Half-Life Calculator
Adjust the inputs below. Results update as you type.
How it works
Remaining = initial × (1/2)^(t/t½), or equivalently initial × e^(−λt) where λ = ln(2)/t½. After n half-lives, (1/2)^n of the original remains. Carbon-14 has a 5,730-year half-life (used in radiocarbon dating). Ibuprofen's half-life is ~2 hours (5 doses ≈ 97% eliminated). Half-life is constant regardless of starting quantity—a key property of first-order processes.
Input guidance
- Check units and decimal placement before running calculations.
- For percentage and ratio tasks, define the baseline value clearly.
- Use rounded output carefully and keep full precision for intermediate steps.
The formula
Remaining amount = initial × (1/2)^(t ÷ half-life). After each half-life, half of the substance remains; the decay is exponential.
Worked example
A substance with a 5-year half-life starting at 100 g leaves 50 g after 5 years, 25 g after 10, and 12.5 g after 15.
More examples to test
- Baseline example: solve with clean numbers first to verify formula direction.
- Edge-case example: test near-zero or boundary values to avoid interpretation errors.
How to interpret results
Use outputs as quick checks, then verify with step-by-step work for graded or high-stakes use.
When this can be inaccurate
Errors usually come from unit mismatch, wrong baseline assumptions, or rounding too early in multistep problems.
Change history
- July 2026: Quality-reviewed for publication with formula checks and explanatory copy updates.
Site-wide corrections also appear on the corrections log.
Build math and logic skills with guided lessons
Educational platform recommendation.
Frequently asked questions
What is a half-life?+
The time it takes for half of a quantity (like a radioactive isotope or a drug in the body) to decay or be eliminated.
How many half-lives until it's gone?+
It approaches zero but never fully reaches it. After about 7 half-lives, less than 1% of the original remains.
Is decay the same as linear?+
No. It is exponential — a fixed fraction is lost each period, not a fixed amount, so the absolute loss slows over time.
Why do my classroom and calculator results differ?+
Differences usually come from rounding conventions, order-of-operations handling, or different baseline assumptions.
What is the safest way to validate an answer?+
Recompute with units shown and check against a second method or manual arithmetic for critical problems.