Half-Life Calculator
Calculate remaining amount, half-life, elapsed time, or initial amount in radioactive decay.
Written by Golam Rabbani, Founder & Lead Engineer
How to use this half-life calculator
- Pick which quantity you want to solve for: remaining amount, half-life, elapsed time, or initial amount.
- Choose a time unit label (seconds, minutes, hours, days, or years) — all four fields use the same unit.
- Fill in the three known values. The tool hides the field you are solving for.
- Press Calculate to see remaining amount, decay constant λ, and the percent left.
About this half-life calculator
The half-life calculator solves the textbook exponential-decay equation N(t) = N₀ × (1⁄2)^(t ⁄ t½), where N₀ is the starting amount, N(t) is what is left at time t, and t½ is the half-life. There are four interlinked quantities: N₀, N, t, and t½. Give the tool any three and it computes the fourth using a rearranged form: t½ = t · ln 2 ⁄ ln(N₀ ⁄ N), or t = t½ · ln(N₀ ⁄ N) ⁄ ln 2. It also returns the decay constant λ = ln 2 ⁄ t½ — useful for first-order rate laws and pharmacokinetics.
Worked example: Carbon-14 has a half-life of 5,730 years. A wood sample today contains 25% of the C-14 it had when the tree was alive. How old is it? Set N₀ = 100, N = 25, t½ = 5730 years, solve for t. The math: t = 5730 × ln(100⁄25) ⁄ ln 2 = 5730 × ln 4 ⁄ ln 2 = 5730 × 2 = 11,460 years. Two half-lives have passed (100 → 50 → 25). The tool also reports λ = 0.000121 per year. Same equation, different domain: a drug with a 6-hour plasma half-life will fall from 500 mg to roughly 31 mg after 24 hours (four half-lives: 500 → 250 → 125 → 62.5 → 31.25).
FAQ
- What is a half-life?
- The time required for half of a quantity to decay. After one half-life 50% remains; after two, 25%; after n, (1/2)ⁿ × N₀.
- What is the decay constant λ?
- λ = ln 2 ⁄ t½. It is the per-unit-time decay rate in dN/dt = −λN — the rate the substance is disappearing at any instant.
- Does the calculator work for drugs, radioactive isotopes, and chemical reactions?
- Yes — any first-order exponential decay process follows the same equation. The tool lets you pick the time-unit label so years (radioisotopes), hours (drugs), or seconds (fast reactions) all work.
- Can it solve for more than one unknown?
- No — you must know three of the four quantities. With only two known, the system has infinitely many solutions.
- How does it handle very long half-lives?
- It uses JavaScript double-precision floats, which give 15–16 significant digits — enough for U-238 (4.5 billion years) and any practical isotope.
- Is the half-life calculator free?
- Yes — free, no signup, runs entirely in your browser.