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Half-Life Calculator | Solve half-life time or quantity

Models radioactive decay and exponential decay problems. Enter any three of the initial quantity, remaining quantity, elapsed time, and half-life, and the tool solves for the missing value using N = N0 × (1/2)^(t/T), with the working shown. Used for radiometric dating, medication dosing, and decay homework.

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.

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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.

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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

lightbulb Worked example

Let's say you are using the Half-Life Calculator. Models radioactive decay and exponential decay problems. Enter any three of the initial quantity, remaining quantity, elapsed time, and half-life, and the tool solves for the missing value using N = Enter the values that match your situation into the input fields and press calculate — using realistic numbers makes the result directly useful for you.

Result: The calculator instantly applies the formula N = N0 x (1/2)^(t / T); T = half-life; decay constant lambda = ln(2) / T and returns the result with appropriate precision.

What this means: Read the result in the context of what you are measuring. The step-by-step breakdown lets you confirm the math and understand which input most affects the outcome.

Formula & methodology

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

How half-life is calculated

The tool applies the exponential decay law N = N₀ × (1/2)^(t ÷ T), where N₀ is the initial amount, t the elapsed time, and T the half-life — the time for half the substance to decay. The decay constant λ = ln(2) ÷ T links the half-life to the exponential rate. Enter any three of the four variables and the tool solves for the missing one.

Example: a 100 mg sample of a substance with an 8-day half-life has 100 × (1/2)^(16÷8) = 25 mg remaining after 16 days — exactly two half-lives.

Reading the result: after n half-lives, 1/2ⁿ of the original remains, which is why the curve halves repeatedly rather than declining at a constant rate. Half-life math underlies radioactive dating, medical dosing, and drug elimination in pharmacology.

Authoritative source: Wolfram MathWorld

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.
What does the Half-Life Calculator do?
Models radioactive decay and exponential decay problems. Enter any three of the initial quantity, remaining quantity, elapsed time, and half-life, and the tool solves for the missing value using N = N0 × (1/2)^(t/T), with the working shown. Used for. The calculator takes your inputs, applies the standard calculation, and returns a clear result so you can make an informed decision without doing the math by hand.
What formula does the Half-Life Calculator use?
The Half-Life Calculator applies the standard formula: N = N0 x (1/2)^(t / T); T = half-life; decay constant lambda = ln(2) / T. The tool walks through each step of the calculation so you can verify the numbers yourself.
Is the Half-Life Calculator free and private?
Yes — the Half-Life Calculator. There is no sign-up, no paywall, no trial, and no limit on how many calculations you can run. CalcaTools covers its costs with non-intrusive display advertising, so the calculator itself never asks for payment or restricts any feature.
How accurate is the Half-Life Calculator?
The Half-Life Calculator applies the standard formula: N = N0 x (1/2)^(t / T); T = half-life; decay constant lambda = ln(2) / T. It is tested against published worked examples before launch and uses native double-precision arithmetic, so results are accurate to typical precision for the values you enter — with no intermediate rounding that could distort the answer.

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