What is the Half-Life Calculator?
Solve radioactive decay problems with the half-life equation N = N₀(½)^(t/t½). Find remaining amount, initial amount, elapsed time, or half-life from any three known values. Also shows decay constant λ, half-lives elapsed, and percent remaining. Works with seconds through years. Free, instant, and browser-based.
How to use the Half-Life Calculator
- Choose what to solve: remaining amount N, initial N₀, elapsed time t, or half-life t½.
- Enter the other three values using consistent amount units (grams, becquerels, etc.).
- Pick a time unit for t and t½ (seconds, minutes, hours, days, or years).
- Read the solved value plus λ, half-lives elapsed, and percent decayed.
- Copy the summary for lab reports or nuclear chemistry homework.
Common use cases
- Finding how much of a radioisotope remains after several half-lives
- Calculating elapsed time from activity measurements
- Determining half-life from experimental N₀, N, and t data
Frequently asked questions
- What is the half-life formula?
- N = N₀(½)^(t/t½), where N₀ is the initial amount, N is what remains after time t, and t½ is the half-life. Equivalently, N = N₀e^(−λt) with λ = ln(2)/t½.
- What units should I use?
- Amounts can be any consistent unit (grams, curies, becquerels, number of atoms). Time and half-life must use the same time unit, which you select in the calculator.
- Can I use this for carbon-14 dating?
- Yes. Enter the C-14 half-life (about 5730 years), the initial activity or amount, and elapsed time to find how much remains — or solve for time given N₀ and N.
- Why must N be less than N₀?
- This tool models first-order radioactive decay where the sample decreases over time. If N ≥ N₀, the elapsed time would be zero or negative.
- What is the decay constant λ?
- λ (lambda) is the probability rate of decay per unit time. It relates to half-life by λ = ln(2)/t½ ≈ 0.693/t½.
