Half Life Calculator · Practical guide
How Much Remains After 3 Half-Lives?
Each half-life halves what is left — so after three, one eighth (12.5%) of the original amount remains.
At a glance
The Short Answer
After 3 half-lives, 12.5% of the original quantity remains — one eighth of it. Each half-life halves the remainder: 100% → 50% → 25% → 12.5%.
Interactive tool
Half Life Calculator
Enter your own values, then compare the result with the examples below.
Result
Percentage Remaining by Half-Lives
| Half-Lives Passed | Fraction Left | Percent Remaining |
|---|---|---|
| 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% |
Worked Example
A lab holds 80 mg of an isotope with a half-life of 6 hours. After 18 hours — exactly 3 half-lives — the sample holds 80 × (0.5)³ = 10 mg, with 70 mg (87.5%) decayed. Enter 80 mg, a 6-hour half-life, and 18 elapsed hours in the calculator above to confirm all four outputs: remaining, decayed, percentage, and half-lives passed.
How Long Until a Substance Is Effectively Gone?
Radioactive material is often treated as negligible after about 7 half-lives (under 1% left) and essentially gone after 10 half-lives (about 0.098% left). For a substance with a 5-year half-life, that is 35 to 50 years; for one with a 30-year half-life, two to three centuries.
Frequently Asked Questions
What fraction remains after 4 half-lives?
One sixteenth, or 6.25%. Every additional half-life halves the previous remainder, so 12.5% after three becomes 6.25% after four.
What if the elapsed time is not a whole number of half-lives?
Use the formula remaining = initial × (0.5)^(elapsed ÷ half-life). After 1.5 half-lives, for example, (0.5)^1.5 ≈ 0.354, so about 35.4% remains.
Does the decayed amount equal the initial minus the remaining?
Yes. Decayed + remaining always equals the starting quantity, so if 12.5% remains, 87.5% has decayed.
Why do some sources say 10 half-lives means 'gone'?
After 10 half-lives only about 0.1% remains — below measurement or safety thresholds for most practical purposes, though never mathematically zero.