Calculating your quantity remaining is straightforward once you know the Half Life formula and what each input means. This guide explains the method in plain language, walks through a manual calculation, and gives worked examples you can follow — then you can do it instantly with the Half Life Calculator.
What is Half Life?
The Half Life calculation tells you your quantity remaining from a few simple inputs. The figure you are solving for here is the quantity remaining.
The Half Life formula
The core formula is:
Quantity remaining = Initial quantity × (0.5)^(Elapsed time ÷ Half-life)Here is what each input means:
- Initial quantity — a number. Example: 100.
- Half-life — a number. Example: 5.
- Elapsed time — a number. Example: 10.
How to calculate it step by step
- Write down the initial quantity (for example, 100).
- Write down the half-life (for example, 5).
- Write down the elapsed time (for example, 10).
- Apply the formula above to get your quantity remaining.
- Double-check the result with the Half Life Calculator.
Worked examples
Example 1
| Input / Output | Value |
|---|---|
| Initial quantity | 100 |
| Half-life | 5 |
| Elapsed time | 10 |
| Quantity remaining | 25.0000 |
| Number of half-lives | 2.00 |
With initial quantity of 100, half-life of 5 and elapsed time of 10, the quantity remaining works out to 25.0000.
Example 2
With initial quantity of 200, half-life of 5 and elapsed time of 10, the quantity remaining works out to 50.0000.
| Result | Value |
|---|---|
| Quantity remaining | 50.0000 |
| Number of half-lives | 2.00 |
Example 3
With initial quantity of 50, half-life of 5 and elapsed time of 10, the quantity remaining works out to 12.5000.
| Result | Value |
|---|---|
| Quantity remaining | 12.5000 |
| Number of half-lives | 2.00 |
Tips for an accurate result
- Keep your units consistent — mixing, say, months with years or grams with kilograms is the most common source of error.
- Round only at the very end. Rounding inputs early can shift the final answer noticeably.
- Re-run the numbers whenever an input changes, rather than estimating from an old result.
Prefer not to do the maths by hand? — the Half Life Calculator does it instantly, for free, with the formula and a worked example built in.
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