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Half-Life Calculator

Choose what you want to find and enter the other three values. You get the answer, the number of half-lives, the percent left, the decay constant and the mean lifetime.

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Result

How we calculate it

In exponential decay the amount halves every half-life T, so after a time t the remaining amount is N = N0 × 2^(−t ÷ T). The calculator rearranges this for whichever value you choose: N0 = N × 2^(t ÷ T), t = T × log2(N0 ÷ N) and T = t × ln 2 ÷ ln(N0 ÷ N).

For example, 100 grams with a half-life of 10 years leaves 12.5 grams after 30 years, which is three half-lives. The decay constant is λ = ln 2 ÷ T and the mean lifetime is τ = T ÷ ln 2, about 1.4427 half-lives.

Assumptions and limits

  • Use the same unit of time for the half-life and the elapsed time. The answer for a time or a half-life is in that unit.
  • The amount can be in any unit, such as grams, atoms, becquerels or percent, as long as the initial and remaining amounts use the same one.
  • This is for a quantity that decays by a constant fraction in equal times, such as a radioactive isotope or a drug that is cleared at a steady rate. The remaining amount must be above zero.

Frequently asked questions

What is a half-life?

The half-life is the time it takes for a quantity to fall to half of its value. After one half-life half is left, after two a quarter, after three an eighth, and so on.

How do I calculate how much is left after a given time?

Divide the time by the half-life to get the number of half-lives, then halve the starting amount that many times: N = N0 × (1/2)^(t ÷ T). 100 grams after 30 years with a 10 year half-life is 100 × (1/2)^3 = 12.5 grams.

What is the half-life of carbon-14?

It is about 5,730 years. After 11,460 years, two half-lives, a quarter of the carbon-14 is left. Use the calculator with 5,730 as the half-life to date a sample.

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Worked example (a fixed example using the starting numbers, it does not change as you type)

Inputs: Solve for = Remaining amount; Initial amount = 100; Half-life = 10; Elapsed time = 30.

  • Remaining amount 12.5
  • Initial amount 100
  • Half-life 10
  • Elapsed time 30
  • Half-lives elapsed 3
  • Percent remaining 12.5
  • Decay constant 0.0693147
  • Mean lifetime 14.427

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Last reviewed: . Formulas and assumptions are described on our methodology page. For information only; not professional advice.