What is the half-life formula?

N = N₀ × (½)^(t ÷ t½), where N₀ is the starting amount, N the amount remaining, t the time elapsed and t½ the half-life.

How much is left after 3 half-lives?

One eighth, or 12.5%. Each half-life halves the amount: 100% → 50% → 25% → 12.5%.

How do I calculate half-life from data?

Find how many half-lives passed with ln(N ÷ N₀) ÷ ln(0.5), then divide the elapsed time by it. A sample falling from 80 g to 20 g in 10 days has gone through 2 half-lives, so its half-life is 5 days.

Can I use percentages or counts instead of grams?

Yes. Any unit works, including atoms, percent remaining or a Geiger counter's counts per minute, as long as the starting and remaining amounts use the same unit.

Half-Life & Radioactive Decay Calculator

The amount left is N = N₀ × (½)^(t ÷ t½). Carbon-14 has a half-life of 5,730 years, so a sample with 25% of its carbon-14 left has gone through 2 half-lives and is about 11,460 years old.

Starting amount (N₀)

Amount remaining (N)

Half-life

years

Time unit

Amounts can be in any unit (grams, atoms, % or counts per minute) as long as both use the same one. For carbon dating, enter 100 and the percent of carbon-14 left.

Time elapsed

11,460 years

Half-lives passed

Fraction remaining

25%

Decay over whole half-lives

Half-lives	Time (years)	Remaining
1	5,730	50 (50%)
2	11,460	25 (25%)
3	17,190	12.5 (12.5%)
4	22,920	6.25 (6.25%)
5	28,650	3.125 (3.125%)
6	34,380	1.5625 (1.563%)

Show the math

1
Fraction remaining
25 ÷ 100 = 0.25
= 25% left

Read the steps as text

Fraction remaining. 25 ÷ 100 = 0.25
Half-lives = log(fraction) ÷ log(½). ln(0.25) ÷ ln(0.5) = 2 Taking the logarithm undoes the power of ½ to count how many halvings happened.
Time = half-lives × half-life. 2 × 5,730 years = 11,460 years

How radioactive decay works

A half-life is the time it takes for half of a radioactive substance to decay. It never changes, however much material there is: after one half-life 50% remains, after two 25%, after three 12.5%, and so on. The formula N = N₀ × (½)^(t ÷ t½) multiplies by ½ once for every half-life that has passed, including fractions of one.

To find a time or a half-life instead, the calculator first works out how many half-lives have passed from the fraction remaining, using logarithms: half-lives = ln(N ÷ N₀) ÷ ln(½). Multiplying by the half-life gives the time; dividing the time by it gives the half-life.

Carbon-14 dating

Living things take in carbon-14 from the atmosphere at a steady level. When they die the intake stops and the carbon-14 decays with a half-life of 5,730 years. Measuring how much is left gives an age: a sample with 10% of its original carbon-14 is about 19,035 years old.

The method works for once-living material up to about 50,000 years old; after that too little carbon-14 remains to measure. Laboratories also correct for past changes in atmospheric carbon-14, so real radiocarbon dates are calibrated rather than taken straight from this formula.

Frequently asked questions

What is the half-life formula?: N = N₀ × (½)^(t ÷ t½), where N₀ is the starting amount, N the amount remaining, t the time elapsed and t½ the half-life.
How much is left after 3 half-lives?: One eighth, or 12.5%. Each half-life halves the amount: 100% → 50% → 25% → 12.5%.
How do I calculate half-life from data?: Find how many half-lives passed with ln(N ÷ N₀) ÷ ln(0.5), then divide the elapsed time by it. A sample falling from 80 g to 20 g in 10 days has gone through 2 half-lives, so its half-life is 5 days.
Can I use percentages or counts instead of grams?: Yes. Any unit works, including atoms, percent remaining or a Geiger counter's counts per minute, as long as the starting and remaining amounts use the same unit.