Half-life and radioactive decay calculator
Decay is exponential: every half-life removes half of whatever remains, forever.
Amount remaining
50
- Fraction remaining
- 50.0000 %
- Amount decayed
- 50
- Half-lives elapsed
- 1.0000
- Decay constant
- 0.000 120 968 per unit time
- Mean lifetime
- 8266.64
Show the working
- Starting amount = 100
- Half-life = 5730
- Time elapsed = 5730
- Half-lives elapsed = 5730 / 5730 = 1
- Amount remaining = 100 * 0.5^1 = 50
- Amount decayed = 100 - 50 = 50
- Fraction remaining = 50 / 100 * 100 = 50
- Decay constant = ln(2) / 5730 = 0.000 120 968
- Mean lifetime = 1 / 0.000 120 968 = 8266.64
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- N = N0 x (1/2)^(t / t_half)
- decay constant lambda = ln(2) / t_half
- mean lifetime = 1 / lambda = t_half / ln(2)
The time unit is whatever you use consistently — the half-life and the elapsed time just have to match.
Carbon-14 has a half-life of 5730 years, which is the default here.