Drug Half-Life Calculator

Enter a starting dose or concentration, the drug's elimination half-life, and elapsed time to find how much drug remains (C = C0 x 0.5^(t / half-life)), plus the elimination rate constant and the time to near-complete clearance.

Quick Facts

Decay formula
C(t) = C0 x (1/2)^(t / t1/2)
Most drugs follow first-order elimination: a constant fraction is cleared per unit of time.
Rate constant
k = ln(2) / t1/2 ≈ 0.693 / t1/2
k is the fraction of drug eliminated per hour; C(t) = C0 x e^(-k x t).
Clinical rule of thumb
~5 half-lives ≈ 96.9% eliminated
Commonly used to estimate washout time or time to steady state with repeated dosing.

Your Results

Calculated
Amount Remaining
-
C(t) = C0 x 0.5^(t / half-life)
Percent of Initial Dose Remaining
-
[C(t) / C0] x 100
Elimination Rate Constant (k)
-
k = ln(2) / half-life
Time to ~97% Elimination
-
Approximately 5 x half-life

Ready

Enter the initial dose, half-life, and elapsed time, then press Calculate. This is an educational estimate, not medical advice - consult a pharmacist or physician for dosing decisions.

About Drug Half-Life and Elimination Kinetics

A drug's elimination half-life (t½) is the time required for the amount of drug in the body, or its concentration in the blood plasma, to drop by half. Most drugs are cleared by first-order kinetics, meaning the body eliminates a constant fraction of the remaining drug per unit time rather than a constant amount — so the half-life itself stays the same no matter how much drug is present. This calculator applies the standard first-order decay equation, C(t) = C0 × (1/2)(t / t½), to show how much of an initial dose or concentration remains after a chosen elapsed time, along with the elimination rate constant and the time until the drug is considered clinically cleared.

How the calculation works

Enter the initial dose or concentration (C0), the drug's published elimination half-life, and the time elapsed since the dose. The calculator first derives the elimination rate constant k = ln(2) / t½ (≈ 0.693 / t½), which is the fraction eliminated per hour. It then computes the remaining amount using the equivalent exponential form C(t) = C0 × e(-k × t), converts that to a percentage of the starting dose, and reports how many hours it would take to reach roughly 5 half-lives — the point at which about 96.9% of the drug has been eliminated and it is generally treated as cleared for practical purposes.

Why half-life matters

  • Dosing intervals: drugs with a short half-life (a few hours) typically need more frequent dosing to keep levels in a therapeutic range; drugs with a long half-life (a day or more) may be dosed once daily.
  • Time to steady state: with repeated dosing at a fixed interval, blood levels rise toward a plateau and reach roughly 90-97% of steady state after about 4-5 half-lives.
  • Washout period: before starting a new medication that interacts with the current one, clinicians often wait about 5 half-lives of the first drug so it is substantially cleared.
  • Individual variation: published half-life values come from population averages; a person's actual elimination rate can differ based on age, kidney and liver function, genetics, other medications, and hydration status.

Important limitations

This tool performs a simplified one-compartment, first-order elimination calculation. Many drugs follow more complex multi-compartment or non-linear (zero-order, saturable) kinetics, especially at high doses, and absorption or distribution phases are not modeled here. This calculator is for general education about pharmacokinetic concepts only — it does not calculate or recommend an actual dose, dosing schedule, or treatment decision. Always refer to the specific drug's prescribing information and consult a pharmacist or physician before making any medication decision.

Frequently Asked Questions

What is a drug's half-life?
A drug's elimination half-life (t½) is the time it takes for the amount of drug in the body, or its concentration in the blood, to fall by half. Most drugs follow first-order elimination, meaning a constant fraction (not a constant amount) is cleared per unit of time, so the half-life stays the same regardless of how much drug is present.
How do you calculate the amount of drug remaining after a given time?
Use C(t) = C0 × (1/2)(t / t½), where C0 is the starting amount or concentration, t is elapsed time, and t½ is the half-life. This is equivalent to C(t) = C0 × e(-k × t), where the elimination rate constant k = ln(2) / t½.
How many half-lives does it take to clear a drug from the body?
After 5 half-lives, roughly 96.9% of a drug has been eliminated, which is generally considered clinically negligible. After about 7 half-lives, over 99% is gone. This rule of thumb is commonly used to estimate washout periods before starting an interacting medication.
How is half-life related to reaching steady state with repeated dosing?
With regular repeated dosing at a fixed interval, a drug's concentration approaches steady state after about 4 to 5 half-lives, since accumulation and elimination reach equilibrium on that same timescale.

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