E=mc² Calculator
Explore Einstein's mass-energy equivalence principle
Note: This equation shows the enormous energy contained in matter. 1kg of mass is equivalent to about 90 petajoules (the energy in 21 megatons of TNT).
Tip: Enter either mass or energy to calculate the other value. The speed of light (c) is 299,792,458 m/s.
Mass (m)
Energy (E)
Calculation Options
Mass-Energy Equivalence
Mass:
Energy:
Speed of Light (c):
0 kg
0 J
299,792,458 m/s
Equation Breakdown:
E = mc²
E = m × (299,792,458 m/s)²
E = 0 J
Understanding E=mc²
The Equation
- E = Energy (in joules)
- m = Mass (in kilograms)
- c = Speed of light in vacuum (299,792,458 m/s)
- Shows mass can be converted to energy and vice versa
Practical Implications
- Explains energy production in stars
- Basis for nuclear power and weapons
- Fundamental to particle physics
- Key component of special relativity
Energy Equivalence Examples
| Object | Mass | Energy Equivalent |
|---|---|---|
| Paperclip | 1 gram | ~90 terajoules (21 tons TNT) |
| Human (avg) | 70 kg | ~6.3 exajoules (1.5 gigatons TNT) |
| 1 liter water | 1 kg | ~90 petajoules (21 kilotons TNT) |
Note: These values represent total mass-energy conversion. Nuclear reactions typically convert only a small fraction (about 0.1-0.3%) of mass to energy.
Frequently Asked Questions
Why is c squared in the equation?
The c² term comes from the relativistic relationship between space and time. It serves as a conversion factor between mass and energy units, and its large magnitude (89,875,517,873,681,764 m²/s²) explains why small masses contain enormous energy.
Can we convert all mass to energy?
In practice, no. Complete conversion only happens when matter meets antimatter. Nuclear reactions convert about 0.1-0.3% of mass to energy, while chemical reactions convert far less (about 1 part per billion).
How accurate is E=mc²?
Extremely accurate. It has been confirmed by countless experiments and is fundamental to modern physics. The more complete form is E² = (mc²)² + (pc)², which reduces to E=mc² when momentum (p) is zero.
Why don't we notice this energy in everyday life?
The energy remains "locked" in the mass during chemical reactions. Only in nuclear reactions does a measurable fraction get released. The enormous scale of c² means everyday mass changes correspond to negligible energy changes.
How does this relate to nuclear power?
Nuclear power plants convert about 0.1% of nuclear fuel's mass to energy (vs 0.0000001% in chemical reactions). A single gram of matter can power a 100W bulb for ~30,000 years if fully converted.