Index / Science
Half-Life Calculator
How much of a sample is left after a given time, or how long it takes to fall to a given fraction, with the decay constant, the mean lifetime and the activity in becquerels and curies. Twenty isotopes are built in and every constant used is printed.
Isotope
Choosing one fills the half-life and the mass
number below. Editing either leaves the preset as a label.
Only used to count atoms in a weighed sample. The
mass number is within about 0.1% of the real molar mass.
Question
100% is now and 0% never arrives, which is what
exponential decay means.
Left after that time
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Half-lives elapsed
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Activity now
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The decay
Time to fall to
from full
The formulas, the constants, and the two figures people quote differently
N(t) = N0 · 2−t/T½, which is the same
thing as N0e−λt with
λ = ln2 / T½. Both forms are computed here and the page
prints the largest disagreement between them, which is a check on the
arithmetic rather than a decoration.
The mean lifetime τ is 1/λ, which is T½ / ln2 = 1.4427 T½ — longer than the half-life, not shorter, because the atoms that survive a long time drag the average up.
A year here is the Julian year: 365.25 days, exactly 31,557,600 seconds. That is the convention half-lives are published in. A calendar year of 365 days would shift every long half-life by 0.07%, which is larger than the measurement uncertainty on several of them.
Activity is A = λN, in becquerels, one decay per second. The curie is exactly 3.7 × 1010 Bq by definition. It was meant to be the activity of one gram of radium-226, and with the modern half-life of 1,600 years a gram of radium comes out at 0.988 Ci here rather than 1.000 — the definition was fixed before the half-life was measured this well, and it is worth seeing the difference rather than being shown a round number.
Radiocarbon has two half-lives in circulation. The measured value is 5,700 ± 30 years and it is the one used here. Conventional radiocarbon ages are still published using Libby's original 5,568 years, so that a laboratory result can be recalculated consistently; an age computed with one and quoted against the other is out by about 3%.
This is one isotope decaying into something stable. No decay chain, no daughter ingrowth, no secular equilibrium. Radium-226 in a sealed tube grows a chain of daughters whose activity eventually matches its own, and the sample's total activity ends up several times what this page reports for the parent alone.
Decay is a property of a population, not a promise about one atom. Nothing here says when a particular nucleus goes; a half-life is the time by which half of a very large number of them have gone, and the counting statistics on a small sample are their own subject.
Nothing is ever printed in scientific notation. A decay constant of 0.0000000000000000049 per second is written out, and so is a half-life of 20,100,000,000,000,000,000 years.
The mean lifetime τ is 1/λ, which is T½ / ln2 = 1.4427 T½ — longer than the half-life, not shorter, because the atoms that survive a long time drag the average up.
A year here is the Julian year: 365.25 days, exactly 31,557,600 seconds. That is the convention half-lives are published in. A calendar year of 365 days would shift every long half-life by 0.07%, which is larger than the measurement uncertainty on several of them.
Activity is A = λN, in becquerels, one decay per second. The curie is exactly 3.7 × 1010 Bq by definition. It was meant to be the activity of one gram of radium-226, and with the modern half-life of 1,600 years a gram of radium comes out at 0.988 Ci here rather than 1.000 — the definition was fixed before the half-life was measured this well, and it is worth seeing the difference rather than being shown a round number.
Radiocarbon has two half-lives in circulation. The measured value is 5,700 ± 30 years and it is the one used here. Conventional radiocarbon ages are still published using Libby's original 5,568 years, so that a laboratory result can be recalculated consistently; an age computed with one and quoted against the other is out by about 3%.
This is one isotope decaying into something stable. No decay chain, no daughter ingrowth, no secular equilibrium. Radium-226 in a sealed tube grows a chain of daughters whose activity eventually matches its own, and the sample's total activity ends up several times what this page reports for the parent alone.
Decay is a property of a population, not a promise about one atom. Nothing here says when a particular nucleus goes; a half-life is the time by which half of a very large number of them have gone, and the counting statistics on a small sample are their own subject.
Nothing is ever printed in scientific notation. A decay constant of 0.0000000000000000049 per second is written out, and so is a half-life of 20,100,000,000,000,000,000 years.