Science & Weather · Physics
Half-Life Calculator — Radioactive Decay, Remaining Amount & Carbon Dating
Solve radioactive (or any exponential) decay for the amount remaining, the starting amount, the time elapsed or the half-life. Pick a known isotope — carbon-14, iodine-131, caesium-137, uranium-238 and more — or enter your own half-life, and see the decay constant, mean lifetime and a half-life-by-half-life table. Works for drug elimination half-lives too.
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Your inputs
Quick start — try a typical case
Your result Live
Amount Remaining
29.6399
29.64% left after 1.754 half-lives
- Fraction Remaining
- 0.296399 (29.64%)
- Decay Constant (λ)
- 3.8534 × 10⁻¹² per second · 0.0001216 per year
- Mean Lifetime (τ = T ÷ ln 2)
- 8,223.4 years
Half-life by half-life
11 rowsHow this is calculated
N = N₀ × (½)^(t ÷ T) · t = T × log₂(N₀ ÷ N) · λ = ln 2 ÷ T · τ = T ÷ ln 2
- T
- Half-life
- λ
- Decay constant
- τ
- Mean lifetime
In each half-life, half of what's left decays. After t, the fraction remaining is ½ raised to the number of half-lives, t ÷ T. Turning that around gives the elapsed time — how carbon dating works: if 25 % of the original carbon-14 remains, two half-lives (about 11,400 years) have passed.
Assumptions & sources
- Pure exponential decay with a constant half-life; no ongoing production of the substance.
- 1NuDat 3 — nuclear structure and decay data (half-lives) — National Nuclear Data Center, Brookhaven National Laboratory
- 2Radioactivity and half-life — NCERT Physics, Class 12 — Nuclei
Calculator ID SCI-HALFLIFE-001 · version 1.0.0
Common questions
How much is left after 3 half-lives?
One-eighth (12.5 %): ½ × ½ × ½.
How old is a sample with 25 % of its carbon-14 left?
Two half-lives: 2 × 5,700 = 11,400 years (older textbooks use 5,730 years, giving 11,460).
Can I use this for medicines?
Yes — drug elimination often follows the same rule. Enter the drug's half-life and the dose to see how much remains over time.