Radioactive Half-Life Calculator
For physics students grinding through nuclear-decay problem sets — the ones where the textbook gives you three numbers and asks for the fourth, and re-deriving T = t·ln2/ln(N₀/N) from the exponential law by hand is where the sign errors happen. This tool calculates remaining quantity, elapsed time, or half-life using the exponential decay law N = N₀·(1/2)t/T.
Enter any three values below; the tool will solve for the blank field.
Disclaimer: results are estimates for educational and preliminary use.
How to Use This Half-Life Calculator
- Pick the unit you're working in (seconds → years) from the time dropdown so T and t stay consistent.
- Type the three values your problem gives you — for example N₀ = 80.0 g, T = 5.27 y (cobalt-60), t = 15.8 y.
- Leave the unknown field empty; the solver labels it and computes live as you type.
- Read the answer plus λ, percent remaining, and half-lives elapsed from the results strip.
- Hit Copy Results to paste the worked values and formula into your lab notebook or homework.
FAQ
Q: How do I find the half-life if I know how much is left after a certain time?
A: Rearrange the decay law to T = t·ln2 / ln(N₀/N) — e.g. 80.0 g decaying to 10.0 g in 15.8 years gives T = 15.8 × 0.6931 / ln(8) ≈ 5.27 years, the textbook value for cobalt-60.
Q: What is the decay constant and how does it relate to half-life?
A: λ = ln2 / T ≈ 0.693/T, in reciprocal time units — a 5.27-year half-life gives λ ≈ 0.1315 y⁻¹, and N = N₀·e^(−λt) is the same law as N = N₀·(1/2)^(t/T).
Q: Why does the calculator say "no decay" when I solve for time?
A: Because ln(N₀/N) is zero or negative whenever N ≥ N₀, which means no net decay occurred — usually a swapped N₀ and N, or a measurement taken before the sample decayed.
Q: How many half-lives until less than 1% of a sample remains?
A: Seven — log₂(100) ≈ 6.64, so 7 half-lives leaves (1/2)⁷ = 0.78% of the original activity; if your problem then moves on to a gas produced by the decay, run the numbers through our Ideal & Combined Gas Laws Calculator.