Half-Life Calculator
Calculate the remaining amount of a radioactive substance after a given time using the half-life decay formula. Also find elapsed time or half-life.
Remaining Amount
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Percent Remaining —
Half-Lives Elapsed —
Elapsed Time —
Half-Life —
How to Use This Calculator
- Select what to solve for: Remaining Amount, Elapsed Time, or Half-Life.
- Enter the initial amount, half-life, and elapsed time (or the two known values).
- Results show remaining amount, percentage remaining, and number of half-lives elapsed.
Formula
N = N₀ × (½)^(t ÷ t½)
t = t½ × log(N₀ ÷ N) ÷ log(2)
t½ = t × log(2) ÷ log(N₀ ÷ N)
Example
Example: N₀ = 100 g, t½ = 5,730 yr, t = 11,460 yr → N = 25 g (25% remaining, 2 half-lives).
Frequently Asked Questions
- A half-life is the time it takes for half of a radioactive substance to decay. After one half-life, 50% remains; after two, 25%; after three, 12.5%.
- Carbon-14 (¹⁴C) has a half-life of 5,730 years, which makes it useful for dating organic materials up to ~50,000 years old.
- Use N = N₀ × (1/2)^(t/t½), where N₀ is initial amount, t is elapsed time, and t½ is the half-life.
- After 10 half-lives, only 0.097% remains. After 20 half-lives, 0.000095%. Practically, 7–10 half-lives is considered safe for radioactive materials.
- Yes — use t = t½ × log(N₀/N) ÷ log(2). The calculator solves this when you select "solve for time".