Half-Life Calculator

Enter your initial quantity (N₀), elapsed time (t), and half-life (T½) to calculate the remaining quantity after radioactive decay. You can also solve for any unknown — find the half-life, decay constant (λ), or mean lifetime (τ) from the values you know. Results update automatically using the standard half-life formula: N(t) = N₀ × 0.5^(t/T½).

The starting amount of the substance (any unit — grams, moles, atoms, etc.)

The amount of time that has passed since the initial measurement.

The time required for the quantity to reduce to half its initial value.

Results

Remaining Quantity N(t)

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Percentage Remaining

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Percentage Decayed

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Decay Constant (λ)

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Mean Lifetime (τ)

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Number of Half-Lives Elapsed

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Results Table

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Frequently Asked Questions

What is half-life?

Half-life is the time required for a quantity to reduce to exactly half its initial value. It is most commonly used to describe the rate of radioactive decay of unstable atomic nuclei, but the concept also applies to drug elimination, chemical reactions, and other exponential processes.

What is the half-life formula?

The standard half-life formula is N(t) = N₀ × 0.5^(t/T½), where N₀ is the initial quantity, t is the elapsed time, T½ is the half-life, and N(t) is the remaining quantity at time t. From this formula you can derive the decay constant λ = ln(2) / T½ and the mean lifetime τ = T½ / ln(2).

How do I calculate the half-life if I know the initial and remaining quantities?

Rearranging the half-life formula gives T½ = t × ln(2) / ln(N₀ / N(t)). Simply enter the initial quantity, remaining quantity, and elapsed time into any half-life solver and it will compute T½ directly. This approach is used in carbon-14 dating to determine the age of organic materials.

What is the half-life of carbon-14?

Carbon-14 has a half-life of approximately 5,730 years. This makes it ideal for dating organic material up to around 50,000 years old — beyond that, the remaining carbon-14 becomes too small to measure reliably. The technique was developed by William Libby and is widely used in archaeology and geology.

What is the half-life of uranium?

There are several uranium isotopes with different half-lives. Uranium-238, the most abundant isotope, has a half-life of about 4.47 billion years. Uranium-235 has a half-life of roughly 704 million years, and Uranium-233 has a half-life of approximately 160,000 years.

What is the difference between decay constant and mean lifetime?

The decay constant (λ) represents the probability per unit time that an atom will decay — a higher λ means faster decay. Mean lifetime (τ), also called average lifetime, is the average time a single atom survives before decaying. They are related by τ = 1/λ = T½ / ln(2) ≈ 1.4427 × T½.

How is half-life used in medicine?

In pharmacology, drug half-life describes how long it takes the body to eliminate half of an administered dose. This helps doctors determine dosing intervals and estimate how long a drug remains active in the bloodstream. Most drugs require about 4–5 half-lives to be considered fully eliminated from the body.

Does half-life depend on the amount of substance present?

No — for radioactive decay and first-order chemical processes, the half-life is a constant that does not depend on the initial quantity. Whether you start with 1 gram or 1 kilogram of a substance, it will always take the same amount of time for half of it to decay.