Half-Life Formula Calculator
Enter a starting amount, half-life and elapsed time or target amount. See the remainder, decay table, curve and worked formula for any substance.
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Need sleep timing context? Use the caffeine half-life calculator.
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How the half life formula works
The half life formula describes how an amount falls by half during each half-life. For any starting amount, the general equation is N(t) = N0 × (1/2)^(t / t½), where t is elapsed time and t½ is the half-life.
This calculator is general enough for caffeine, medicines, chemicals and radioactive decay. Caffeine in healthy adults averages roughly 5 hours, but genetics, smoking, pregnancy, oral contraceptives and liver function can change that substantially. The sibling caffeine half-life calculator is for sleep timing; this page focuses on the general formula.
The equivalent exponential form is N(t) = N0 × e^(-λt), where λ = ln(2) / t½. After five half-lives, 3.125% remains, so about 97% is gone—the usual rule for effectively cleared.
N(t) = N0 * (1/2)^(t / t½) · t = t½ * log2(N0 / N) This calculator provides a mathematical estimate, not dosing advice or a safe-intake recommendation. Caffeine response varies, and the result should not be used to make medical decisions.
Half-life formula FAQ
What is the half life formula?
N(t) = N0 × (1/2)^(t / t½). It gives the amount N(t) remaining from starting amount N0 after time t, using half-life t½.
How do I solve for time instead?
Use t = t½ × log2(N0 / N), where N is the target amount. The target must be below the starting amount.
How much remains after five half-lives?
3.125% remains after five half-lives, meaning about 97% is gone.
What half-life should I use for caffeine?
Roughly 5 hours is an average for healthy adults, but the range is about 2 to 10 hours and can vary with genetics, smoking, pregnancy, oral contraceptives and liver function.
Does this give caffeine dosing or safety advice?
No. It only applies the decay formula. It does not recommend an intake or determine what is safe for you.