Calculate the energy equivalent of a mass (E = mc²), or the mass equivalent of an energy, in joules, kWh, and megatons of TNT.
Inputs
kg
Rest mass, in kilograms.
Energy Equivalent
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Enter a mass above.
Inputs
J
Energy, in joules. Scientific notation (e.g. 8.988e16) is accepted.
Mass Equivalent
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Enter an energy above.
Try your own mass
kg
Optional — see its energy equivalent below.
Reference Comparisons
Object
Mass
Energy (E = mc²)
TNT equivalent
4 min read3 steps6 terms3 examples6 FAQsE = mc²
E = mc² is perhaps the most famous equation in physics: it states that mass and energy are two forms of the same underlying quantity.
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Walk-through
How to Use This Calculator
3 steps▸
1
Choose a direction
Pick the Mass → Energy tab to find the energy locked inside a given mass, or Energy → Mass to find the mass equivalent of a given amount of energy. Use the Comparisons tab to see the equivalence for everyday objects.
2
Enter the value
Type a mass in kilograms (Mass → Energy) or an energy in joules (Energy → Mass) — scientific notation like 8.988e16 is accepted. The result updates instantly as you type.
3
Read the result
The headline number is the energy (in joules, with kWh and megaton-of-TNT equivalents) or the mass, depending on the tab. Because c² is a huge number, tiny masses convert to enormous energies — the result panel switches to scientific notation automatically for very large or very small values.
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Reference
Formula & Methodology
2 formulas▸
Mass-energy equivalence
E = mc²
Einstein's mass-energy equivalence: the rest energy E (joules) of an object equals its mass m (kilograms) times the speed of light c (299,792,458 m/s) squared. Because c² ≈ 9×10¹⁶ m²/s², even a tiny mass corresponds to an enormous amount of energy.
Reverse — mass from energy
m = E / c²
Solving E = mc² for mass gives the rest-mass equivalent of any energy. This is the same relationship used to explain the mass defect in nuclear binding energy and the energy released in nuclear reactions.
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Glossary
Key Terms Explained
6 terms▸
Mass-energy equivalence ↗The principle, from Einstein's special relativity, that mass and energy are interchangeable — expressed by E = mc². A system's rest mass is a measure of the total energy it contains.
Rest energy ↗The energy an object has purely because of its mass, when it is at rest (not moving) relative to the observer. This is the E computed by E = mc² — it excludes any additional kinetic energy from motion.
Speed of light (c) ↗The exact value 299,792,458 meters per second, the speed at which light travels in a vacuum. It is a fixed constant by the SI definition of the meter, and its square (c²) is the huge conversion factor between mass and energy.
Joule (J) ↗The SI unit of energy. One joule is a relatively small amount of everyday energy (about the energy to lift a small apple one meter), which is why mass-energy conversions — even for tiny masses — produce results in the range of 10¹³–10¹⁷ joules.
TNT equivalent ↗A way of expressing a large amount of energy by comparing it to the energy released when detonating an equal quantity of TNT. One megaton (Mt) of TNT releases 4.184 × 10¹⁵ joules; one kiloton (kt) is one-thousandth of that.
Einstein ↗Albert Einstein derived E = mc² in 1905 as a consequence of special relativity, showing that mass is a concentrated form of energy — a relationship later confirmed experimentally in nuclear fission and fusion reactions.
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Scenarios
Real-World Examples
3 worked examples▸
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1 kilogram of mass
Mass → Energy
Mass 1 kg
1 kg × (299,792,458 m/s)² ≈ 8.99 × 10¹⁶ joules — about 25 billion kilowatt-hours, or roughly 21.5 megatons of TNT. This is why nuclear reactions, which convert only a tiny fraction of a percent of their mass into energy, still release such enormous amounts of it.
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1 gram of mass
Mass → Energy
Mass 0.001 kg
A single gram — about the mass of a paperclip — converts to roughly 8.99 × 10¹³ joules, equivalent to about 21.5 kilotons of TNT (comparable to a small nuclear weapon). This illustrates just how energy-dense mass is.
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Energy → Mass
Reverse calculation
Energy 1 × 10¹² J
One terajoule of energy (roughly a large power plant's output over a few minutes) has a mass equivalent of about 1.11 × 10⁻⁵ kg — just 11 milligrams. Everyday amounts of energy correspond to vanishingly small masses, which is why the mass-energy link is invisible in daily life.
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Reference
Cite This Calculator
APA & MLA▸
Use either format to cite this calculator in a paper, report, or resource list.
E = mc² is perhaps the most famous equation in physics: it states that mass and energy are two forms of the same underlying quantity. This calculator converts between them directly, using the same relationship that explains why nuclear reactions release so much more energy than chemical ones.
How the calculator works
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The calculator applies Einstein's mass-energy equivalence formula, E = mc², where c is the exact speed of light in a vacuum (299,792,458 m/s). On the Mass → Energy tab, entering a mass in kilograms multiplies it by c² to get the rest energy in joules, which is then also expressed in kilowatt-hours and in megatons (or kilotons) of TNT equivalent for intuition. The Energy → Mass tab rearranges the formula to m = E/c², solving for the mass equivalent of a given energy.
Why the numbers are so large
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The speed of light squared, c², is approximately 8.99 × 10¹⁶ m²/s² — an enormous conversion factor. That means even a single gram of matter, if fully converted to energy, would release about 21.5 kilotons of TNT equivalent — comparable to a small nuclear weapon. In practice, most energy sources (chemical combustion, even nuclear fission) convert only a minuscule fraction of their mass into energy; nuclear fission of uranium-235, for example, converts roughly 0.1% of the reacting mass into energy, and nuclear fusion in the sun converts about 0.7%.
Where this formula applies
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E = mc² describes an object's rest energy — the energy content due to mass alone, when the object is not moving relative to the observer. It does not include additional kinetic energy from motion; for objects moving at a significant fraction of the speed of light, the full relativistic energy formula (E² = (pc)² + (mc²)²) is needed instead. This calculator is best used for rest-mass/rest-energy conversions such as nuclear binding energy, particle physics, and back-of-the-envelope energy estimates — not for objects already moving near light speed.
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Questions
Frequently Asked Questions
6 questions▸
What is the formula for E=mc²?+
E = mc², where E is energy in joules, m is mass in kilograms, and c is the speed of light in a vacuum (299,792,458 m/s). Squaring c gives an enormous conversion factor of roughly 8.99 × 10¹⁶ m²/s², which is why converting even a small mass yields a huge amount of energy.
How much energy is in 1 gram of mass?+
About 8.99 × 10¹³ joules, which is roughly equivalent to 21.5 kilotons of TNT — in the range of a small nuclear weapon's yield. This is a theoretical maximum assuming 100% conversion of mass to energy, which real-world processes never achieve.
How do I find the mass equivalent of an energy?+
Use the Energy → Mass tab and enter the energy in joules; the calculator computes m = E/c². For example, a very large energy release still corresponds to a surprisingly small mass, since c² is such a large divisor.
What units does this calculator use?+
Mass is entered in kilograms and energy in joules. Results are also shown in kilowatt-hours (kWh) and in kilotons or megatons of TNT equivalent, since raw joule values for everyday masses are so large that they're easier to grasp in these more familiar units.
Why do nuclear reactions release so much energy?+
Nuclear reactions convert a small but non-negligible fraction of their reactants' mass directly into energy via E = mc², whereas chemical reactions (like burning fuel) only rearrange electron bonds and convert a far tinier fraction of mass. That's why a kilogram of nuclear fuel can release millions of times more energy than a kilogram of chemical fuel.
Is this the rest energy or the total relativistic energy?+
This calculator computes rest energy — the energy an object has due to its mass alone, at rest. An object moving at relativistic speeds also carries kinetic energy on top of this, described by the full relativistic energy-momentum relation, not by E = mc² alone.
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