Half Life Calculator
Remaining amount after any span from starting amount and half-life.
What it does
Half-life is the time for half of a decaying quantity to transform. After one half-life 50% remains, after two 25%, after three 12.5%, with each period halving whatever survived before.
The tool above takes the starting amount, one half-life, and the elapsed time in a shared unit. It returns the remainder with the percent left and the count of half-lives elapsed.
The default of 100 with a 5 day half-life over 15 days runs 3 halves to 12.5 remaining (12.5%). Carbon-14 dating runs the same math with a 5730 year half-life instead of days.
The decay law follows OpenStax University Physics nuclear chapters with state health fact sheets behind them. Both write N = N0 times one half to the elapsed half-lives, equivalently the exponential with decay constant 0.693 over half-life.
How to use
- Enter the starting amount in any unit (grams, becquerels).
- Enter one half-life in your time unit.
- Enter the elapsed time in the same unit.
- Set the unit label to match for the record.
- Read remainder first, then percent and halves.
Formula
- halves
- Elapsed half-life count, decimals allowed.
- (1/2)^halves
- Surviving fraction after that count.
- 0.693
- ln 2 linking decay constant to half-life.
Spans past 100 half-lives are rejected since the remainder is physically zero there. Amount units ride along unchanged; only the two times must share units.
Worked example
Example: 100, half-life 5 days, 15 days
Start 100, half 5 days, elapsed 15 days.
- Halves: 15 / 5 = 3.
- Fraction: (1/2)^3 = 1/8 = 0.125.
- Remainder: 100 x 0.125 = 12.5.
- Percent: 12.5%.
- Tool shows 12.5 left, 12.5%, 3 half-lives.
Reference table
| Halves | Left | Percent |
|---|---|---|
| 1 | 50 | 50% |
| 2 | 25 | 25% |
| 3 | 12.5 | 12.5% |
| 7 | 0.78 | under 1% |
| 10 | about 0.1 | under 0.1% |
Limits
- Single isotope assumed; chains need Bateman math.
- Constant half-life assumed regardless of conditions.
- Chemical toxicity stays when radioactivity fades.
- dating contexts add contamination caveats.
Common mistakes
- Subtracting halves linearly instead of halving repeatedly.
- Mixing days with years between the two times.
- Reading 10 half-lives as zero instead of 1/1024.
- Confusing half-life with average lifetime (half-life x 1.44).
- Applying decay math to biological clearance rates.
Try it yourself
Quick checks. Answers sit tucked under each question.
100 with 5730 year half-life after 5730 years?
1 half: 50 left, 50%.
100 with 8 day half-life after 24 days?
3 halves: 12.5 left, 12.5%.
Fraction after 10 halves?
(1/2)^10 = 1/1024, under 0.1%.
Questions
What is half-life?
Time for half a decaying quantity to transform: 100 becomes 50, then 25, then 12.5.
How much is left after 3 half-lives?
One eighth (12.5%). Halve three times in a row.
When is it effectively gone?
After 7 halves under 1% remains; after 10 under 0.1%.
Half-life vs lifetime?
Average lifetime is half-life divided by 0.693 (x 1.44 longer).
Does temperature change it?
Essentially no for nuclear decay. Chemistry cannot reach nuclear energies.
Carbon dating half-life?
5730 years for carbon-14, good back tens of thousands of years.