Mass-Energy Equivalence (E = mc²)
Einstein's E = mc² shows that mass and energy are interchangeable.
Learn the most famous physics formula with worked examples.
The Formula
Mass-energy equivalence reveals that mass and energy are two forms of the same thing. A small amount of mass can be converted into an enormous amount of energy because the speed of light squared is a huge number.
Albert Einstein published this relationship in 1905 as a consequence of special relativity. It is arguably the most famous equation in all of science. The formula explains the energy source of nuclear reactions, both fission (splitting atoms) and fusion (combining atoms).
The speed of light c equals approximately 3 × 10⁸ m/s. Therefore c² is about 9 × 10¹⁶ m²/s², which means even 1 kilogram of mass contains 9 × 10¹⁶ joules of energy. That is roughly equivalent to the energy released by 21 megatons of TNT.
Variables
| Symbol | Meaning |
|---|---|
| E | Energy (joules, J) |
| m | Mass (kilograms, kg) |
| c | Speed of light in vacuum (3 × 10⁸ m/s) |
Example 1
In nuclear fission of uranium-235, about 0.1% of the mass is converted to energy. If we start with 1 kg of uranium, how much energy is released?
Mass converted: m = 0.001 × 1 = 0.001 kg
Apply the formula: E = mc² = 0.001 × (3 × 10⁸)²
E = 0.001 × 9 × 10¹⁶
E = 9 × 10¹³ J (about 21.5 kilotons of TNT equivalent)
Example 2
An electron (mass 9.11 × 10⁻³¹ kg) and a positron annihilate completely. What energy is released?
Total mass: m = 2 × 9.11 × 10⁻³¹ = 1.822 × 10⁻³⁰ kg
Apply: E = mc² = 1.822 × 10⁻³⁰ × (3 × 10⁸)²
E = 1.822 × 10⁻³⁰ × 9 × 10¹⁶
E = 1.64 × 10⁻¹³ J = 1.022 MeV (released as two gamma ray photons)
When to Use It
Use E = mc² to calculate the energy equivalent of mass or the mass equivalent of energy.
- Calculating energy released in nuclear fission and fusion reactions
- Finding the rest energy of subatomic particles
- Understanding the energy source of stars
- Computing the mass defect in nuclear binding energy problems