Half-Life Calculator guide
Half-Life Calculator: Radioactive and Exponential Decay
Use our half-life calculator to work out the amount remaining, the half-life or the time taken for radioactive or exponential decay.
By the AllCalculator editorial teamUpdated 16 October 20261 min read
The half-life of a substance is the time it takes for half of it to decay. It's used for radioactive elements, medicines in the body and anything that decays exponentially. Our Half-Life Calculator works out any part of the calculation.
How to use the calculator (Half-Life Calculator)
- Choose what to find: the amount remaining, the half-life or the time taken.
- Enter the other values. Use the same time units for the time and half-life.
The formula
N(t) = N₀ × (½)^(t ÷ T½)
- N₀ is the starting amount
- N(t) is the amount left after time t
- T½ is the half-life
Rearranged:
- Half-life: T½ = t × ln 2 ÷ ln(N₀ ÷ N)
- Time: t = T½ × ln(N₀ ÷ N) ÷ ln 2
A worked example
With the calculator's default settings, 100g of a substance with a half-life of 10 years, after 30 years:
- 30 ÷ 10 = 3 half-lives
- 100 × ½ × ½ × ½ = 12.5g left
Some half-lives
| Substance | Half-life |
|---|---|
| Iodine-131 | About 8 days |
| Caesium-137 | About 30 years |
| Carbon-14 | About 5,730 years |
| Uranium-238 | About 4.5 billion years |
Frequently asked questions
Does it ever reach zero?
In theory, no: half of what's left always remains. In practice, after about 10 half-lives, less than 0.1% is left.
What's the decay constant?
λ = ln 2 ÷ T½. It's the fraction that decays per unit of time.
How does carbon dating work?
Living things take in carbon-14. After they die, it decays with a half-life of about 5,730 years, so measuring how much is left shows how old something is.
Sources and further reading
Links open official and independent websites in a new tab.
This guide is general information to help you understand your options. It isn't financial, tax, legal or building advice and doesn't take your personal circumstances into account. Figures were checked when the guide was last updated and can change, so confirm anything important with GOV.UK, HMRC, a regulated adviser or a qualified tradesperson.