Half-Life Calculator
Work out how much of a radioactive sample is left, how long it takes, or what its half-life is — with every step of the working, a decay curve, carbon-14 dating and conversions between grams, becquerels and atoms.
At a glance
- Solves N = N₀ × (½)^(t ÷ T½) for any one of the four: the amount left, the starting amount, the time or the half-life — and accepts a decay constant λ or a mean life τ instead of the half-life.
- Shows the working step by step, a decay curve with a mark at every half-life, and a table of the amount after each of the first ten half-lives.
- Half-lives of 67 isotopes — carbon-14, iodine-131, technetium-99m, uranium-238 and more — with their uncertainties, from NUBASE2020, the international evaluation published by the IAEA. Carbon-14’s half-life there is 5,700 ± 30 years.
- Carbon-14 dating gives both the conventional radiocarbon age that laboratories report (with Libby’s half-life of 5,568 years, by international convention) and the age with the real half-life.
- Converts between mass, activity, atoms and moles for any of the isotopes, with atomic masses from AME2020: one gram of radium-226 is 0.989 curie.
- Works with numbers far beyond a calculator’s range by keeping their logarithms, so it can tell you that 10⁻⁶⁷⁴⁵¹ of a sample is left rather than 0.
Step by step
How to calculate half-life problems
- 1
Choose what to find
Pick Amount left, Starting amount, Time or Half-life.
- 2
Pick an isotope (optional)
Choose one from the list, such as C-14 or I-131, to fill in its half-life — or type your own.
- 3
Enter the other values
Use the same unit for both amounts (grams, atoms, becquerels or %). The time and half-life can use different units.
- 4
Read the answer and the working
The answer appears at once, with the fraction left, half-lives passed, decay constant and mean life, then the working step by step.
- 5
Check with the curve and table
The decay curve marks your point, and the table lists the amount after each half-life.
Features
Everything you need, nothing you don’t
Solve for anything
Choose what to find and fill in the rest. Units can differ: give the time in days and the half-life in hours, and the tool converts.
Working you can copy
Every answer comes with the formula, the numbers put into it and each step to the result — the way a teacher would want it written.
Real isotope data
Pick an isotope and its half-life, uncertainty, decay mode, daughter and everyday use appear, all from the current international evaluation.
Carbon dating done properly
See the radiocarbon age a laboratory would report and the age with the true half-life, and why the two differ.
Activity and mass
How many becquerels is a microgram of iodine-131? How many atoms in 1 GBq of technetium-99m? Convert in either direction, with specific activity.
Free and private
Everything is worked out in your browser. No sign-up, and your last inputs are remembered on this device only.
The half-life formulas
| To find | Formula |
|---|---|
| Amount left | N = N₀ × (½)^(t ÷ T½) |
| Starting amount | N₀ = N × 2^(t ÷ T½) |
| Time passed | t = T½ × log₂(N₀ ÷ N) |
| Half-life | T½ = t × ln 2 ÷ ln(N₀ ÷ N) |
| Decay constant | λ = ln 2 ÷ T½ ≈ 0.693 ÷ T½ |
| Mean life | τ = 1 ÷ λ = T½ ÷ ln 2 ≈ 1.443 × T½ |
| Activity | A = λ × N |
A worked example
Iodine-131 has a half-life of 8.0249 days. How much of a 400 MBq dose is left after 24 days? The time is 24 ÷ 8.0249 = 2.991 half-lives, so the amount left is 400 × (½)^2.991 = 50.3 MBq — just over an eighth, because three half-lives would take 24.07 days.
And how long until only 1 % is left? t = 8.0249 × log₂(100) = 8.0249 × 6.644 = 53.3 days. A rule of thumb follows from this: after 7 half-lives less than 1 % remains, and after 10 less than 0.1 %.
Half-lives of common isotopes
| Isotope | Half-life (NUBASE2020) | Known for |
|---|---|---|
| Fluorine-18 | 109.734 minutes | PET scans |
| Technetium-99m | 6.0066 hours | medical imaging |
| Iodine-131 | 8.0249 days | thyroid treatment |
| Radon-222 | 3.8215 days | radon in homes |
| Cobalt-60 | 5.2714 years | radiotherapy |
| Caesium-137 | 30.04 years | fallout |
| Carbon-14 | 5,700 years | radiocarbon dating |
| Uranium-238 | 4.463 billion years | dating the oldest rocks |
FAQ
Frequently asked questions
What is a half-life?
How do I calculate the half-life from two measurements?
T½ = t × ln 2 ÷ ln(N₀ ÷ N). For example, if a count rate falls from 800 to 100 in 15 hours, N₀ ÷ N = 8 = 2³, so three half-lives passed and the half-life is 5 hours. Choose Half-life in the calculator to get the working.What is the difference between half-life, decay constant and mean life?
Why do radiocarbon labs use 5,568 years instead of 5,700?
Does a sample ever decay completely?
Can I use this for medicines, caffeine or other exponential decay?
Where do the half-lives come from?
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