Nuclear Fission Energy Calculator Formula
Understand the math behind the nuclear fission energy calculator. Each variable explained with a worked example.
Formulas Used
Mass Difference
mass_diff = mass_reactants - mass_productsEnergy Released per Fission
energy_mev = (mass_reactants - mass_products) * 931.494Energy per Fission
energy_j = (mass_reactants - mass_products) * 931.494 * 1.602e-13Energy per kg of Fuel
energy_per_kg = (mass_reactants - mass_products) * 931.494 * 1.602e-13 * 6.022e23 / (mass_reactants / 1000)Variables
| Variable | Description | Default |
|---|---|---|
mass_reactants | Total Mass of Reactants(u) | 236.0526 |
mass_products | Total Mass of Products(u) | 235.8295 |
How It Works
Nuclear Fission Energy
Fission releases energy because the products have higher binding energy per nucleon than the parent nucleus. The energy comes from the mass difference between reactants and products.
Formula
E = delta_m × 931.494 MeV/u
A typical U-235 fission releases about 200 MeV, which is roughly 80 million times more energy per reaction than a typical chemical reaction (~2.5 eV for TNT).
Worked Example
U-236 fissions: total reactant mass 236.0526 u, total product mass 235.8295 u.
- 01delta_m = 236.0526 - 235.8295 = 0.2231 u
- 02E = 0.2231 × 931.494 = 207.8 MeV
- 03E = 207.8 × 1.602 × 10⁻¹³ = 3.33 × 10⁻¹¹ J per fission
Frequently Asked Questions
How much energy does 1 kg of U-235 produce?
About 8.2 × 10¹³ J (82 TJ), equivalent to about 20,000 tons of TNT. This is roughly 2 million times the energy content of coal per unit mass.
Where does the fission energy go?
About 85% goes to kinetic energy of fission fragments, 2.5% to prompt neutrons, 2.5% to prompt gamma rays, 3% to beta decay energy, 3% to delayed gamma rays, and 4% to antineutrinos (lost).
What about energy from fusion vs fission?
Per reaction, fission releases more energy (~200 MeV vs ~17.6 MeV for D-T fusion). But per unit mass, fusion releases more because the fuel is much lighter. Fusion fuel has about 4x the energy density.
Ready to run the numbers?
Open Nuclear Fission Energy Calculator