Radioactive Decay Calculator

How it works

1. 1Enter the initial quantity N₀, the half-life t½, and the elapsed time t — all in whatever unit you choose (seconds, years, etc.).
2. 2The calculator applies N = N₀·(½)^(t ÷ t½) for the remaining quantity and derives λ = ln2 ÷ t½ for the decay constant.
3. 3The decay curve plots the remaining quantity from t = 0 out to five half-lives for a clear visual of the decline.

Use cases

• Nuclear medicine — how much of a radioactive tracer remains after a given time.
• Archaeology — applying carbon-14 decay (t½ ≈ 5,730 years) to estimate remaining C-14.
• Industrial radiography — confirming a source is strong enough, or scheduling safe disposal.

Frequently asked questions

What formula does this calculator use?

The decay law N = N₀·(½)^(t ÷ t½), equivalent to N = N₀·e^(−λt) where λ = ln2 ÷ t½ ≈ 0.693 ÷ t½. Both describe the same exponential decrease; the half-life form is often more intuitive.

What units should I use for half-life and time?

Any unit works as long as half-life and elapsed time share it. With t½ = 10 years and t = 30 years you get three half-lives. Mixing units (years and seconds) gives a wrong result, so always match them.

Can you walk through a worked example?

Start with N₀ = 100 and t½ = 10 years. After 10 years: 100 × (½)¹ = 50. After 20 years: 25. After 30 years: 12.5 remain (87.5% decayed). The decay constant is λ = ln2 ÷ 10 ≈ 0.0693 per year.