Case 1
- Starting amount
- 100
- Elapsed time
- 11460
- Half-life
- 5730
25.000000
Open with these valuesRadioactive Decay Calculator
25.000000same unit
Result: 25.000000 same unitHalve the starting amount once for every half-life that has passed: N = N₀ × ½^(t ÷ t½). One hundred grams of carbon-14 leaves 25 g after 11 460 years, two half-lives. Elapsed time and half-life must share a unit; the answer comes back in the unit of the starting amount.
Worked examples
Case 2
- Starting amount
- 100
- Elapsed time
- 5730
- Half-life
- 5730
50.000000
Open with these valuesCase 3
- Starting amount
- 50
- Elapsed time
- 17190
- Half-life
- 5730
6.250000
Open with these valuesHow it's calculated
N = N₀ × ½^(t ÷ t½)
- StepEnter the starting amount in any unit — grams, atoms, becquerel.
- StepEnter the elapsed time and the half-life in one shared time unit.
- ResultDivide them for the number of half-lives, then halve that many times.
Reference table
| Start, elapsed, half-life | Half-lives passed | Left over |
|---|---|---|
| 100, 0, 5730 | none | 100.000000 |
| 1, 1, 2 | half of one | 0.707107 |
| 100, 5730, 5730 | one | 50.000000 |
| 100, 11460, 5730 | two | 25.000000 |
| 80, 10, 5 | two | 20.000000 |
| 50, 17190, 5730 | three | 6.250000 |
Questions
How do I calculate radioactive decay?
Multiply the starting amount by one half raised to the number of half-lives elapsed: N = N₀ × ½^(t ÷ t½). One hundred grams of carbon-14 after 11 460 years is 100 × ½² = 25 g.
What is a half-life?
A half-life is the span over which exactly half of a radioactive substance decays. Whatever amount is present, half of it is gone after one half-life, no matter how much you started with. Carbon-14 has a half-life of 5730 years.
Why do two half-lives leave a quarter, not nothing?
Each half-life halves what is currently present, not the original amount. After one half-life half remains; halving that again leaves a quarter. The share left runs 100 %, 50 %, 25 %, 12.5 %, approaching zero without reaching it.
Do the elapsed time and the half-life need the same unit?
Yes. The exponent is the elapsed span divided by the half-life, so both must be in the same unit for the ratio to be a clean count of half-lives. Which unit that is does not matter — years, days or seconds all work, as long as both fields agree.
How is radioactive decay used in carbon dating?
Carbon dating runs the formula in reverse: measure the fraction of carbon-14 left in a sample, compare it with the living-tissue level, and you have the number of half-lives elapsed. Multiplying by 5730 years gives the sample's age.
Does the remaining amount ever reach zero?
Mathematically no — halving repeatedly always leaves something, so the curve approaches zero without touching it. In practice the smooth formula stops applying once only a handful of atoms remain, because decay is then random nucleus by nucleus.
Sources and last check
Information, not professional advice.