CalcaTools

Half-Life Calculator

A Half-Life Calculator is a free online tool that solves radioactive decay calculator using radioactive decay calculator, exponential decay, how to calculate half-life. Students, teachers, and engineers use it to check homework, prep for exams, and verify hand calculations.

Last updated: June 2026 · Free · No sign-up required

Results

Enter values above and click Calculate to see your result instantly.

Quick reference

Half-lives elapsedFraction remaining
150%
225%
312.5%
46.25%
10≈ 0.1%

functions Shows the working, not just the answer

For students and teachers, the final number is only half the value. Every math tool here exposes the formula it applied, the intermediate steps, and the rounding rule, so you can follow along, check your homework, or use the answer in a proof or report with confidence.

calculate Accurate to the spec

Calculations use 64-bit floating point with sensible rounding for the domain (currency to 2 decimals, percentages to 4 decimals, algebra to 6 significant figures). Where exact rational arithmetic matters — fractions, factorials, simplification — we use a dedicated BigNumber path so 1/3 + 1/6 returns ½, not 0.49999.

school Free for classroom use

Educators are welcome to link to any math calculator on CalcaTools from a class site, Google Classroom, or worksheet. The pages are mobile-friendly, free, ad-supported (so we can keep them free) and have no sign-up wall — students just click and use them in class or at home.

tips_and_updates Pair with the spoke articles

Below the calculator we link a small set of plain-English explainer pages — "What is a percentage?", "Why does PEMDAS matter?", and so on. They cover the underlying concept in 4–6 short paragraphs. Read those before the calculator if the topic is new, or after if you want the extra context.

Interpretation guide

IsotopeHalf-life
Carbon-145,730 years
Iodine-1318.02 days
Uranium-2384.47 billion years
Technetium-99m6.01 hours

Formula & methodology

Formula: N = N0 x (1/2)^(t / T); T = half-life; decay constant lambda = ln(2) / T

How half-life decay is calculated

Half-life (T) is the time for a quantity to fall to half its value. After each half-life, whatever remains is halved again.

Example

Start with 80 g of a substance whose half-life is 5 years. After 15 years that is 3 half-lives: 80 → 40 → 20 → 10 g. Using the formula: N = 80 x (1/2)^(15/5) = 80 x (1/2)^3 = 80 x 0.125 = 10 g.

To find the half-life from a decay constant, T = ln(2) / lambda ≈ 0.693 / lambda. The same exponential model describes drug elimination and other first-order decay.

Frequently asked questions

What is half-life?
Half-life is the time it takes for a quantity to decrease to half its original value. After one half-life, 50% remains; after two, 25%; after three, 12.5%, and so on. It is a constant for a given substance, which is why it is used to characterize radioactive isotopes and drug elimination.
How do you calculate the remaining amount after several half-lives?
Use N = N0 x (1/2)^(t/T), where N0 is the starting amount, t is elapsed time, and T is the half-life. Divide the elapsed time by the half-life to get the number of half-lives, then halve the starting amount that many times. 80 g after 3 half-lives is 80 x 0.125 = 10 g.
How do you find the half-life from the decay constant?
The half-life T equals the natural log of 2 divided by the decay constant lambda: T = ln(2) / lambda ≈ 0.693 / lambda. Conversely, lambda = ln(2) / T. The decay constant is the probability per unit time that a given atom decays, so a larger lambda means a shorter half-life.
Does half-life depend on the starting amount?
No. Half-life is independent of how much you start with — it always takes the same time to halve, whether you begin with 1 gram or 1 kilogram. This is the defining feature of exponential (first-order) decay and is what makes carbon dating and drug dosing predictable.
How is half-life used in carbon dating?
Living things absorb carbon-14, which stops replenishing at death and decays with a 5,730-year half-life. By measuring how much carbon-14 remains compared to a living sample and applying N = N0 (1/2)^(t/T), scientists solve for t — the time since death. This reliably dates organic material up to roughly 50,000 years old.