Half-Life Calculator
Choose what to solve for, then enter the known values to calculate first-order decay - used for radioactive decay and first-order chemical reaction kinetics.
Last updated: September 22, 2026
Frequently asked questions
What is the formula for first-order half-life?
Half-life = ln(2) / k, where k is the rate constant. Equivalently, k = ln(2) / half-life. This applies to both radioactive decay and first-order chemical reaction kinetics.
How much of a substance remains after several half-lives?
N(t) = N₀ × (1/2)^(t / half-life). After 1 half-life, 50% remains; after 2, 25%; after 3, 12.5% - each half-life cuts the remaining amount in half, regardless of the starting amount.
How much of 100 units remains after 25 time units, with a half-life of 10?
About 17.7 units (17.7% of the original) - 100 × (1/2)^(25/10) = 100 × 0.5^2.5 ≈ 17.68.
Does this apply to both radioactive decay and chemical reactions?
Yes, for first-order processes - radioactive decay is inherently first-order, and many chemical reactions (where the rate depends on the concentration of a single reactant) follow the same exponential decay math.
Can I find the half-life if I know the rate constant instead?
Yes - use the same relationship rearranged: half-life = ln(2) / k. If a reaction has a rate constant k = 0.0231 per year, its half-life is ln(2) / 0.0231 ≈ 30 years.
How long until only 5% of a substance remains?
About 4.32 half-lives - solve (1/2)^n = 0.05 for n, which gives n = ln(0.05) / ln(0.5) ≈ 4.32. Multiply that by the half-life to get the elapsed time.
Is half-life the same as the average lifetime of a particle?
No - the mean lifetime (often called τ) is 1/k, which is longer than the half-life. Half-life = ln(2) × mean lifetime ≈ 0.693 × mean lifetime, since half-life measures when half the population has decayed, not the average time any single particle survives.