Half-Life Calculator
Solve the radioactive decay equation for any unknown — remaining quantity, elapsed time, half-life, or initial amount.
How to use the Half-Life Calculator
- Enter your inputs into the Half-Life Calculator above.
- Results update instantly as you type — no submit button needed.
- Adjust any value to see how the result changes in real time.
The radioactive decay formula
N(t) = N₀ × (1/2)^(t/T) · · · or N(t) = N₀ × e^(−λt) where λ = ln(2)/T
N₀ is the initial quantity, T is the half-life, t is elapsed time, λ is the decay constant. After one half-life, half remains; after two, one-quarter; after n half-lives, (1/2)^n.
Worked example
Carbon-14 has half-life 5,730 years. A sample with 25% remaining: (1/2)^(t/5730) = 0.25 = (1/2)². So t = 2 × 5,730 = 11,460 years old. This is the principle behind radiocarbon dating.
Frequently asked questions
What is the decay constant λ?
λ = ln(2) / T ≈ 0.693 / T. It's the fractional decay rate per unit time. Larger λ means faster decay.
Does this apply to anything other than radioactivity?
Yes — any exponential decay process: drug pharmacokinetics, capacitor discharge, light absorption, population die-off in some models. Same math, different context.
Why does decay never quite reach zero?
Exponential decay is asymptotic — each half-life cuts the amount in half, theoretically forever. In practice, after ~10 half-lives, less than 0.1% remains and effectively rounds to zero.