Library / Foundations: Physics / FPH-39
Foundations: Physics
Mass–energy equivalence
Energy released when a mass defect is converted.
- Ref
- FPH-39
- Rev
- v1
- Field
- Foundations: Physics
- Result
- ΔE [TJ]
A nuclear mass defect in kg gives a binding energy in J. c = 2.998×10⁸ m/s.
A tiny amount of mass corresponds to an enormous amount of energy, because c² is huge.
Calculator
TJ
g
- TNT equivalent21.48 kt
- Energy in GWh24.97 GWh
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
Energy (TJ) current value 89.88 TJ
ΔmMass convertedKey driver
0.089989,900
- Converting just one gram of matter to energy releases about 21 kilotons of TNT.
- In real fission and fusion only a small fraction of a per cent of mass is converted.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (TJ) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Δm Mass converted | 0.001 to 1,000 g | 0.08988 | 89,880 | 89,880 | +10% | +10 % |
Sweep of Mass converted
| Mass converted (g) | Energy (TJ) |
|---|---|
| 0.001 | 0.08988 |
| 0.005623 | 0.5054 |
| 0.03162 | 2.842 |
| 0.1778 | 15.98 |
| 1 | 89.88 |
| 5.623 | 505.4 |
| 31.62 | 2,842 |
| 177.8 | 15,980 |
| 1,000 | 89,880 |
Sweep one variable
Energy (TJ)Hover, touch, or use the arrow keys on the chart
Variables and how each one contributes
ΔE
Energy
What the equation gives you. Everything else feeds it.
Δm
Mass converted
Mass converted to energy. Directly proportional.
Worked example with the values above
- Mass: 1 g = 0.001 kg.
- c² = 8.988×1016 m²/s².
- ΔE = 89.88 TJ.
Assumptions and limits
- Mass fully converted (idealised).
- Rest-mass energy only.
Common mistakes
- Using grams without converting to kg.
- Forgetting to square c.
Statistics and uncertainty
Mass defects are tiny differences between large masses, so they must be measured very precisely to give a reliable energy.
Where it is used
- Nuclear binding energy and yield estimates.
- Energy scales of nuclear processes.
Maths you need
- Mass and energy: kg and J
- Powers of ten: c² ≈ 9×10¹⁶