Model exponential decay with this free half life decay calculator. It solves for the amount remaining, elapsed time, or the half-life itself, and shows the fraction left, decay constant and mean lifetime.
Use any consistent time unit (seconds, years…) – keep time and half-life in the same unit. Amount can be mass, atoms, activity or a percentage; only the ratio matters.
Decay follows N = N0 x (½)^(t / T½). The decay constant is λ = ln2 / T½, and the mean lifetime is τ = 1 / λ = T½ / ln2. After each half-life, half of what remains decays.
How the Half-Life Decay Calculator Works
Half-life describes how long it takes for half of a decaying quantity — radioactive atoms, a drug in the bloodstream, or anything that decays exponentially — to disappear. The calculator solves for the remaining amount, the elapsed time, or the half-life itself, depending on which two values you provide.
Formula: N = N0 × (1/2)^(t ÷ T½), where N0 is the initial amount, N is the amount remaining, t is elapsed time, and T½ is the half-life, both in the same time unit. The decay constant is λ = ln2 ÷ T½, and the mean lifetime is τ = 1 ÷ λ = T½ ÷ ln2.
- N0 (Initial amount) — the starting quantity entered in the Initial amount field
- N (Remaining amount) — the quantity left after time t, entered or computed in the Remaining amount field
- t (Elapsed time) — the time that has passed, entered in the Elapsed time field, in any consistent unit
- T½ (Half-life) — the time it takes for half the quantity to decay, entered in the Half-life field, in the same unit as t
Example Scenarios
| Initial Amount (N0) | Half-Life (T½) | Elapsed Time (t) | Remaining Amount (N) |
|---|---|---|---|
| 100 | 2 | 4 | 25 |
| 200 | 5 | 10 | 50 |
| 80 | 3 | 3 | 40 |
| 1000 | 10 | 30 | 125 |
| 50 | 6 | 18 | 6.25 |
Getting Reliable Answers from a Half Life Decay Calculator
The maths behind a half life decay calculator is simple, so errors usually come from the setup. Keep time units consistent: if the half-life is in years, the elapsed time must be in years too. Mixing hours and days is the most common reason a result looks absurd.
As a check, after 5 half-lives about 3% remains (1/32), and after 10 half-lives roughly 0.1% (1/1024). If your half life decay calculator says far more or less is left, recheck the inputs. The same fraction applies to mass, atom count and activity, so any consistent unit works.
- Radioactive decay is statistical. A half life decay calculator describes large samples well but cannot say when one atom will decay.
- Medicine half-lives are averages for a typical adult and vary with age, kidney and liver function, and other drugs, so use a half life decay calculator for learning, never for dosing, and ask a pharmacist about your own medication.
For the derivation linking half-life, decay constant and mean lifetime, the half-life article on Wikipedia is a clear starting point before returning to the half life decay calculator.
Half-Life Decay Calculator FAQ
What time unit should I use for t and the half-life?
Any unit works — seconds, days, years — as long as you use the exact same unit for both elapsed time and half-life. The calculator only cares about the ratio t / T½, so mixing units, like years for one and days for the other, will give a wrong result.Can I use this for things other than radioactive decay?
Yes. The same N = N0 × (1/2)^(t/T½) formula applies to anything that decays exponentially by halving over a fixed interval, including drug elimination from the bloodstream, capacitor discharge, or population decline modeled as half-life decay.What’s the difference between half-life and mean lifetime?
Half-life is the time for exactly half a quantity to decay, while mean lifetime (τ) is the average time a single particle or unit survives before decaying. Mean lifetime is always longer than half-life, related by τ = T½ ÷ ln2, about 1.44 times as long.How do I find the half-life if I know the starting and remaining amounts?
Switch the Solve for toggle to Half-life, then enter the initial amount, remaining amount, and elapsed time. The calculator rearranges the decay formula to solve for T½ directly.Why does the amount never quite reach zero?
Exponential decay approaches zero but mathematically never reaches it, since each half-life only removes half of whatever remains. In practice, physical quantities eventually become effectively negligible once only a handful of atoms or molecules remain.What does the decay constant λ actually represent?
The decay constant is the fraction of the remaining quantity that decays per unit time in continuous exponential decay — it’s related to half-life by λ = ln2 ÷ T½, and a larger λ means faster decay and a shorter half-life.Related Calculators
Since half-life decay is an exponential calculation, the exponent calculator and scientific notation converter are useful for working with the very large or very small numbers involved. If you’re using half-life alongside other physics calculations, the light year calculator covers another common science conversion.