Enter three of the initial amount, remaining amount, elapsed time and half-life to find the fourth, plus the decay constant.
Last updated: November 8, 2026
The exponential decay formula
The half-life (T) is the time it takes for half of a substance to decay. Each half-life halves what is left: • N = N₀ × (1/2)^(t / T) • T = t × ln 2 ÷ ln(N₀ / N) • t = T × log₂(N₀ / N) • Decay constant λ = ln 2 ÷ T, mean lifetime τ = T ÷ ln 2 Example: 100 g of a substance with a half-life of 5 years leaves 100 × 0.5² = 25 g after 10 years (two half-lives). The same formula works for radioactive isotopes, drugs in the body and anything else that decays exponentially. Enter the time and the half-life in the same unit.
Common questions about half-life
The time it takes for half of an amount to decay or be cleared from the body. It doesn't depend on how much you start with.
Other tools you may find useful
Any unit (g, mg, atoms, %).
Same time unit as the half-life.
Seconds, hours, years… same as the time.