Drug Half-Life Calculator
Calculate the elimination half-life (t½) and elimination rate constant (kₑ) of a drug from two concentration measurements at different time points.
Drug Half-Life Calculator
intermediateCalculate elimination half-life and rate constant from concentration data
Formula
t½ = -ln(2) × t / ln(Cₜ/C₀)
How It Works
The elimination half-life is the time required for a drug's concentration in the body to decrease by half. It is a fundamental pharmacokinetic parameter used to determine dosing intervals and time to steady state.
Formulas:
kₑ = ln(C₀/Cₜ) / t
t½ = ln(2) / kₑ = 0.693 / kₑ
Step-by-step: (1) Calculate the elimination rate constant kₑ from the natural log of the concentration ratio divided by time. (2) Calculate half-life as ln(2)/kₑ.
Example
A patient has an initial drug concentration of 100 mg/L at peak. After 8 hours, the concentration is 25 mg/L:
kₑ = ln(100/25) / 8 = ln(4) / 8 = 1.386 / 8 = 0.173 h⁻¹
t½ = 0.693 / 0.173 = 4.0 hours
After 4 hours, concentration drops to 50 mg/L; after 8 hours, to 25 mg/L — confirming the calculation.
Frequently Asked Questions
How many half-lives to reach steady state?
It takes approximately 4-5 half-lives to reach steady state (94-97% of steady-state concentration). For a drug with a 4-hour half-life, steady state is reached in about 16-20 hours.
What factors affect drug half-life?
Age, liver function, kidney function, genetics, drug interactions, and body composition all influence drug half-life. Patients with impaired liver or kidney function typically have longer half-lives.
Why is half-life clinically important?
Half-life determines dosing frequency (drugs with short half-lives need more frequent dosing), time to steady state, and washout period after discontinuation.