Half-Life Calculator
Anything decaying at a constant rate loses half of what is left in each equal interval. This shows how much remains after a given time, how many half-lives have passed, and the decay constant behind it.
| Starting amount | g |
| Half-life | years |
| Elapsed time | years |
Result
Your result will appear here.
How it works
Radioactive decay and many chemical or biological eliminations follow first-order kinetics: the rate of loss is proportional to how much is present. That produces a halving pattern — after one half-life half remains, after two a quarter, after three an eighth — rather than a straight-line decline.
The result also reports the decay constant λ, which is the probability per unit time that any one atom or molecule decays. It is the same information as the half-life, expressed differently, and it is what appears in equations for mixtures and dosing.
Formula
Time and half-life must be in the same unit; the calculator does not convert between them.
- Remaining = starting amount × (1/2)time ÷ half-life
- Remaining = starting amount × e−λt, where λ = ln 2 ÷ half-life
- Half-lives elapsed = time ÷ half-life
- Mean lifetime = 1 ÷ λ = half-life ÷ ln 2
Worked example
100 g of a substance with a 5.27-year half-life (cobalt-60) after 10 years: 10 ÷ 5.27 = 1.898 half-lives, so 100 × 0.51.898 = 26.8 g remains — about 27% of the original, with λ = 0.1315 per year.
Assumptions
The substance decays by a single pathway with a constant half-life, and nothing is being produced or added during the period. Real samples may contain a parent that decays into a daughter which is itself radioactive, and biological half-lives change with dose, organ and health. Results assume a large number of atoms, where the statistical average is reliable.
Reading the result
Half-life is not the time until everything is gone. Because each interval only halves the remainder, a small fraction persists for a very long time: about 1% after 6.64 half-lives, and one part per million after nearly 20. For drugs, effect usually fades well before the amount does, and steady state on repeated dosing is reached in roughly four to five half-lives.
For general information only. Radiation safety and clinical dosing decisions require qualified advice.
How to use the Half-Life Calculator
It takes a few seconds, and every figure is calculated in your browser.
- Enter the starting amount.
- Enter the half-life.
- Enter the elapsed time.
- Press Calculate — the result appears in the dark panel beside the form.
- Use Copy, CSV, Share or Print under the result if you want to keep it.
Half-Life Calculator — frequently asked questions
What formula does the Half-Life Calculator use?
Time and half-life must be in the same unit; the calculator does not convert between them. Remaining = starting amount × (1/2) time ÷ half-life Remaining = starting amount × e −λt, where λ = ln 2 ÷ half-life Half-lives elapsed = time ÷ half-life Mean lifetime = 1 ÷ λ = half-life ÷ ln 2
How does the Half-Life Calculator work?
Radioactive decay and many chemical or biological eliminations follow first-order kinetics: the rate of loss is proportional to how much is present. That produces a halving pattern — after one half-life half remains, after two a quarter, after three an eighth — rather than a straight-line decline. The result also reports the decay constant λ, which is the probability per unit time that any one atom or molecule decays.
What assumptions and limitations should I know about?
The substance decays by a single pathway with a constant half-life, and nothing is being produced or added during the period. Real samples may contain a parent that decays into a daughter which is itself radioactive, and biological half-lives change with dose, organ and health. Results assume a large number of atoms, where the statistical average is reliable.
Can you walk through a worked example?
100 g of a substance with a 5.27-year half-life (cobalt-60) after 10 years: 10 ÷ 5.27 = 1.898 half-lives, so 100 × 0.5 1.898 = 26.8 g remains — about 27% of the original, with λ = 0.1315 per year.
Last updated 10 November 2026 · Formula, worked example and assumptions are documented above, and every result is calculated in your browser.