Radioactive Decay Calculator
Find how much of a radioactive sample remains after a given time from its half-life, plus the decay constant.
How it works
N = N₀ × (1/2)^(t ÷ t½) · decay constant λ = ln(2) ÷ t½ · fraction remaining = (1/2)^(t ÷ t½)
Radioactive decay is exponential: each half-life the remaining amount is halved, so after n half-lives a fraction (1/2)ⁿ is left. The half-life and elapsed time only need to share the same unit — years, days or seconds — because the calculation depends on their ratio. The decay constant λ = ln(2)/t½ is the equivalent continuous rate, used in N = N₀e^(−λt).
Worked example
Carbon-14 has a half-life of 5730 years. After exactly one half-life (5730 years), a 100 g sample decays to 100 × (1/2)¹ = 50 g, with 50% remaining.
Sources: Half-life — Wikipedia
Frequently asked questions
What if the elapsed time is not a whole number of half-lives?
The formula handles fractions directly: raise 1/2 to the power (time ÷ half-life). For example 0.5 half-lives leaves (1/2)^0.5 ≈ 70.7% of the sample.
How is the decay constant related to the half-life?
λ = ln(2) ÷ t½ ≈ 0.693 ÷ t½. It is the fraction that decays per unit time in the continuous form N = N₀e^(−λt), which gives the same result as the halving formula.
Does this work for any amount unit?
Yes — grams, number of atoms or activity (becquerels) all decay by the same fraction, so you can enter whichever quantity you are tracking.
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