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Half-Life Calculator
Work out half-life problems in any direction: how much is left after a given time, how much there was to start with, how long a decay takes, or what the half-life is. Enter amounts in any unit and times in seconds through years; the answer also shows the number of half-lives elapsed and the mean lifetime.
- Amount remaining
- 88.6062
- Initial amount
- 100
- Share remaining
- 88.6062%
- Half-lives elapsed
- 0.1745
- Time elapsed
- 1,000 yr
- Half-life
- 5,730 yr
- Mean lifetime (τ = T ÷ ln 2)
- 8,266.64 yr
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Formula
How to use it
- Choose what to solve for.
- Enter the amounts in the same unit, whatever it is — grams, milligrams, atoms or becquerels.
- Enter the times, choosing a unit for each; they do not need to match.
- Read the answer and the number of half-lives; check it against the table of halvings below.
Worked examples
100 g of carbon-14 after 1,000 years: N = 100 × (½)^(1,000 ÷ 5,730)
- Answer
- 88.61 (88.61% of the start)
- Amount remaining
- 88.6062
- Half-lives elapsed
- 0.1745
- Mean lifetime (τ = T ÷ ln 2)
- 8,266.64 yr
How long until carbon-14 falls from 100 to 25? log₂(100 ÷ 25) = 2 half-lives
- Answer
- 11,460 years
- Time elapsed
- 11,460 yr
- Half-lives elapsed
- 2
- Share remaining
- 25%
50 mCi of iodine-131 (half-life 8.02 days) after 20 days
- Answer
- 8.877 (17.75% of the start)
- Amount remaining
- 8.8771
80 g decays to 10 g in 24 hours — three halvings, so the half-life is 8 hours
- Answer
- 8 hours
- Half-life
- 0.0009126 yr
- Half-lives elapsed
- 3
Initial amount if 12.5 g is left after 17,190 years of carbon-14 decay (3 half-lives)
- Answer
- 100
- Initial amount
- 100
200 mg of caffeine after 12 hours, with a 5-hour half-life
- Answer
- 37.89 (18.95% of the start)
- Amount remaining
- 37.8929
Halvings at a glance
After 1 half-life 50% remains, after 2 25%, after 3 12.5%, after 4 6.25%, after 5 3.125%, after 7 about 0.78% and after 10 about 0.098%. If the time is a whole number of half-lives you can check the answer in your head.
Common half-lives
Carbon-14: 5,730 years, the value used in most textbook dating problems. Published radiocarbon ages are still quoted on the older Libby half-life of 5,568 years by convention and then calibrated, so lab dates differ from this simple calculation. Iodine-131: 8.02 days. Uranium-238: about 4.47 billion years.
The idea applies beyond radioactivity: the body clears many drugs with a roughly constant half-life. Caffeine’s is commonly quoted at around 5 hours, though it varies widely between people.
Questions people ask
How do you calculate half-life?
Divide the elapsed time by log₂ of the starting amount over the amount left. 80 g falling to 10 g in 24 hours: log₂(8) = 3, so T = 24 ÷ 3 = 8 hours.
How much carbon-14 is left after 1,000 years?
88.61% of it: 100 × (½)^(1,000 ÷ 5,730) = 88.61.
How long does it take for 75% of a sample to decay?
Two half-lives, because 25% remains. For carbon-14 that is 11,460 years.
What is the difference between half-life and mean lifetime?
The half-life is the time for half to decay. The mean lifetime, the average time an atom survives, is longer by a factor of 1/ln 2 ≈ 1.443: 8,267 years for carbon-14.