Pharmacokinetics Calculator

Calculate half-life, elimination rate constant, volume of distribution, clearance, loading dose, and maintenance dose — with full support for both first order and zero order kinetics. Built for pharmacists, physicians, nurses, and pharmacy students.

What Is Pharmacokinetics?

Pharmacokinetics (PK) is the branch of pharmacology that studies what the body does to a drug after it is administered. It covers four fundamental processes — absorption, distribution, metabolism, and excretion — collectively known as ADME. These processes determine how quickly a drug reaches its target site, how long it remains active in the body, and how it is eventually eliminated.

This free pharmacokinetics calculator covers the six core PK parameters used daily in clinical and academic settings: half-life, elimination rate constant, volume of distribution, clearance, loading dose, and maintenance dose — with full support for both first order and zero order kinetics. For the practical clinical tools that use these PK values — calculating actual patient doses and infusion rates — see our dose calculator and IV calculator.

PK Parameters at a Glance — Summary Table

The table below summarizes all six pharmacokinetic parameters this calculator covers, their formulas, and what each one tells you clinically:

First Order vs Zero Order Kinetics

First order kinetics is the most common model. A constant fraction of the drug is eliminated per unit time, and the elimination rate is proportional to plasma concentration. As concentration falls, so does the rate of removal — producing an exponential decline in drug levels.

Zero order kinetics occurs when elimination pathways become saturated. A constant amount of drug is removed per unit time regardless of concentration, leading to a linear decline. This model carries a higher risk of toxic accumulation because small dose increases can produce disproportionately large rises in plasma levels. Classic examples include ethanol, phenytoin at high doses, and aspirin in overdose.

Pharmacokinetic Formulas — Complete Reference with Examples

1. Half-Life (t½)

Half-life is the time required for plasma concentration to decrease by 50%. It determines dosing frequency, time to steady state (approximately 5 half-lives), and how long a drug remains active after discontinuation.

First Order

Formula: t½ = 0.693 ÷ k

Example: If k = 0.2 hr⁻¹ → t½ = 0.693 ÷ 0.2 = 3.46 hours

Zero Order

Formula: t½ = C₀ ÷ (2 × K₀)

Example: If C₀ = 100 mg/L, K₀ = 10 mg/L/hr → t½ = 100 ÷ 20 = 5 hours

2. Elimination Rate Constant (k)

The elimination rate constant describes the fraction of drug removed from the body per unit time. It is inversely related to half-life and represents the slope of the log-linear concentration–time curve.

First Order

Formula: k = 0.693 ÷ t½

Example: If t½ = 6 hr → k = 0.693 ÷ 6 = 0.115 hr⁻¹

Zero Order

Formula: k₀ = (C₀ − C) ÷ t

Example: C₀ = 100 mg/L, C = 60 mg/L, t = 4 hr → k₀ = 40 ÷ 4 = 10 mg/L/hr

3. Volume of Distribution (Vd)

Volume of distribution is a theoretical volume that relates the total amount of drug in the body to its measured plasma concentration. A high Vd indicates extensive tissue binding; a low Vd suggests the drug largely remains in plasma.

Formula: Vd = A ÷ Cp

Example: 500 mg administered, Cp = 10 mg/L → Vd = 50 L

4. Clearance (Cl)

Clearance is the volume of plasma completely cleared of drug per unit time. It is the primary parameter for calculating maintenance doses and is directly affected by renal and hepatic function.

First Order

Formula: Cl = k × Vd

Example: k = 0.1 hr⁻¹, Vd = 40 L → Cl = 4 L/hr

Zero Order

Formula: Cl = K₀ ÷ C

Example: K₀ = 20 mg/hr, C = 10 mg/L → Cl = 2 L/hr

5. Loading Dose (LD)

A loading dose is a higher initial dose given to rapidly achieve a therapeutic plasma concentration. It is essential for drugs with long half-lives where waiting for steady state would take clinically unacceptable time.

Formula: LD = (Vd × Cp) ÷ F

Example: Vd = 30 L, Cp = 5 mg/L, F = 0.5 → LD = 300 mg

6. Maintenance Dose (MD)

The maintenance dose replaces the amount of drug eliminated between doses, keeping plasma concentrations within the therapeutic window.

Formula: MD = (Cl × Cp × τ) ÷ F

Example: Cl = 4 L/hr, Cp = 10 mg/L, τ = 12 hr, F = 0.8 → MD = 600 mg

Common Drug PK Parameters — Reference Table

The following table provides approximate PK values for commonly studied and clinically monitored drugs. Use these as reference points when working through calculations. Values are for healthy adults and may differ significantly in renal or hepatic impairment.

*Phenytoin follows first order kinetics at low concentrations but switches to zero order (Michaelis-Menten saturation) at higher therapeutic and toxic concentrations — one of the reasons it requires careful therapeutic drug monitoring.

Clinical Importance of Pharmacokinetic Calculations

Pharmacokinetic calculations are fundamental to individualizing drug therapy. Incorrect dosing can lead to subtherapeutic levels, treatment failure, or toxic accumulation. Key scenarios requiring PK-guided dose adjustment include:

• Renal impairment — reduces clearance of renally excreted drugs (vancomycin, gentamicin, digoxin, metformin), requiring dose reduction or interval extension
• Hepatic disease — impairs first-pass metabolism and hepatic clearance, increasing bioavailability and plasma levels
• Pediatric and geriatric dosing — body composition, renal function, and enzyme activity differ from standard adult values. Use our weight-based dose calculator as a starting point for pediatric dose estimation
• Obesity — alters Vd for lipophilic drugs, affecting loading dose calculations. Our BMI calculator can help classify the patient's weight status
• Drug interactions — enzyme inducers (rifampicin) and inhibitors (fluconazole) directly alter clearance and half-life of co-administered drugs
• Therapeutic drug monitoring (TDM) — drugs with narrow therapeutic indices (lithium, aminoglycosides, cyclosporine, phenytoin) require regular plasma level monitoring guided by PK principles

How This Calculator Fits With Other Clinical Tools

Pharmacokinetic parameters inform the calculations performed by our other clinical tools:

• Dose Calculator — uses patient weight and a prescribed mg/kg rate to calculate the total dose in mg. The mg/kg rate itself is derived from PK studies of the drug.
• Dose Stock Calculator — converts the mg dose into tablets or mL of liquid from available stock. Used after the dose is determined.
• IV Calculator — calculates infusion rate (mL/hr) and drip rate (drops/min) for IV delivery. The infusion rate depends on the PK-derived dose and the drug's concentration.

How to Use This Pharmacokinetics Calculator

• Step 1: Select the PK parameter you want to calculate — half-life, elimination rate constant, Vd, clearance, loading dose, or maintenance dose.
• Step 2: Choose the kinetic model — first order or zero order — based on the drug's known elimination behavior.
• Step 3: Enter the required input values.
• Step 4: Click Calculate to see your result instantly, with a visual gauge showing where the value falls on a general clinical scale.

Frequently Asked Questions