Half-Life Calculator (Pharmacokinetics)
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/5/2026
The amount of a substance remaining is calculated with initial dose × 0.5^(elapsed time ÷ half-life). For a 500 mg dose with a 4-hour half-life, after 8 hours (two half-lives), about 125 mg remains.
Explanation
A substance's biological half-life (a drug, a hormone, any molecule eliminated by the body) is the time needed for the amount present in the body to be cut in half, under the most common first-order elimination model, where the elimination rate is proportional to the amount remaining. This model produces a characteristic exponential decay: after one half-life, 50% of the initial dose remains; after two half-lives, 25% (half of half); after three, 12.5%, and so on, never reaching exactly zero in this theoretical model, with the remaining amount approaching zero asymptotically. It's the exact same mathematical principle as the exponential growth or decay found elsewhere in science (see our doubling time calculator for the reverse phenomenon, growth), applied here to the elimination of a substance. Half-life varies enormously by substance: from a few minutes for some molecules to several days, or more, for others. This calculator gives a theoretical estimate for informational and educational purposes, based on a simplified mathematical model: the actual pharmacokinetics of a drug in a given person can be more complex (multiple elimination phases, the influence of kidney or liver function, interactions with other substances), and this calculation should never be used to determine a dosage or dosing interval, a decision that belongs exclusively to a healthcare professional or the medication's official label.
Example: a 500 mg dose, 4-hour half-life, after 8 hours
Inputs
Initial dose: 500 mg. Half-life: 4 hours. Elapsed time: 8 hours.
Calculation
8 hours represents exactly 2 half-lives (8 ÷ 4 = 2). Amount remaining = 500 × 0.5² = 500 × 0.25 = 125 mg.
Result
After 8 hours, about 125 mg remains, or 25% of the initial dose.
Frequently asked questions
Why does the amount remaining never reach exactly zero in this model?
Because exponential decay reduces the remaining amount by the same proportion at each equal time interval, never bringing it fully to zero in the theoretical model: after enough half-lives (generally 5 to 7 in practice), the remaining amount becomes so small it's considered negligible or undetectable, even though it's mathematically never exactly zero.
Can this calculation be used to decide when to take another dose?
No, this calculator gives a theoretical, informational estimate based on a simplified mathematical model, not a basis for deciding a dosing interval or dosage. The actual pharmacokinetics of a drug in a given person is influenced by many individual factors (kidney function, liver function, age, drug interactions): only a healthcare professional or the medication's official label should guide that kind of decision.
Do all substances follow this simple exponential decay model?
No, this model (called first-order, single-phase) is a simplification that fits many substances well, but some follow more complex pharmacokinetics, with multiple elimination phases at different rates, or elimination that isn't exactly proportional to the amount remaining (so-called saturation elimination, less common). This calculator assumes the simple, most widespread model.