Pharmacokinetics Calculator

Half-Life, Clearance, Volume of Distribution & Dosing Calculator

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, and how it is eventually eliminated from the body.

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.

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 directly proportional to plasma concentration. As concentration falls, so does the rate of removal — producing an exponential decline in drug levels over time.

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

First Order Kinetics

Formula: t½ = 0.693 ÷ k

• t½ = half-life (hours)
• k = elimination rate constant (hr⁻¹)

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

Zero Order Kinetics

Formula: t½ = C₀ ÷ (2 × K₀)

• C₀ = initial concentration (mg/L)
• K₀ = zero order elimination rate constant (mg/L/hr)

Example: If C₀ = 100 mg/L and K₀ = 10 mg/L/hr
t½ = 100 ÷ (2 × 10) = 5 hours

2. Elimination Rate Constant (k)

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

First Order Kinetics

Formula: k = 0.693 ÷ t½

• k = elimination rate constant (hr⁻¹)
• t½ = half-life (hours)

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

Zero Order Kinetics

Formula: k₀ = (C₀ − C) ÷ t

• k₀ = zero order elimination rate constant (mg/L/hr)
• C₀ = initial concentration (mg/L)
• C = final concentration (mg/L)
• t = time elapsed (hours)

Example: C₀ = 100 mg/L, C = 60 mg/L, t = 4 hr
k₀ = (100 − 60) ÷ 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. It reflects how extensively a drug distributes into body tissues beyond the bloodstream. A high Vd indicates extensive tissue binding; a low Vd suggests the drug largely remains in plasma.

Formula (applies to both kinetic orders)

Formula: Vd = A ÷ Cp

• Vd = volume of distribution (liters)
• A = total amount of drug in the body (mg)
• Cp = plasma drug concentration (mg/L)

Example: Drug amount = 500 mg, Plasma concentration = 10 mg/L
Vd = 500 ÷ 10 = 50 L

4. Clearance (Cl)

Clearance is the volume of plasma completely cleared of a drug per unit time. It is the primary parameter that determines the correct maintenance dose and is directly affected by renal and hepatic function.

First Order Kinetics

Formula: Cl = k × Vd

• Cl = clearance (L/hr)
• k = elimination rate constant (hr⁻¹)
• Vd = volume of distribution (L)

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

Zero Order Kinetics

Formula: Cl = K₀ ÷ C

• K₀ = zero order elimination rate constant (mg/hr)
• C = plasma concentration at that time (mg/L)

Example: K₀ = 20 mg/hr, C = 10 mg/L
Cl = 20 ÷ 10 = 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 used for drugs with long half-lives where waiting for steady state through regular dosing alone would take clinically unacceptable amounts of time. Common examples include digoxin, amiodarone, phenytoin, and vancomycin.

Formula (applies to both kinetic orders)

Formula: LD = (Vd × Cp) ÷ F

• LD = loading dose (mg)
• Vd = volume of distribution (L)
• Cp = desired target plasma concentration (mg/L)
• F = bioavailability (F = 1.0 for IV; use actual fraction for oral, e.g. 0.8 for 80% bioavailability)

Example: Vd = 30 L, Cp = 5 mg/L, F = 0.5
LD = (30 × 5) ÷ 0.5 = 300 mg

6. Maintenance Dose (MD)

The maintenance dose is administered at regular intervals to replace the amount of drug eliminated between doses, keeping plasma concentrations within the therapeutic window. It is calculated using clearance, target concentration, dosing interval, and bioavailability.

Formula (applies to both kinetic orders)

Formula: MD = (Cl × Cp × τ) ÷ F

• MD = maintenance dose (mg)
• Cl = clearance (L/hr)
• Cp = target plasma concentration (mg/L)
• τ (tau) = dosing interval (hours)
• F = bioavailability (F = 1 for IV injections; use appropriate fraction for oral routes)

Example: Cl = 4 L/hr, Cp = 10 mg/L, τ = 12 hr, F = 0.8
MD = (4 × 10 × 12) ÷ 0.8 = 600 mg

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 clinical scenarios requiring PK dose adjustment include:

• Renal impairment — Reduces clearance of renally excreted drugs (vancomycin, gentamicin, digoxin, metformin), requiring dose reduction or interval extension based on eGFR or CrCl.
• Hepatic disease — Impairs first-pass metabolism and hepatic clearance, increasing bioavailability and plasma levels of hepatically metabolized drugs.
• Pediatric and geriatric dosing — Body composition, renal function, and enzyme activity differ significantly from standard adult values, requiring PK-adjusted dosing.
• Obesity — Alters Vd for lipophilic drugs, affecting loading dose calculations.
• 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 to Use This Pharmacokinetics Calculator

• Step 1: Select the PK parameter you want to calculate (half-life, Vd, clearance, loading dose, etc.)
• 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 such as half-life, plasma concentration, volume of distribution, or bioavailability.
• Step 4: Click "Calculate" to instantly see your result with the applied formula.

Frequently Asked Questions