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Half-Life Calculator
Calculate radioactive decay or first-order reaction kinetics. Enter any three of the initial amount, remaining amount, time and half-life to find the fourth. You also get the decay constant, the number of half-lives, step-by-step working and a decay curve.
Fill in any three values and leave the one you want to find blank.
Half-life from a rate constant (any reaction order)
Half-life formulas
N = N₀ × (1/2)^(t / t½) N = N₀ × e^(−kt) k = ln 2 / t½ ≈ 0.693 / t½
t = t½ × ln(N₀/N) / ln 2 t½ = t × ln 2 / ln(N₀/N) mean lifetime τ = 1/k = t½ / ln 2
Radioactive decay and every first-order reaction follow the same law. The half-life is constant and does not depend on how much you start with. For other reaction orders the half-life changes as the reaction proceeds:
| Order | Integrated rate law | Half-life | Units of k |
|---|---|---|---|
| Zero | [A] = [A]₀ − kt | t½ = [A]₀ / 2k | M s⁻¹ |
| First | ln[A] = ln[A]₀ − kt | t½ = ln 2 / k | s⁻¹ |
| Second | 1/[A] = 1/[A]₀ + kt | t½ = 1 / (k[A]₀) | M⁻¹ s⁻¹ |
Remaining after n half-lives
| Half-lives | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 10 |
|---|---|---|---|---|---|---|---|---|
| % remaining | 50 | 25 | 12.5 | 6.25 | 3.125 | 1.5625 | 0.78125 | 0.0977 |
Common radioisotope half-lives
| Isotope | Half-life | Used for |
|---|---|---|
| Carbon-14 | 5,730 years | Radiocarbon dating |
| Iodine-131 | 8.02 days | Thyroid treatment |
| Technetium-99m | 6.01 hours | Medical imaging |
| Fluorine-18 | 109.7 minutes | PET scans |
| Cobalt-60 | 5.27 years | Radiotherapy, sterilisation |
| Strontium-90 | 28.8 years | Fission product |
| Caesium-137 | 30.1 years | Fission product |
| Radium-226 | 1,600 years | Historical radiotherapy |
| Uranium-238 | 4.47 billion years | Dating rocks |
| Potassium-40 | 1.25 billion years | K–Ar dating |
Values from IAEA/NNDC nuclear data, rounded.
Worked examples
How much I-131 is left?
100 g, t½ = 8.02 d, after 24.06 d: 24.06/8.02 = 3 half-lives, so 100 × (1/2)³
12.5 g remain
Radiocarbon age
A sample has 25% of its original C-14. ln(100/25)/ln 2 = 2 half-lives × 5,730 y
Age ≈ 11,460 years
Find the half-life
80 mg falls to 10 mg in 30 min. ln(8)/ln 2 = 3 half-lives in 30 min
t½ = 10 min
First-order rate constant
k = 1.5 × 10⁻³ s⁻¹: t½ = 0.693 / 1.5 × 10⁻³
t½ = 462 s (7.7 min)
Drawing structures for your notes? MolDraw is a free online chemical structure editor for molecules, reactions and lab diagrams.
Open MolDraw editorFrequently asked questions
How do you calculate half-life?
Use t½ = t × ln 2 / ln(N₀/N), where N₀ is the starting amount and N is the amount left after time t. If you know the first-order rate constant, t½ = ln 2 / k ≈ 0.693 / k.
How do you calculate how much remains after a given time?
N = N₀ × (1/2)^(t/t½). Divide the time by the half-life to get the number of half-lives, then halve the amount that many times. For example, 3 half-lives leave 12.5%.
What is the relationship between half-life and the rate constant?
For first-order processes, including radioactive decay, k = ln 2 / t½ and t½ = 0.693 / k. The decay constant λ is the same quantity as k.
Does half-life depend on the starting amount?
Not for first-order reactions or radioactive decay. For zero-order reactions t½ = [A]₀/2k, and for second-order reactions t½ = 1/(k[A]₀), so it does depend on the starting concentration.
How long until only 1% remains?
About 6.64 half-lives, because ln(100)/ln 2 = 6.64. After 10 half-lives about 0.1% remains.
Can I use this for drug or caffeine half-life?
Yes. Most drugs are eliminated by first-order kinetics, so the same formula applies. Caffeine has a half-life of roughly 5 hours in healthy adults. This tool is for education, not medical advice.