Half-Life Calculator
Find a half-life, the quantity remaining, the initial quantity or the time elapsed, and convert between half-life, decay constant and mean lifetime.
Change the values and press Calculate to work out your own figures.
Half-life from a measurement
Enter the initial and remaining quantities and the time between.
Show the working
- t½ = t × ln 2 ÷ ln(N₀ ÷ Nₜ)
Quantity remaining
Enter the initial quantity, the time and the half-life.
Show the working
- Nₜ = N₀ × (1/2)^(t ÷ t½)
Initial quantity
Enter the remaining quantity, the time and the half-life.
Show the working
- N₀ = Nₜ ÷ (1/2)^(t ÷ t½)
Time elapsed (dating)
Enter the initial and remaining quantities and the half-life.
Show the working
- t = t½ × ln(N₀ ÷ Nₜ) ÷ ln 2
Half-life, decay constant and mean lifetime
Enter one of the three.
Show the working
- λ = ln 2 ÷ t½
- τ = 1 ÷ λ = t½ ÷ ln 2
How to use it
Enter the initial and remaining quantities and the time between. Enter the initial quantity, the time and the half-life. Enter the remaining quantity, the time and the half-life. Enter the initial and remaining quantities and the half-life. Enter one of the three.
Number boxes accept whole numbers, decimals, fractions (3/4), powers (2^10), roots (sqrt(2)) and the constants pi and e. Show the working lists the steps.
Key facts
Nₜ = N₀ × (1/2)^(t ÷ t½); λ = ln 2 ÷ t½; τ = 1 ÷ λ
After n half-lives
1/2, 1/4, 1/8 … of the sample is left: 1/2ⁿ.
Fraction left
| Half-lives | Fraction left | Percent left |
|---|---|---|
| 0 | 1/1 | 100% |
| 1 | 1/2 | 50% |
| 2 | 1/4 | 25% |
| 3 | 1/8 | 12.5% |
| 4 | 1/16 | 6.25% |
| 5 | 1/32 | 3.125% |
| 6 | 1/64 | 1.5625% |
| 7 | 1/128 | 0.78125% |
| 8 | 1/256 | 0.390625% |
| 9 | 1/512 | 0.1953125% |
| 10 | 1/1024 | 0.09765625% |
Questions
How old is a sample with 15% of its carbon-14 left?
About 15,683 years (t½ = 5,730 years).
What is the decay constant of carbon-14?
0.000120968 per year.
Formulas
Nₜ = N₀ × (1/2)^(t ÷ t½); λ = ln 2 ÷ t½; τ = 1 ÷ λ
Sources
Limitations
- Expressions up to 500 characters; matrices up to 10 × 10.
- Big-number results up to 100,000 digits; factorials up to 10,000!.
- Numbers in words up to 10^102 (short scale).