How do I use the Half-Life Calculator?

Enter the required values, then calculate. The Half-Life Calculator shows results, formulas, and step-by-step work when available. No account is required.

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How it works

Uses N_t = N₀·(1/2)^(t/t½) = N₀·e^(−λt). Constants: t½ = ln(2)·τ = ln(2)/λ.

N_t = N₀ · (1/2)^(t / t½)

When to use

Use this tool when you need to: decay: leave one blank. Example C-14: N₀=100, N_t=25, t½=5730 → t≈11460. Constants: enter only t½, τ, or λ.

How to use this tool

Enter your values in the fields above.
Review the formula and any mode options for your problem.
Read the result and the step-by-step solution.

Decay: leave one blank. Example C-14: N₀=100, N_t=25, t½=5730 → t≈11460. Constants: enter only t½, τ, or λ.

Frequently asked questions

What is the Half-Life Calculator?: Uses N_t = N₀·(1/2)^(t/t½) = N₀·e^(−λt). Constants: t½ = ln(2)·τ = ln(2)/λ.
How do I use the Half-Life Calculator?: Enter the required values, then calculate. The Half-Life Calculator shows results, formulas, and step-by-step work when available. No account is required.
What formula does the Half-Life Calculator use?: N_t = N₀ · (1/2)^(t / t½)

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Half-life calculator

Generate any one of N₀, N_t, t, or t½ from the other three in the exponential decay formula — or convert among half-life, mean lifetime τ, and decay constant λ.

How it works

What is half-life?

Half-life is the amount of time it takes a given quantity to decrease to half of its initial value. The term is most commonly used for atoms undergoing radioactive decay, but also describes many other exponential declines. A well-known application is carbon-14 dating. The half-life of carbon-14 is about 5,730 years, and it can measure dates up to roughly 50,000 years. After an organism dies, ¹⁴C decays and the remaining fraction reveals elapsed time.

Definition and formulas

Three equivalent formulas describe exponential decay: N_t = N₀ · (1/2)^(t / t½) N_t = N₀ · e^(−t / τ) N_t = N₀ · e^(−λ t) where N₀ is the initial quantity, N_t the remaining quantity after time t, t½ the half-life, τ the mean lifetime, and λ the decay constant.

Solving for time (carbon-14 example)

If a fossil sample contains 25% of the carbon-14 of a living sample, and t½ ≈ 5,730 y: t = t½ · ln(N_t/N₀) / ln(1/2) t = 5730 · ln(0.25) / ln(0.5) = 11,460 years That age equals exactly two half-lives, since (1/2)² = 1/4.

Half-life, mean lifetime, and decay constant

These three quantities are interchangeable: t½ = ln(2) · τ = ln(2) / λ τ = t½ / ln(2) = 1 / λ λ = ln(2) / t½ = 1 / τ Enter any one in the constants mode to obtain the other two.

Related calculators

Logs and exponents underpin the rearrangements used in half-life algebra; the scientific calculator evaluates more general expressions.

How it works

Uses N_t = N₀·(1/2)^(t/t½) = N₀·e^(−λt). Constants: t½ = ln(2)·τ = ln(2)/λ.

N_t = N₀ · (1/2)^(t / t½)

When to use

Use this tool when you need to: decay: leave one blank. Example C-14: N₀=100, N_t=25, t½=5730 → t≈11460. Constants: enter only t½, τ, or λ.

How to use this tool

Enter your values in the fields above.
Review the formula and any mode options for your problem.
Read the result and the step-by-step solution.

Decay: leave one blank. Example C-14: N₀=100, N_t=25, t½=5730 → t≈11460. Constants: enter only t½, τ, or λ.

Frequently asked questions

What is the Half-Life Calculator?: Uses N_t = N₀·(1/2)^(t/t½) = N₀·e^(−λt). Constants: t½ = ln(2)·τ = ln(2)/λ.
How do I use the Half-Life Calculator?: Enter the required values, then calculate. The Half-Life Calculator shows results, formulas, and step-by-step work when available. No account is required.
What formula does the Half-Life Calculator use?: N_t = N₀ · (1/2)^(t / t½)

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