Half-Life Calculator
Calculate radioactive decay, drug half-life, or any exponential decay. Solve for remaining amount, time elapsed, half-life, or initial amount.
Result
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Percentage Remaining
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Half-lives Elapsed
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What is Half-Life Calculator?
The half-life calculator uses the exponential decay formula N(t) = N₀ × (1/2)^(t/t½) to solve for any unknown given the other values. It applies to radioactive decay, pharmacokinetics, and any process that decreases by a constant fraction over time.
How to use
- 1 Select what you want to solve for: remaining amount, time elapsed, half-life, or initial amount.
- 2 Enter the known values in the fields that appear.
- 3 Click Calculate to get your result.
- 4 Results include the percentage remaining and number of half-lives elapsed.
- 5 Switch modes to solve for different unknowns using the same data.
Formula
Example calculation
If a substance has a half-life of 5 days and starts at 100 g, after 15 days: N = 100 × (0.5)^(15/5) = 100 × 0.125 = 12.5 g remaining (3 half-lives elapsed, 12.5% remaining).
Frequently asked questions
What is a half-life?
A half-life is the time required for exactly half of a substance to decay or be eliminated. It is constant for a given substance and independent of the initial amount.
Does half-life apply to medications?
Yes. In pharmacokinetics, drug half-life describes how long it takes the body to eliminate half of a drug dose. After 4–5 half-lives, approximately 94–97% of the drug has been cleared.
What is the difference between half-life and mean lifetime?
Half-life (t½) is when 50% remains. Mean lifetime (τ) is the average time a particle exists: τ = t½ / ln(2) ≈ 1.443 × t½.
Can this apply to population decay or investment loss?
Yes. Any process following exponential decay — including certain population models, capacitor discharge, and cooling — follows the same mathematical form.
What units should I use?
Any consistent time unit works (seconds, minutes, hours, days, years). The half-life and elapsed time must be in the same units.