Nuclear Fusion Energy Calculator Formula
Understand the math behind the nuclear fusion energy calculator. Each variable explained with a worked example.
Formulas Used
Mass Difference
mass_diff = mass_reactants - mass_productsEnergy Released
energy_mev = (mass_reactants - mass_products) * 931.494Energy per Nucleon
energy_per_nucleon = (mass_reactants - mass_products) * 931.494 / round(mass_reactants)Variables
| Variable | Description | Default |
|---|---|---|
mass_reactants | Total Mass of Reactants(u) | 5.0305 |
mass_products | Total Mass of Products(u) | 5.0116 |
How It Works
Nuclear Fusion Energy
Fusion of light nuclei releases energy because the products have higher binding energy per nucleon. The energy comes from the mass difference, just like fission.
Formula
E = delta_m × 931.494 MeV/u
The D-T fusion reaction (²H + ³H → ⁴He + n) releases 17.6 MeV. Per unit mass, fusion fuel releases about 4 times more energy than fission fuel, making it the ultimate energy source.
Worked Example
D-T fusion: D(2.0141) + T(3.0164) → He-4(4.0026) + n(1.0087) + energy.
- 01Reactant mass = 2.0141 + 3.0164 = 5.0305 u
- 02Product mass = 4.0026 + 1.0087 = 5.0113 u
- 03delta_m = 5.0305 - 5.0116 = 0.0189 u
- 04E = 0.0189 × 931.494 = 17.6 MeV
Frequently Asked Questions
Why is fusion so hard to achieve?
Both nuclei are positively charged and repel each other strongly. Overcoming this Coulomb barrier requires temperatures of 100 million °C or more. Containing this plasma is the central engineering challenge.
What is the most promising fusion reaction?
D-T (deuterium-tritium) has the lowest ignition temperature and highest cross section. D-D and D-He3 are harder but produce fewer neutrons. Proton-boron (p-B11) is aneutronic but requires much higher temperatures.
How much energy does 1 kg of D-T fuel produce?
About 3.4 × 10¹⁴ J (340 TJ), equivalent to about 80,000 tons of TNT. One gallon of seawater contains enough deuterium for the equivalent of 300 gallons of gasoline.
Ready to run the numbers?
Open Nuclear Fusion Energy Calculator