Half-Life Calculator
Enter a starting amount, a half-life, and how much time has passed to see how much of a decaying substance remains — and what fraction of the original it is.
Amount and percentage at once
Enter the initial amount, the half-life, and the elapsed time and the calculator returns the remaining quantity and the fraction still present as a percentage.
Use one time unit
The half-life and the elapsed time must share the same time unit — both in years, or both in hours — so their ratio is correct.
What is half-life?
The time it takes to halve
A half-life is the time it takes for half of a quantity to decay or be removed. Starting from an initial amount N₀, after one half-life half remains, after two half-lives a quarter remains, and after three an eighth — the amount keeps halving on every interval. The half-life calculator turns three numbers, the initial amount, the half-life, and the elapsed time, into the remaining quantity and the fraction of the original still present. It is the maths behind carbon-14 dating, the clearance of a drug from the bloodstream, and the decay of any radioactive isotope.
Enter an initial amount, a half-life, and the time elapsed to get the remaining quantity and the percentage still present instantly.
The remaining quantity is the initial amount multiplied by one half raised to the number of half-lives that have passed, and the fraction remaining is that decay factor expressed as a percentage.
N = N₀ × (½)^(t / t½)The exponent t / t½ is simply how many half-lives have elapsed — it does not have to be a whole number. Because the half-life and the elapsed time appear only as a ratio, their units cancel, so any consistent time unit works as long as both use the same one. The fraction remaining, (½)^(t / t½) × 100, is the same percentage whether you started with one gram or one thousand.
Suppose you start with 100 g of carbon-14, whose half-life is 5730 years, and 5730 years pass.
Count the half-lives
t / t½ = 5730 ÷ 5730 = 1 — exactly one half-life has elapsed.
Apply the decay factor
(½)^1 = ½ = 0.5 — half of the original is left.
Multiply by the initial amount
100 × 0.5 = 50 — the remaining quantity. The fraction remaining is 0.5 × 100 = 50%.
The formula is exact for ideal exponential decay, but a couple of practical points are worth keeping in mind.
Consistent units and ideal decay
Keep the half-life and the elapsed time in the same unit — mixing years with days makes the ratio meaningless and the answer wrong. The model assumes pure exponential decay with a constant half-life, so it does not capture decay chains where one isotope feeds another, biological processes that vary with dose, or any situation where the half-life itself changes over time.