The time required for half of a substance to decay or be eliminated. After one half-life, 50% remains; after two, 25%; after three, 12.5%.

Does half-life apply to medicine?

Yes. The biological half-life of a drug is the time for its concentration in the body to reduce by half, determining dosing intervals.

What is the decay constant?

λ = ln(2) / t₁/₂ ≈ 0.693 / t₁/₂. It describes the fraction of atoms that decay per unit time.

Half-Life Calculator

Use this half-life calculator to model exponential decay: find the remaining quantity N(t), back-calculate the half-life t₁/₂, or determine the elapsed time for a substance to reach a target level.

How to use this calculator

Select what you want to find: remaining amount, half-life, or elapsed time.
Enter the known values in the visible fields.
Read the result along with the decay constant λ and number of half-lives elapsed.

Formula & method

Exponential half-life decay formula

N(t) = N₀ × (½)^(t/t₁/₂) · t₁/₂ = t × ln(2) / ln(N₀/N(t)) · λ = ln(2) / t₁/₂

N₀ = initial amount, N(t) = remaining at time t, t₁/₂ = half-life, λ = decay constant.

Example

N₀ = 100, t₁/₂ = 5, t = 15 → 3 half-lives → N(15) = 100 × (1/2)³ = 12.5.

Key insights

After each half-life, exactly 50% of the substance remains: 100 → 50 → 25 → 12.5.
The decay constant λ = ln(2) / t₁/₂ — it represents the probability of decay per unit time.
Carbon-14 has a half-life of 5,730 years — the basis of radiocarbon dating.
Pharmaceuticals use half-life to schedule dosing: a drug with t₁/₂ = 6 hours needs re-dosing every 6–12 hours.

How to interpret your result

Exponential decay

N(t) = N₀ × (1/2)^(t/t₁/₂). After n half-lives, only N₀/2ⁿ remains.

Decay constant λ

λ = ln(2) / t₁/₂ ≈ 0.693 / t₁/₂. Larger λ means faster decay.

Frequently asked questions

What is half-life?: The time required for half of a substance to decay or be eliminated. After one half-life, 50% remains; after two, 25%; after three, 12.5%.
Does half-life apply to medicine?: Yes. The biological half-life of a drug is the time for its concentration in the body to reduce by half, determining dosing intervals.
What is the decay constant?: λ = ln(2) / t₁/₂ ≈ 0.693 / t₁/₂. It describes the fraction of atoms that decay per unit time.

Related calculators

Exponent Calculator — Calculate bᵉ for any base and exponent — positive, negative, or fractional — with scientific notation and exponent rules.
Log Calculator — Calculate common log (log₁₀), natural log (ln), binary log (log₂) and any custom base logarithm for any positive number.
Scientific Notation Calculator — Convert any number to scientific notation and perform arithmetic (add, subtract, multiply, divide) on numbers in scientific notation.

See all math calculators · Explore all online calculators