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Half Life

The Half-Life Calculator computes radioactive decay, biological half-lives, and any exponential decay problem. Enter the initial quantity, half-life period, and elapsed time to find the remaining amount — or enter any three variables to solve for the fourth. Used in nuclear physics, pharmacology, environmental science, and carbon dating calculations.

Remaining Quantity

% Remaining:
% Decayed:
Half-lives elapsed:
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Science

About the Half-Life Calculator

The Half-Life Calculator computes radioactive decay, biological half-lives, and any exponential decay problem. Enter the initial quantity, half-life period, and elapsed time to find the remaining amount — or enter any three variables to solve for the fourth. Used in nuclear physics, pharmacology, environmental science, and carbon dating calculations.

How to use it

  1. Enter the initial quantity (atoms, mass, concentration).
  2. Enter the half-life duration and its unit (seconds, days, years).
  3. Enter the elapsed time.
  4. See the remaining quantity and percentage remaining.

Formula & methodology

N(t) = N0 * (1/2)^(t/t_half). Or equivalently: N(t) = N0 * e^(-lambda * t). Where lambda = ln(2) / t_half = 0.693 / t_half. Remaining percentage: (N/N0) * 100. Half-lives elapsed: n = t / t_half. After n half-lives: N = N0 * (1/2)^n. Time for given remaining: t = t_half * log2(N0/N).

Common use cases

  • Nuclear physics: calculating radioactive decay of isotopes
  • Pharmacology: drug elimination half-life and dosing intervals
  • Carbon-14 dating: estimating age of organic materials
  • Nuclear medicine: calculating isotope activity for imaging or therapy
  • Environmental science: decay of radioactive contaminants

Frequently asked questions

Carbon-14 has a half-life of 5,730 years. Living organisms constantly exchange carbon with the atmosphere, maintaining a stable C-14 ratio. At death, no new C-14 is absorbed. The C-14 decays at a known rate. By measuring the remaining C-14 vs stable C-12 ratio and comparing to atmospheric reference, age is calculated: t = -t_half / ln(2) * ln(N/N0). Reliable for materials up to ~50,000 years old (after which C-14 becomes undetectable).
Physical half-life: the time for a radioactive isotope to decay by half (purely nuclear physics). Biological half-life: the time for a substance to be eliminated from a biological organism by half (metabolism, excretion). Effective half-life: combines both — the actual decay in the body = (physical * biological) / (physical + biological). Used in nuclear medicine dosing. A drug with a 6-hour biological half-life is mostly eliminated after 5-6 half-lives (~30-36 hours).

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