Half-Life Calculator
Calculate radioactive decay: how much remains, how long it takes, or the half-life.
Please note: Results come from idealised models that assume clean, standard conditions. Real measurements deviate, and published constants carry their own tolerances. Use these for study and estimation, not for engineering sign-off.
What the Half-Life Calculator does
Radioactive decay removes a constant fraction of the remaining material in each equal interval, so the amount left follows an exponential curve. The half-life is the time for exactly half to decay, and it stays the same no matter how much material you start with.
Formula
N = N₀ × (1/2)^(t ÷ t½)t = t½ × log₂(N₀ ÷ N)t½ = t × ln(2) ÷ ln(N₀ ÷ N)λ = ln(2) ÷ t½, τ = 1 ÷ λ
Inputs explained
| Input | Unit | Required | Notes |
|---|---|---|---|
| Solve for | one of 3 options | Yes | — |
| Initial amount | number | Yes | Any unit — grams, atoms or becquerels. The answer comes back in the same one. Accepts more than 0. |
| Remaining amount | number | In some modes | Accepts 0 or more. Shown Solve for is Time elapsed, or Solve for is Half-life. |
| Half-life | number | In some modes | Shown Solve for is Amount remaining, or Solve for is Time elapsed. |
| Half-life unit | one of 6 options | In some modes | Shown Solve for is Amount remaining, or Solve for is Time elapsed. |
| Time elapsed | number | In some modes | Shown Solve for is Amount remaining, or Solve for is Half-life. |
| Time elapsed unit | one of 6 options | In some modes | Shown Solve for is Amount remaining, or Solve for is Half-life. |
How to use it
- Choose Solve for.
- Enter Initial amount.
- Fill in the remaining inputs the form shows for your choice.
- Select Calculate.
Worked example
100 g of carbon-14, half-life 5,730 years, after 11,460 years.
- Initial
- 100
- Half-life
- 5730 years
- Elapsed
- 11460 years
That is exactly 2 half-lives, so 100 × (1/2)² = 25 g remains — 25% of the original.
Frequently asked questions
Why does material never fully disappear?
Because each half-life removes half of whatever is left, not a fixed quantity. Mathematically the curve approaches zero without ever reaching it, though in practice you eventually run out of atoms.
How does carbon dating work?
Living things maintain a constant carbon-14 level. Once they die, it decays with a 5,730-year half-life, so measuring what remains gives the time since death — useful out to roughly 50,000 years.