Radioactive Decay and Half-Life Calculator
Calculate how much of a radioactive sample remains after a given time, find the half-life or decay constant, and compute activity from the decay law.
What this calculator does
Enter the starting amount, the half-life and the elapsed time to get the amount left, the number of half-lives, the decay constant and the percent remaining.
When you need it
Half-life calculations are used for radiocarbon dating, nuclear medicine, handling radioactive waste and any decay process that follows first-order kinetics.
Formulas
- N = N₀ (1/2)^(t ÷ t½)
- λ = ln 2 ÷ t½
- N = N₀ e^(−λt)
- A = λN
How to use it
- Choose what to find: remaining amount, half-life or activity.
- Enter the initial amount, half-life and time in the same time unit.
- Read the amount remaining, the fraction remaining and the half-lives elapsed.
Worked example
Iodine-131 has a half-life of about 8.0 days. How much of 80.0 g is left after 24 days?
- Half-lives elapsed = 24 ÷ 8.0 = 3
- N = 80.0 × (1/2)³ = 80.0 ÷ 8 = 10.0 g
Answer
10.0 g of iodine-131 remains, which is 12.5% of the original.
Common mistakes
- Using a half-life in years with a time in days.
- Treating the decay as linear instead of exponential.
- Confusing the decay constant λ with the half-life.
Related tools
Frequently asked questions
What is a half-life?
The time it takes for half of the radioactive nuclei in a sample to decay.
How is carbon dating calculated?
By comparing the carbon-14 left in a sample with the starting amount. Carbon-14 has a half-life of 5730 years, so a sample with 25% left is 2 half-lives old, about 11 460 years.
How is the decay constant related to the half-life?
λ = ln 2 ÷ t½. A shorter half-life means a larger decay constant.