Pharmacokinetics
Half-Life Calculator
Works out a drug's elimination half-life (t½) from kₑ, from clearance and volume of distribution, or from two measured concentrations.
Elimination half-life (t½)
6.93hours
Intermediate half-life - once or twice daily dosing
Inputs
The fraction of drug eliminated per hour, e.g. 0.1 h⁻¹.
The unit the half-life is reported in.
Try an example drug
Working
Elimination pattern
Drug remaining after each half-life.
t½ = 0.693 ÷ kₑ
kₑ = Cl ÷ Vd → t½ = 0.693 × Vd ÷ Cl
kₑ = [ln(C₀) − ln(Cₜ)] ÷ t → t½ = 0.693 × t ÷ ln(C₀/Cₜ)
kₑ (elimination rate constant) is the fraction of drug removed per unit time, in time⁻¹ (h⁻¹). Cl (clearance) is the volume of plasma cleared per unit time (L/h), independent of concentration for first-order kinetics. Vd (volume of distribution) is an apparent, theoretical volume (Vd = Dose ÷ C₀ = Cl ÷ kₑ), not a physiological one.
0.693 is ln 2. Because elimination is exponential, the same fraction of drug is removed in every half-life — 50%, then 25%, 12.5%, and so on.
Keep learning
References
- Ducharme MP, Shargel L, editors. Shargel and Yu's Applied Biopharmaceutics & Pharmacokinetics. 8th ed. New York: McGraw Hill; 2022.
- Rowland and Tozer's Clinical Pharmacokinetics and Pharmacodynamics: Concepts and Applications. 5th ed. Philadelphia: Wolters Kluwer; 2019.
Common questions
Drug sitting in tissues is not in the plasma passing through the liver and kidneys. With the same clearance, a larger volume means a smaller fraction of the body's drug is cleared each hour, so t½ = 0.693 × Vd ÷ Cl gets longer.
No, as long as C₀ and Cₜ are in the same unit. The formula uses their ratio, so the unit cancels out.
Both after distribution is complete (in the elimination phase) and ideally at least one half-life apart. Samples too close together magnify assay error.
About 3.3 half-lives removes 90% and about 6.6 removes 99%. For practical purposes a drug is considered eliminated after 4–5 half-lives (≈94–97%).
Prepared by the PharmaWallah student team. Verify results with your textbook or instructor. Report an error · Editorial policy