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

Name: Mass-Energy E=mc² Calculator
Availability: InStock
Author: Nham Vu

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

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.

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: 2026-07-01 · Reviewed by Nham Vu