☢️ Half-Life Calculator (Radioactive Decay)
Work with exponential decay: enter three of initial amount, remaining amount, elapsed time and half-life to find the fourth.
Elapsed time (t)
11460 time
Radioactive decay: N = N₀ · (½)^(t / t½). Use the same time unit for t and the half-life. 🔒 Computed in your browser.
How the half-life calculator (radioactive decay) works
Radioactive decay follows N = N₀ · (½)^(t/t½), where N₀ is the initial amount, N the amount remaining after time t, and t½ the half-life. Enter any three and the tool solves for the fourth; keep the elapsed time and half-life in the same unit. Equivalently, the number of half-lives elapsed is n = t/t½ and the fraction remaining is (½)ⁿ, while solving for time uses t = t½·log₂(N₀/N).
From carbon-14 dating to dosimetry: after one half-life, half remains; after two, a quarter; after n, (½)ⁿ. Works for any first-order decay, not just nuclear.
Frequently asked questions
What is a half-life?
The time for half of a decaying substance to be gone. After each half-life the amount halves: 100 → 50 → 25 → 12.5, and so on.
How do I calculate how much remains?
N = N₀ · (½)^(t/t½). Enter the initial amount, elapsed time and half-life (same time unit for both), and the tool gives what remains.
How do I find the age from remaining amount?
Solve for t: t = t½ · log₂(N₀/N). With carbon-14 (t½ ≈ 5730 years), 25% remaining gives an age of two half-lives ≈ 11,460 years.
Can I find the half-life itself?
Yes, given the initial and remaining amounts and the elapsed time, the tool solves t½ = t / log₂(N₀/N).
Does this work for non-radioactive decay?
Yes, any first-order (exponential) decay with a constant half-life follows the same equation, such as drug elimination described by a biological half-life.
How much of a sample remains after 3 half-lives?
(½)³ = 1/8, or 12.5%. After 4 half-lives it is 1/16 (6.25%). Each half-life multiplies what is left by one half.
How is half-life related to the decay constant?
By t½ = ln 2 ÷ λ ≈ 0.693/λ, where λ is the first-order rate constant. A larger λ (faster decay) means a shorter half-life.
How long until a sample decays to 10% of its original amount?
Solve t = t½ · log₂(N₀/N) with N₀/N = 10: log₂(10) ≈ 3.32, so it takes about 3.32 half-lives. For a 6-hour half-life that is roughly 20 hours.
Why does a radioactive sample never reach exactly zero?
Decay is exponential, so each half-life removes half of what remains, not a fixed amount. The quantity approaches zero but never mathematically reaches it, which is why decay is described by half-lives rather than a fixed lifetime.