Pharmacokinetics

Volume of Distribution Calculator

Works out the apparent volume of distribution (Vd) from an IV dose and the plasma concentration it produced.

Volume of distribution

Enter the IV dose and the plasma concentration at time zero (C₀).

Inputs

Dose administered (mg)

The total dose given as an intravenous bolus.

Plasma concentration C₀ (mg/L)

mg/L

Concentration at time zero after the IV bolus (back-extrapolated).

Body weight (kg) — optional

Used only for Vd per kg. Left blank, 70 kg is assumed.

Try an example drug

Interpreting Vd

Bands from the MSD Manual, in litres per kilogram.

< 0.1 L/kgPlasma Volume

0.1 – 0.3 L/kgExtracellular Fluid

0.3 – 0.7 L/kgTotal Body Water

0.7 – 2 L/kgTissue Binding

2 – 10 L/kgExtensive Distribution

≥ 10 L/kgExtreme Distribution

Vd = Dose / C₀

Vd (L/kg) = Vd / body weight

Dose is the IV bolus in mg; C₀ is the plasma concentration at time zero in mg/L, usually found by back-extrapolating the log-concentration line to t = 0. Dividing the amount by the concentration gives litres.

Expressing Vd per kg lets you compare it with real body spaces: plasma is about 0.04 L/kg, extracellular fluid about 0.2 L/kg and total body water about 0.6 L/kg. Anything much larger means the drug is held in tissues. Interpretation per the MSD Manual.

Worked example: Vd from an IV bolus, with C₀ found by back-extrapolation

A 64 kg volunteer in a teaching study receives 500 mg of Drug X as an IV bolus. Plasma levels are 10.0 mg/L at 2 h and 6.4 mg/L at 6 h, both on the log-linear elimination phase. Find C₀, then the volume of distribution in L and L/kg.

Dose (IV bolus): 500 mg
C at 2 h: 10.0 mg/L
C at 6 h: 6.4 mg/L
Body weight: 64 kg

Elimination rate constant
kₑ = ln(C₁ ÷ C₂) ÷ (t₂ − t₁) = ln(10.0 ÷ 6.4) ÷ 4 h = 0.1116 h⁻¹
Back-extrapolate to t = 0
C₀ = C₁ × e^(kₑ·t₁) = C₁ × (C₁ ÷ C₂)^(t₁ ÷ (t₂ − t₁)) = 10.0 × 1.5625^0.5 = 12.5 mg/L
Volume of distribution
Vd = Dose ÷ C₀ = 500 mg ÷ 12.5 mg/L = 40.00 L
Per kilogram
Vd = 40.00 L ÷ 64 kg = 0.625 L/kg

Vd = 40.00 L (0.625 L/kg) — the calculator's 'Total Body Water' band.

To give 12.5 mg/L, the 500 mg behaves as if it were dissolved in 40 L — close to total body water for a 64 kg adult (about 0.6 L/kg). It also gives the loading dose for a target level: 40 L × 15 mg/L = 600 mg. It does not say where the drug actually is: Vd is an apparent volume, and a value like this is equally consistent with a drug spread through body water or one partly bound in tissue and partly in plasma. Illustrative values for an educational calculation.

Common mistakes

Using a level drawn some time after the dose as C₀. Concentration has already fallen, so Dose ÷ C overestimates Vd; back-extrapolate the log-linear line to t = 0.

Mixing units: a level reported in µg/L or ng/mL must be converted to mg/L first (1 ng/mL = 0.001 mg/L), or Vd is out by a factor of 1000.

Using an oral dose. After oral dosing only the fraction F reaches the circulation and absorption overlaps distribution, so Dose ÷ C₀ is not Vd.

Extrapolating from samples taken during the distribution phase. Early points of a two-compartment drug lie above the elimination line and give a C₀ that is too high and a Vd that is too small.

Leaving body weight blank for a real patient. The L/kg figure then uses the 70 kg default, and the band can change.

Reading Vd as a physical place. A Vd of 500 L does not mean the patient holds 500 L; it means the drug is held outside plasma.

Assumptions and limitations

Assumes a one-compartment model with instantaneous distribution; for multi-compartment drugs Dose ÷ C₀ gives the initial (central) volume, not Vss or Varea.

Assumes linear pharmacokinetics and an IV bolus with complete availability.

Vd changes with oedema, ascites, obesity, pregnancy, age and protein binding; a population figure may not fit an individual.

The distribution bands are broad teaching categories, not drug-specific or diagnostic ranges.

Guide: Pharmacokinetic Parameters: AUC, Clearance, Half-Life and BioavailabilityThe concept in full, with practice questions.Ke CalculatorCombine this Vd with clearance to get kₑ = CL ÷ Vd, or go from dose and C₀ straight to kₑ.Vancomycin AUC CalculatorSee Vd used in dosing: it assumes a population 0.7 L/kg rather than measuring it.

References

Ducharme MP, Shargel L, editors. Shargel and Yu's Applied Biopharmaceutics & Pharmacokinetics. 8th ed. New York: McGraw Hill; 2022.
Rowland and Tozer's Clinical Pharmacokinetics and Pharmacodynamics: Concepts and Applications. 5th ed. Philadelphia: Wolters Kluwer; 2019.

Common questions

Because it is an apparent volume. If a drug binds strongly in tissue, very little stays in plasma, so the measured concentration is low and Dose ÷ C₀ becomes huge. Chloroquine and digoxin are classic examples.

Dose in mg and concentration in mg/L, giving Vd in litres. If your level is reported in µg/L or ng/mL, convert it to mg/L first (1 ng/mL = 0.001 mg/L), otherwise the answer is out by a factor of a thousand.

The plasma concentration at the instant of the IV bolus, before any elimination. You cannot sample at exactly t = 0, so plot log concentration against time and extrapolate the straight elimination line back to the y-axis.

Mainly for loading doses: loading dose = Vd × target concentration. A large Vd also warns that a drug will be slow to leave the body and poorly removed by dialysis.

Prepared by the PharmaWallah student team. Verify results with your textbook or instructor. Report an error · Editorial policy