What does E=mc² mean?

E is the rest energy of an object in joules, m is its rest mass in kilograms, and c is the speed of light in a vacuum (299,792,458 m/s). The equation shows that mass and energy are two forms of the same quantity; a small mass is equivalent to a very large amount of energy because c² ≈ 9×10¹⁶ J/kg.

Why is the energy so enormous even for a tiny mass?

The speed of light squared — about 8.99×10¹⁶ m²/s² — acts as the conversion factor. Multiplying even a milligram by that number produces terajoules. This is why nuclear reactions (which convert a small fraction of mass to energy) release far more energy per kilogram of fuel than chemical reactions.

How many joules is 1 atomic mass unit?

1 u = 1.66054×10⁻²⁷ kg, so E = 1.66054×10⁻²⁷ × (299,792,458)² ≈ 1.4924×10⁻¹⁰ J, which equals about 931.5 MeV. This is the standard nuclear-physics conversion factor.

Does this calculator account for kinetic energy?

No. E=mc² gives rest energy only — the energy of an object that is not moving. To include kinetic energy at relativistic speeds, use the full formula E_total = γmc², where γ is the Lorentz factor. The relativistic kinetic energy tool on this site handles that case.

What is a megaton of TNT in joules?

1 megaton of TNT is defined as exactly 4.184×10¹⁵ joules (4.184 petajoules). It is a convenient unit for expressing very large energy releases such as nuclear weapons or asteroid impacts.

Can I use this to calculate nuclear bomb yield?

The calculator shows the theoretical maximum energy if all mass were converted. In real fission or fusion devices, only a tiny fraction of the fuel mass (typically 0.05%–0.7%) is converted, so actual yield is much lower. The calculation is still useful for understanding theoretical upper bounds.

Mass-Energy E=mc² Calculator

Enter a mass in kg, g, lb, or atomic mass units to get its energy equivalent in joules, kilowatt-hours, electron-volts, and megatons of TNT via E=mc².

Mass Input

Mass (m)

Quick examples

Energy Equivalent (E = mc²)

Enter a mass above and click Calculate to see results.

Common Mass Reference

Object	Mass	E = mc² (J)
Electron	9.109×10⁻³¹ kg	8.187×10⁻¹⁴ J
Proton	1.673×10⁻²⁷ kg	1.503×10⁻¹⁰ J
1 atomic mass unit	1.661×10⁻²⁷ kg	1.492×10⁻¹⁰ J
1 microgram	1×10⁻⁹ kg	8.988×10⁷ J
1 gram	0.001 kg	8.988×10¹³ J
1 kilogram	1 kg	8.988×10¹⁶ J

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Summary

Einstein's equation E=mc² states that mass and energy are interchangeable: a mass m at rest contains an energy E equal to that mass multiplied by the square of the speed of light (c = 299,792,458 m/s). Even a tiny mass holds an enormous amount of energy — 1 gram is equivalent to roughly 90 terajoules, enough to power a city for several hours. This calculator converts any mass into its energy equivalent across six common units, and displays the rest energy of common reference masses for quick comparison.

How it works

Select the mass unit (kg, g, lb, or atomic mass unit u).
Enter the mass value — positive numbers only.
The calculator multiplies m (in kg) by c² = (299,792,458)² ≈ 8.9876×10¹⁶ m²/s².
Results are shown in joules, kilojoules, kilowatt-hours, electron-volts, and megatons of TNT.
A reference table shows the rest energy of common masses (1 electron, 1 proton, 1 g, 1 kg) for comparison.
Negative or zero mass returns an error; values are displayed in scientific notation when very large or very small.

Use cases

Physics students verifying E=mc² homework problems involving rest energy.
Nuclear engineers estimating the energy yield of fission or fusion reactions.
Science teachers demonstrating why even microgram masses hold extraordinary energy.
Researchers converting particle rest-mass energies between joules and electron-volts.
Science communicators illustrating how many cities a gram of matter could power.

Frequently Asked Questions

Last updated: 2026-06-15 · Reviewed by Nham Vu