Case 1
- Half-life
- 5730
- Elapsed time
- 5730
50.000000%
Open with these valuesHalf-Life Calculator
50.000000%
Result: 50.000000 %After one half-life 50 % remains, after two 25 %, after three 12.5 %. The share left depends only on how many half-lives have passed, never on how much you started with. Enter the half-life and the elapsed time in the same unit — years against years, hours against hours.
Worked examples
Case 2
- Half-life
- 5730
- Elapsed time
- 11460
25.000000%
Open with these valuesCase 3
- Half-life
- 8
- Elapsed time
- 24
12.500000%
Open with these valuesHow it's calculated
share = 100 × ½^(t ÷ t½)
- StepEnter the half-life in any time unit you like.
- StepEnter the elapsed time in that same unit.
- StepDivide the two to get the number of half-lives passed.
- ResultHalve 100 % once for each of them.
Reference table
| Half-life, elapsed time | Half-lives passed | Still present (%) |
|---|---|---|
| 5730, 0 | none | 100.000000 |
| 10, 5 | half of one | 70.710678 |
| 5730, 5730 | one | 50.000000 |
| 5730, 11460 | two | 25.000000 |
| 8, 24 | three | 12.500000 |
| 10, 33.2 | about 3.32 | 10.013373 |
Questions
What is a half-life?
A half-life is the time it takes for half of a quantity to decay or be removed. After one half-life 50 % remains, after two 25 %, after three 12.5 %. Because the decay is exponential the amount never reaches exactly zero — it just keeps halving.
How do I work out the percentage still present?
Divide the elapsed time by the half-life to get the number of half-lives, then halve 100 % that many times. Written out that is 100 × ½^(t ÷ t½), and the exponent does not have to be a whole number.
Do the half-life and elapsed time need the same unit?
Yes. Both must use the same time unit — both in years, both in hours, both in seconds. Only their ratio enters the formula, so the units cancel; mixing years with days gives a wrong answer.
Why is the starting amount not asked for?
Because it cannot change the percentage. One gram and one kilogram both leave 25 % after two half-lives. If you want the absolute amount left rather than the share, use the radioactive decay calculator instead.
What is half-life used for?
It describes any exponential decay: radioactive isotopes and carbon-14 dating, the clearance of a drug from the bloodstream, the discharge of a capacitor. The same formula applies wherever a quantity falls by a fixed fraction over equal time intervals.
What happens when no time has elapsed?
The exponent becomes zero, and anything raised to the power zero is one, so 100 % is still present. That is the sanity check at the top of the table.
Sources and last check
Information, not professional advice.