Nuclear Science Calculators
Free nuclear physics calculators: radioactive decay, half-life, binding energy, radiation dose, and fission energy. All formulas shown with worked examples.
Nuclear Science Calculators - Radioactivity, Binding Energy, and Fission
Nuclear physics governs the energy locked inside atomic nuclei - from the slow decay of a radioactive isotope to the enormous energy released in fission. These calculators cover the five core quantitative topics in nuclear science: radioactive decay kinetics, half-life determination, nuclear binding energy, radiation dose assessment, and fission Q-value estimation. Every page shows the governing equation, defines all variables with SI units, cites the relevant physical constants, and walks through worked examples with real isotopes.
Five Nuclear Physics Calculators
What These Calculators Cover
The Radioactive Decay Calculator applies N(t) = N₀ · e^(−λt) to find the remaining number of nuclei (or remaining activity) after any elapsed time, given either the decay constant λ or the half-life t½. It also returns the fraction decayed and the activity in becquerels.
The Half-Life Calculator converts between the three equivalent measures of decay rate: half-life (t½), decay constant (λ = ln2/t½), and mean lifetime (τ = 1/λ). Enter any one to get the other two.
The Nuclear Binding Energy Calculator computes mass defect (Δm) from proton count Z, neutron count N, and atomic mass number A, then converts to binding energy via E = Δm · c² (Einstein’s mass-energy equivalence), giving total binding energy in MeV and binding energy per nucleon - the key stability indicator.
The Radiation Dose Calculator converts absorbed dose (gray, Gy) to equivalent dose (sievert, Sv) using radiation weighting factors (wR) per ICRP Publication 103, and further to effective dose using tissue weighting factors. Covers alpha, beta, gamma/X-ray, neutron, and proton radiation.
The Nuclear Fission Energy Calculator computes the Q-value of a fission reaction from reactant and product atomic masses, converting the mass defect to energy in MeV and joules, and scaling to energy released per gram and per kilogram of fissile material.
Who Uses These Calculators
Students taking nuclear physics at the undergraduate or postgraduate level use these for problem-set verification and exam preparation. NEET and JEE aspirants studying modern physics rely on the radioactive decay and binding energy calculators - both are high-weightage topics. Medical physicists and radiographers use the radiation dose calculator to cross-check dose estimates. Nuclear engineering students use the fission energy calculator when studying reactor physics and fuel cycle economics.
Frequently Asked Questions
What is radioactive decay and how is it calculated?
Radioactive decay is the spontaneous transformation of an unstable nucleus into a more stable one, emitting radiation in the process. The rate of decay follows first-order kinetics: N(t) = N₀ · e^(−λt), where λ is the decay constant. The Radioactive Decay Calculator applies this equation directly.
How is nuclear binding energy related to nuclear stability?
Binding energy per nucleon is the most direct measure of nuclear stability. The higher the binding energy per nucleon, the more energy is required to disassemble the nucleus, and therefore the more stable it is. Iron-56 has the highest binding energy per nucleon (~8.79 MeV) and is the most stable nucleus. The Nuclear Binding Energy Calculator computes this for any nuclide.
What is the difference between gray (Gy) and sievert (Sv)?
Gray measures absorbed dose - the energy deposited per unit mass of tissue (1 Gy = 1 J/kg), regardless of radiation type. Sievert measures equivalent dose, which weights the gray by a radiation weighting factor (wR) that accounts for the biological damage potential of the radiation type. See the Radiation Dose Calculator for full wR tables.
How much energy is released in uranium-235 fission?
A single U-235 fission event releases approximately 200 MeV (3.2 × 10⁻¹¹ J). Per gram of U-235, this translates to roughly 8.2 × 10¹⁰ J - about 20,000 tonnes of TNT equivalent per kilogram. Use the Nuclear Fission Energy Calculator to compute Q-values for specific reactions.