Volume of Distribution Calculator (Vd)
Calculate pharmacokinetic Volume of Distribution Vd = Dose/C₀.
Classifies distribution as plasma-bound, extracellular, or tissue-bound with reference drugs.
What volume of distribution actually is
The Volume of Distribution, abbreviated Vd, is one of those pharmacokinetics terms that sounds physical but isn’t. It is not a real volume of body fluid. It is a proportionality constant that says: if I put X mg of this drug into the bloodstream and measure Y mg/L in plasma, the “apparent volume” the drug spread into is X/Y liters. That number is sometimes smaller than total blood volume (the drug stayed in the bloodstream) and sometimes hundreds of liters larger than the person (the drug bound heavily to tissues so very little is left in plasma).
The formula
Vd = Dose / C₀
Where Dose is in mg (assumed IV, so all of it enters circulation) and C₀ is the plasma concentration immediately after distribution equilibrium, in mg/L. The result is in liters. Dividing by body weight gives Vd per kilogram, which is how most clinical references quote it.
Reference Vd values for common drugs (L/kg)
| Drug | Vd (L/kg) | Where it goes |
|---|---|---|
| Warfarin | 0.14 | Mostly in plasma (highly protein-bound) |
| Aspirin | 0.15 | Plasma, extracellular fluid |
| Heparin | 0.06 | Blood (large molecule, can’t leave) |
| Ethanol | 0.6 | Total body water |
| Theophylline | 0.5 | Total body water |
| Lithium | 0.8 | Body water + slight tissue uptake |
| Morphine | 3.5 | Tissue uptake |
| Diazepam | 1.1 | Lipid-soluble, body fat |
| Digoxin | 7.0 | Heart and skeletal muscle binding |
| Amiodarone | 60 | Lipid stores, deep tissue |
| Chloroquine | 200 | Liver, retina, deep tissue |
A 70 kg adult has roughly 3 L of plasma, 14 L of extracellular fluid, and 42 L of total body water. A drug with Vd around 3 L stays in plasma. Vd around 14 L means extracellular distribution. Vd around 42 L means it equilibrates with all body water. Vd above 42 L per person (equivalent to about 0.6 L/kg in a 70 kg adult) means tissue binding beyond what body water can hold.
Why Vd matters clinically
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Loading dose calculation. If you want a target plasma concentration of C_target, the loading dose is Vd × C_target. For digoxin, Vd is huge, so loading doses are larger than maintenance doses by a factor of 5-10. For warfarin, Vd is small, so loading doses are not much bigger than maintenance.
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Dialysis effectiveness. Hemodialysis filters plasma. If most of the drug is sitting in plasma (small Vd), dialysis pulls it out efficiently. If most of the drug is in tissue (large Vd), dialysis is nearly useless. You might filter out plasma, but more drug just leaches back out of tissue. Aspirin and lithium overdose: dialysis works. Tricyclic antidepressant overdose: dialysis is ineffective.
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Drug interaction predictions. A drug that displaces another from tissue binding will spike the second drug’s plasma concentration even at the same total body amount. This is the mechanism behind several classical drug-drug interactions, especially with warfarin.
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Pediatric and geriatric dosing. Vd scales with body composition. Infants have higher total body water per kg. Elderly patients have more body fat and less water. The same drug has different effective Vd values across the life span, which is why pediatric dosing guidelines are not just adult-dose-divided-by-weight.
The classification this calculator uses
| Vd (L/kg) | Class | Implication |
|---|---|---|
| < 0.2 | Confined to plasma | High protein binding, dialyzable |
| 0.2–0.7 | Extracellular fluid | Limited tissue penetration |
| 0.7–2.0 | Total body water | Distributes into all body water |
| 2.0–10 | Moderate tissue binding | Slower elimination, larger loading dose |
| > 10 | Extensive tissue binding | Loading dose dominates, dialysis ineffective |
Worked example
A patient receives 100 mg of an IV drug. Plasma concentration measured 30 minutes later (after distribution): 1.4 mg/L. Patient weight: 70 kg.
Vd = 100 mg / 1.4 mg/L = 71.4 L Vd per kg = 71.4 / 70 = 1.02 L/kg
That falls in the total body water range, consistent with ethanol, theophylline, or a similar small water-soluble molecule.
Practical notes
- C₀ should be measured AFTER distribution, not immediately at injection. For IV bolus drugs that’s typically 15-60 minutes post-dose. Drawing too early gives an artificially high C₀ and thus a falsely small Vd.
- For drugs with complex multi-compartment kinetics (anesthetics, some psychiatric drugs), the apparent Vd changes over time. The “steady-state Vd” reported in references is the long-term value.
- Vd is not measured directly in clinical practice; it is looked up. References like Goodman & Gilman, Stockley’s, and Sanford Guide list Vd for thousands of drugs. This calculator is the inverse: given dose and measurement, what is the Vd? Used in pharmacokinetic teaching and research, not bedside dosing.