Half-Life Calculator
Find the remaining quantity, elapsed time or half-life of a decaying substance.
About the Half-Life Calculator
Choose what to solve for (remaining quantity, time elapsed or half-life) and enter the other values. The calculator also gives the share remaining, the number of half-lives passed and the decay constant, with a decay curve.
Radioactive decay, and first-order processes like drug elimination, halves the quantity every half-life. Carbon-14's half-life of 5,730 years makes it useful for dating material up to about 50,000 years old.
The formula
N = N₀ × (½)^(t ÷ t½); t = t½ × ln(N₀ ÷ N) ÷ ln 2
- N₀
- starting quantity
- N
- quantity left
- t
- time elapsed
- t½
- half-life, in the same time unit as t
Worked example
Carbon-14 (half-life 5,730 years)
- After 11,460 years = 2 half-lives: 100 → 25, so 25% remains
- How long until 10% remains? 5,730 × ln 10 ÷ ln 2
- = about 19,035 years (3.32 half-lives)
Questions people ask
What units should I use?
Any, as long as time and half-life share them.
Does decay ever reach zero?
Mathematically no; physically, once few atoms remain, decay becomes random.
How is it used for medicines?
A drug's elimination half-life tells you how long until levels halve; after about 5 half-lives most of it is gone.