Half-Life Calculator
Find the remaining quantity after a given number of half-lives.
Your numbers
Your results
Quantity remaining
Quantity remaining
—
Fraction remaining
—
Number of half-lives
—
Decay constant λ (per unit time)
—
Half-Life Calculator by TheCalcTools
How the Half-Life Calculator works
Enter the starting amount, the half-life and the elapsed time in the same unit.
Every half-life halves the amount.
The calculator evaluates N₀ × (½)^(t ÷ half-life).
The formula
N(t) = N₀ × (1/2)^(t ÷ t½)λ = ln 2 ÷ t½
Worked example
Using the default values shown in the calculator:
| Initial quantity | 100 |
|---|---|
| Half-life | 5730 |
| Elapsed time (same unit) | 10000 |
- 10,000 years is 10,000 ÷ 5,730 = 1.745 half-lives.
- Remaining = 100 × (½)^1.745 = 29.83.
- That is 29.8% of the original.
Result:
| Quantity remaining | 29.8292 |
|---|---|
| Fraction remaining | 29.83% |
| Number of half-lives | 1.745 |
| Decay constant λ (per unit time) | 1.210 × 10^-4 |
Frequently asked questions
What is the half-life of carbon-14?
About 5,730 years, which is why it is used to date organic remains up to roughly 50,000 years old.
Does it work for medicines?
Yes. Many drugs are eliminated approximately exponentially, so half-life tells you how long they stay in the body.
Sources and further reading
Related calculators
More in Physics · All calculators
This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.