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N = N₀ × (½)^(t ÷ t½)

Half life calculator

Give a starting amount, a half-life and an elapsed time to see what is left, how many half-lives have passed and the decay constant.

Short answer: 100 units with a 5-unit half-life after 15 units of time is12.5 — three half-lives, so 12.5% remains. The decay constant is 0.1386 per unit time.

Half-lives, not line, not linear

Decay looks like a curve that never quite reaches zero. After ten half-lives about 0.1% is left, and after twenty about 0.0001% — which is why "it will still be slightly radioactive" stays true long after the amount has become negligible in practice.

Worked example

A drug with a 6-hour half-life given as 500 mg: after 24 hours four half-lives have passed and 500 × (½)⁴ = 31.25 mg remains. That is the arithmetic behind a four-times-a-day dosing schedule.

Half-life questions

What does half-life mean?

The time for half of a quantity to decay or be eliminated. After one half-life 50% remains, after two 25%, after three 12.5% — it is always half of what is left, never half of the original.

What is the formula?

N = N₀ × (½)^(t ÷ t½). The page also computes the decay constant λ = ln 2 ÷ t½, so the same answer can be written N = N₀ e^(−λt), which is the form used in exponential decay problems.

Does it matter whether the half-life is in seconds or years?

No, as long as the elapsed time uses the same unit. The ratio t ÷ t½ is dimensionless, so 5 hours with a 1-hour half-life behaves exactly like 5 years with a 1-year half-life.

Where is this used outside physics?

Drug elimination (a drug’s half-life sets the dosing interval), carbon dating, and radioactive waste management. The same equation governs any first-order decay process.

Related tools

Logarithm calculatorThe logarithms behind exponential decay.Compound interest calculatorThe same curve, growing instead of falling.Molarity calculatorConcentration of the sample being measured.