Half-Life Calculator
Exponential decay, solved three ways — with the formula shown step by step and a decay chart.
Solve for the quantity left after time t.
Dashed lines mark each half-life — watch the quantity halve at every one. The gold dot is your answer.
How to use the half-life calculator
- Pick what to solve for. Remaining quantity, elapsed time, or the half-life itself — the labels update to match.
- Enter the three known values. Initial quantity, and two of: remaining, half-life, elapsed time.
- Press Calculate. You get the answer, the formula with your values substituted in, and a decay chart with half-life markers.
- Read the chart. The dashed lines show where each half-life falls — the gold dot marks your exact point on the curve.
Frequently asked questions
What is the half-life formula?
N = N₀·(1/2)^(t/T): after each half-life T, half the quantity remains. After t/T half-lives, the fraction left is (1/2) raised to that count.
How do you find elapsed time from decay?
Solve the decay law for t: t = T·log₂(N₀/N). It counts how many half-lives it takes to fall from N₀ to N, then multiplies by T.
What does one half-life do?
It halves the quantity — whatever you have, one half-life later you have exactly half. Two half-lives leave a quarter, three leave an eighth.
Can the remaining quantity exceed the initial quantity?
No — that would be growth, not decay. If your remaining amount is larger, either the initial value is wrong or you need a growth model instead.
Does the quantity ever reach zero?
Mathematically, never: each half-life halves what is left, so the curve approaches zero but only reaches it after infinite time.
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