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Half-Life Calculator
Your sample
Half-life: 5 days
The field for the value you are solving for is filled in by the calculator. Elapsed time and half-life can use different units — the calculator converts them.
Example: 100 g of a sample with a 5-day half-life, after 15 days → 12.5 g remaining.
Behind the numbers
How half-life is calculated
After each half-life, half of the sample remains, so the amount left is the starting amount times one-half raised to the number of half-lives that have passed. The same equation rearranges to find the elapsed time or the half-life itself, using base-2 logarithms.
Worked example — 100 g, half-life 5 days, elapsed 15 days: the number of half-lives is 15 ÷ 5 = 3, so N = 100 × (1/2)3 = 100 × 1/8 = 12.5 g. A custom isotope works the same way: 100 g of “Testium” with a 10-day half-life, after 20 days, is 100 × (1/2)2 = 25 g. To find the time instead, t = T × log2(N0 ÷ N); to find the half-life, T = t ÷ log2(N0 ÷ N).
Examples
Example decays
| Sample | Solve for | Answer |
|---|---|---|
| 100 g, half-life 5 days, 15 days elapsed | Remaining | 12.5 g |
| 200 g of Iodine-131 (8.02 days), 8.02 days elapsed | Remaining | 100 g |
| 100 g down to 25 g, half-life 10 days | Elapsed time | 20 days |
| 100 g down to 25 g in 20 days | Half-life | 10 days |
| 100 g of “Testium” (10 days), 20 days elapsed | Remaining | 25 g |
Tips before you use it
Each half-life halves the sample: after 1 half-life 50% is left, after 2 it is 25%, after 3 it is 12.5%.
Keep the time units consistent. If the half-life is in years and the elapsed time is in days, convert one of them first — this calculator does that for you.
The remaining amount must be smaller than the starting amount when you solve for time or half-life; a sample cannot grow by decaying.
After 10 half-lives only about 0.1% of the sample remains, so for most purposes it is treated as gone.
Good to know
Frequently asked questions
What is a half-life?
A half-life is the time it takes for half of a radioactive sample to decay. After one half-life, half remains; after two, a quarter; after three, an eighth. The half-life is a fixed property of each isotope and does not depend on how much you start with.
Does the starting amount change the half-life?
No. Whether you start with 100 g or 1 g, half of it decays in one half-life. The starting amount changes how much is left in grams, not how fast the fraction falls.
What units can I use for time?
Any unit, as long as the elapsed time and the half-life use the same unit. This calculator converts hours, days and years for you: pick the unit for the elapsed time and it converts the isotope's half-life to match.
How many half-lives until a sample is gone?
Mathematically, never quite: each half-life halves what is left. After 10 half-lives about 0.1% remains (1/1,024 of the start). In practice, after 10 half-lives the sample is treated as effectively gone.