Half-Life Decay Calculator
Calculate the remaining quantity of a radioactive substance after a given time using the half-life decay formula.
any unit (g, kg, mol, etc.)
time units
same time units as t½
Results will appear here.
Formulas Used
Remaining Quantity: N = N₀ × (½)t / t½ = N₀ × e−λt
Initial Quantity: N₀ = N ÷ (½)t / t½
Elapsed Time: t = t½ × log₂(N₀ / N) = t½ × ln(N₀ / N) / ln(2)
Half-Life: t½ = t × ln(2) / ln(N₀ / N)
Decay Constant: λ = ln(2) / t½ ≈ 0.693147 / t½
Number of Half-Lives: n = t / t½
Assumptions & References
- Assumes first-order (exponential) radioactive decay — the standard model for all radioactive isotopes.
- The half-life (t½) is constant and independent of temperature, pressure, or chemical state.
- All time values must use the same units (seconds, years, etc.).
- Quantity units are arbitrary and consistent (grams, moles, number of atoms, etc.).
- Remaining quantity N must be ≤ initial quantity N₀ (decay only, no production).
- Formula source: Rutherford–Soddy exponential decay law (1902); see also NIST Radioactive Decay Data.
- Example: Carbon-14 has a half-life of ~5,730 years, used in radiocarbon dating (Libby, 1949).