an error in the last digits of the answer.
• Reading the number of kilowatt hours as the power a device uses. Energy and power are different things, and kilowatt hours belong on the meter.
• Comparing the energy of a kilogram with a bomb and concluding that matter is dangerous. Ordinary matter is not close to converting.
• Forgetting that the relation works in both directions, so an energy figure always implies a mass.
• Using the ton of TNT as a mass. It is an energy unit defined by a detonation, so it divides an energy and not a mass.

Try it yourself

Quick checks. Answers sit tucked under each question.

Questions

Sources

• NIST: Einstein was right again, experiments confirm E = mc squared
• NIST: the speed of light in vacuum from the CODATA values
• NIST: introduction to the fundamental physical constants

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