# Drug Half-Life Concentration Calculator Estimate plasma drug concentration at a chosen time after an IV bolus using a one-compartment model with first-order elimination: C(t) = (Dose / Vd) · e^(-k·t), where k = ln2 / t½. Includes initial concentration C0, elimination rate constant k, percent remaining, and number of half-lives elapsed. Valid only for linear pharmacokinetics — NOT for Michaelis-Menten drugs (phenytoin, high-dose ethanol) or multi-compartment distribution. Reference: theophylline Vd ≈ 0.45 L/kg, t½ ≈ 8 h. Not medical advice. > Canonical page: https://elysiatools.com/en/tools/drug-half-life-dose - **Category:** Health - **Keywords:** pharmacokinetics, half-life, drug concentration, C(t), IV bolus, one-compartment, first-order elimination, elimination rate constant, drug dosing, pk, drug, medicine ## Overview The Drug Half-Life Concentration Calculator estimates plasma drug concentration after an IV bolus using a one-compartment model with first-order elimination. Enter the dose, volume of distribution, half-life, and elapsed time to calculate C0, C(t), the elimination rate constant, percentage remaining, and half-lives elapsed. ## Inputs - **Dose (mg)** (number): IV bolus dose. Must be positive. - **Volume of distribution Vd (L)** (number): Apparent volume of distribution. Must be positive. - **Half-life t½ (h)** (number): Elimination half-life in hours. Must be positive. - **Elapsed time t (h)** (number): Time elapsed since the IV bolus, in hours. Cannot be negative. - **Decimal Places** (number) ## When to use - Estimate concentration after a single IV bolus when linear pharmacokinetics apply. - Calculate how much of the initial concentration remains after a selected number of hours. - Review basic pharmacokinetic values such as C0 and the elimination rate constant. ## How it works - Enter a positive IV bolus dose in milligrams, volume of distribution in liters, half-life in hours, and non-negative elapsed time. - The calculator computes the elimination rate constant as k = ln(2) / t½. - It calculates initial concentration as C0 = Dose / Vd and concentration at time t as C(t) = C0 · e^(-k·t). - The JSON result reports C0, C(t), k, half-lives elapsed, percentage remaining, and percentage eliminated. ## Use cases - Teaching first-order drug elimination and half-life calculations. - Estimating post-bolus concentration for a drug with known linear pharmacokinetic parameters. - Checking the relationship between elapsed time, half-lives, and percentage of concentration remaining. ## Frequently asked questions ### What model does this calculator use? It uses a one-compartment IV bolus model with first-order elimination. ### What inputs are required? Dose, volume of distribution, elimination half-life, and elapsed time are required. Decimal places are optional. ### What units should I use? Enter dose in mg, volume of distribution in L, and both half-life and time in hours. Concentration is reported in mg/L. ### Can I use it for phenytoin or high-dose ethanol? No. The model is not valid for Michaelis-Menten or other nonlinear pharmacokinetics, including phenytoin and high-dose ethanol. ### Is this a dosing recommendation? No. It is an educational calculation and is not medical advice. It also does not model multi-compartment distribution. ## Related tools - [Bioavailability Calculator (F = AUC_po · Dose_iv / AUC_iv · Dose_po)](https://elysiatools.com/en/tools/bioavailability-calculator): Calculate the absolute bioavailability F of an extravascular (typically oral) dose: F = (AUC_po · Dose_iv) / (AUC_iv · Dose_po), where AUC_po and AUC_iv are the areas under the concentration-time curve after oral and IV dosing, and the doses correct for any difference in amount administered. F is dimensionless and lies in \[0, 1\]; IV bioavailability is by definition 1, while oral F < 1 reflects incomplete absorption and/or first-pass metabolism. AUC can be in any consistent unit (e.g. mg·h/L) since it cancels out of the ratio. Valid only for linear pharmacokinetics, the same drug molecule, and doses within the linear range. 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