Half-Life Calculator
How much of a radioactive isotope, drug or first-order reactant remains after a time, from its half-life — with the decay constant and the number of half-lives elapsed.
What is left after so many half-lives.
How the half-life calculator works
First-order decay halves the amount every half-life: N = N₀ × (½)^(t ÷ t½), equivalently N₀ e^(−kt) with k = ln 2 ÷ t½. After one half-life 50% remains, after two 25%, after ten about 0.1%. The same arithmetic covers radioactive isotopes, drug elimination and any first-order reaction. Use the same time unit for the half-life and the elapsed time.
Formula: N = N₀ × 0.5^(t ÷ t½) · k = ln 2 ÷ t½
Worked examples
| Inputs | Amount remaining | Note |
|---|---|---|
| Carbon-14 (5,730 y) after 10,000 years | 29.8292 | 29.8% remains |
| Iodine-131 (8.02 days) after 30 days | 7.4809 | 7.5% remains |
| 200 mg of a drug with a 6-hour half-life after 24 h | 12.5 | 12.5 mg — four half-lives |
FAQFrequently asked questions
How many half-lives until it is "gone"?
It never quite is, but after 10 half-lives 0.1% remains, which most fields treat as negligible.
Does the starting amount change the half-life?
No — that is what makes first-order decay special: the fraction lost per unit time is constant whatever the amount.
How do I go from half-life to a rate constant?
k = ln 2 ÷ t½ = 0.693 ÷ t½, in reciprocal time units.
Is drug elimination really first-order?
For most drugs at therapeutic doses, yes; alcohol and a few others saturate the enzymes and eliminate at a constant rate instead (zero-order).
Where these figures come from
- IUPAC — Standard atomic weights (2021 conventional values) — the molar-mass table
- NIST — CODATA 2018 fundamental physical constants — Avogadro constant, gas constant, speed of light
- NIST Chemistry WebBook — thermochemical data
- Royal Society of Chemistry — the UK chemistry professional body
Last checked: September 2026. Atomic masses are the IUPAC conventional values; constants are CODATA 2018; equations are the standard textbook forms.