Nuclear Fusion Energy Calculator Formula

Understand the math behind the nuclear fusion energy calculator. Each variable explained with a worked example.

Formulas Used

Energy Released

energy = 0.007 * hydrogen_mass * pow(299792458, 2)

Energy (megatons TNT)

energy_megatons = 0.007 * hydrogen_mass * pow(299792458, 2) / 4.184e15

Variables

VariableDescriptionDefault
hydrogen_massHydrogen Mass(kg)1

How It Works

Stellar Nuclear Fusion Energy

In the pp-chain and CNO cycle, four hydrogen nuclei fuse into one helium nucleus. The mass difference (0.7%) is converted to energy via E = mc².

Formula

E = 0.007 × m × c²

where m is the hydrogen mass consumed and c = 299 792 458 m/s.

The Sun converts about 600 million tonnes of hydrogen per second, releasing 3.8 × 10²⁶ W.

Worked Example

Energy from fusing 1 kg of hydrogen.

hydrogen_mass = 1
  1. 01E = 0.007 × 1 × (2.998e8)²
  2. 02= 0.007 × 8.988e16
  3. 03= 6.291e14 J
  4. 04≈ 150 kilotons of TNT equivalent.

Frequently Asked Questions

Why only 0.7% efficiency?

In hydrogen-to-helium fusion, 99.3% of the original mass remains as helium. Only the mass deficit (binding energy difference) is converted to energy.

How much hydrogen does the Sun burn per second?

About 620 million tonnes per second, of which about 4.3 million tonnes become energy.

How does fusion compare to fission?

Fission converts about 0.09% of mass to energy; fusion converts about 0.7%, making fusion roughly 8 times more energy-dense per unit mass.

Ready to run the numbers?

Open Nuclear Fusion Energy Calculator