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Half-Life Calculator
Half-life, decay constant, mean lifetime and remaining amount.
Time and half-life must use the same unit — seconds, years, whatever you like. The arithmetic does not care which, only that they match.
Decay over time
| Half-lives | Time | Remaining | % left |
|---|
Common half-lives
| Isotope | Half-life | Used for |
|---|---|---|
| Carbon-14 | 5,730 years | Radiocarbon dating |
| Uranium-238 | 4.47 billion years | Dating rocks and the Earth |
| Potassium-40 | 1.25 billion years | Potassium-argon dating |
| Iodine-131 | 8.02 days | Thyroid treatment and imaging |
| Technetium-99m | 6.01 hours | Medical imaging |
| Caesium-137 | 30.17 years | Fallout and contamination studies |
| Radon-222 | 3.82 days | Indoor air quality |
| Plutonium-239 | 24,110 years | Nuclear waste management |
Remaining quantity
—
Derived values
Decay constant (λ)—
Mean lifetime (τ)—
Half-lives elapsed—
Fraction remaining—
—
Amount that has decayed away
Half-life is independent of the starting quantity — one gram and one tonne of the same isotope halve in the same time. The same exponential law governs drug elimination and capacitor discharge, so the calculator is not limited to radioactivity.
Quick Tool Overview
The Half-Life Calculator solves exponential decay in any direction. Give any three of initial quantity, remaining quantity, elapsed time and half-life, and it finds the fourth, along with the decay constant and mean lifetime.
- What it does
- Solves for any missing value in an exponential decay
- You give it
- Any three of initial, remaining, time and half-life
- You get back
- The fourth value plus decay constant and mean lifetime
- Best for
- Physics and chemistry problems, and dating calculations
About the Half-Life Calculator
Solve exponential decay problems in whichever direction you need. Give any three of initial quantity, remaining quantity, elapsed time and half-life, and the fourth is calculated, along with the decay constant and mean lifetime.
Half-life is the time for a quantity to fall to half its value, and the reason it is such a useful description is that it does not depend on how much you started with — one gram and one tonne of the same isotope both halve in the same time. The same arithmetic covers a good deal more than radioactivity: drug elimination, capacitor discharge and radiocarbon dating all follow the identical exponential law, and a table of common isotopes is included for reference.
Key features of the Half-Life Calculator
Solves in any direction
Remaining amount, elapsed time, half-life or starting quantity — whichever you leave out.
Decay constant and mean lifetime
Both derived figures are shown, since problems often ask for one of them rather than the half-life itself.
Common isotopes listed
Carbon-14, uranium-238, iodine-131 and others, so you have a reference value to hand.
Works beyond radioactivity
The page notes that drug elimination and capacitor discharge follow the identical law.
Units are yours
Any consistent time unit works — the arithmetic does not care whether you use seconds or millennia.
How to use the Half-Life Calculator
-
1
Choose what to solve for
Remaining amount, elapsed time, half-life or the initial quantity.
-
2
Fill in what you know
Any three of the four values. Units for time are yours to choose, as long as you are consistent.
-
3
Read the answer
The missing value, plus the decay constant and mean lifetime that follow from it.
-
4
Check the half-life table
Common isotopes are listed if you need a reference value rather than your own.
Frequently asked questions
The amount remaining is N = N₀ × (1/2)^(t/T), where N₀ is the starting amount, t is elapsed time and T is the half-life. Equivalently N = N₀ × e^(−λt), with λ the decay constant.
The decay constant λ equals the natural logarithm of 2 divided by the half-life, roughly 0.693 ÷ T. Mean lifetime is the reciprocal, 1/λ.
Rearranging gives t = T × log₂(N₀/N). This is exactly how radiocarbon dating works, using carbon-14 with a half-life of 5,730 years.
Yes. Any process with a constant proportional rate of loss follows the same law, including drug elimination from the bloodstream and the discharge of a capacitor.
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