Medicine & HealthcarePharmacologyA-Level
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Drug Half-Life Calculator

Calculate drug concentration after multiple half-lives.

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Final Concentration

Formula first

Overview

The drug half-life equation models the exponential decay of a pharmaceutical substance's concentration in the bloodstream over time. It specifically describes first-order kinetics, where a constant percentage of the drug is eliminated per unit of time rather than a constant amount.

Symbols

Variables

C_t = Final Concentration, C_0 = Initial Concentration, n = Number of Half-Lives

Final Concentration
Initial Concentration
Number of Half-Lives

Apply it well

When To Use

When to use: This formula is applied when a drug follows first-order elimination kinetics, which applies to the vast majority of medications at therapeutic doses. It is used to estimate the remaining amount of a drug in the body or to determine how many half-life intervals have passed since administration.

Why it matters: Calculating half-life is essential for clinicians to establish safe dosing schedules and avoid drug toxicity. It allows medical professionals to predict when a drug will reach a steady state or when it will be effectively cleared from a patient's system for surgery or drug testing.

Avoid these traps

Common Mistakes

  • Confusing half-life with duration of action.
  • Not considering accumulation.

One free problem

Practice Problem

A patient is administered a 400 mg dose of a medication. If the drug follows first-order kinetics, calculate the amount of drug remaining in the patient's system after exactly 3 half-lives have elapsed.

Initial Concentration400 mg
Number of Half-Lives3

Solve for:

Hint: Use the formula Ct = C0 × (1/2)ⁿ where n is the number of half-lives.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Katzung & Trevor's Basic & Clinical Pharmacology
  2. Wikipedia: Pharmacokinetics
  3. Goodman & Gilman's The Pharmacological Basis of Therapeutics
  4. Basic and Clinical Pharmacology by Bertram G. Katzung
  5. Half-life (pharmacology) (Wikipedia article)
  6. Goodman & Gilman's The Pharmacological Basis of Therapeutics, 13th Edition
  7. Basic and Clinical Pharmacology, 14th Edition, Bertram G. Katzung
  8. Rang and Dale's Pharmacology, 9th Edition