Pharmacokinetics Calculator — Half-Life, Vd, Clearance

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.

Created by Ashar PervaizMedically reviewed by Dr. Syeda Khadija AkbarLast reviewed 14 October 2026

Half-Life Is the Parameter Everything Else Hangs Off

Of the six quantities this calculator handles, half-life is the one most people arrive looking for, and it is also the one that answers the largest number of practical questions. How long until the drug works. How long until it has gone. How often it needs to be given. Whether a level taken this morning tells you anything useful.

Half-life is the time for the plasma concentration to fall by half. In first-order kinetics that interval is constant regardless of where you start, which is the property that makes the whole framework useful.

t½ = 0.693 ÷ k

The 0.693 is the natural logarithm of 2 and appears wherever exponential decay is halved. If you know the elimination rate constant k, you have the half-life; if you know the half-life, you have k.

Getting Half-Life From Two Measured Levels

In practice half-life is often not given — it is derived from two concentrations taken a known time apart:

k = (ln C₁ − ln C₂) ÷ (t₂ − t₁)
t½ = 0.693 ÷ k

A level of 18 mg/L falling to 6 mg/L over eight hours gives ln 18 = 2.890, ln 6 = 1.792, so k = (2.890 − 1.792) ÷ 8 = 0.137 per hour, and t½ = 0.693 ÷ 0.137 = 5.1 hours.

Both samples must be drawn in the elimination phase for this to hold. A level taken while the drug is still distributing out of the bloodstream into tissue falls for a reason that has nothing to do with elimination, and a half-life calculated from it will be far too short. This is the single most common source of a nonsensical result.

Why Five Half-Lives Keeps Coming Up

The same figure governs both directions: accumulation towards steady state on repeated dosing, and washout after stopping. Each half-life closes half the remaining gap.

Five half-lives is a convention rather than a threshold — it is simply where the remaining gap becomes small enough to ignore for most purposes. Nothing changes at that point.

The practical consequences are worth spelling out. A drug with a six-hour half-life reaches steady state inside about thirty hours, so a level drawn on day two is meaningful. A drug with a half-life measured in weeks will not be at steady state for months, which means a level checked a fortnight in is still on the way up, and dose decisions made from it will systematically under-dose the patient. The same arithmetic explains why a drug stopped for a suspected adverse effect may take days to clear, and why an interacting drug started today may not show its full effect until next week.

Volume of Distribution Is Not a Volume

Vd is the parameter that causes the most confusion, because its name suggests a physical space and it is not one.

Vd = Dose ÷ Plasma concentration

It is the volume that would be needed to hold the whole dose at the concentration actually measured in plasma. If a drug leaves the bloodstream and binds extensively to tissue, very little remains in plasma to be measured, the denominator is small, and the calculated Vd becomes enormous — larger than the body, which is the clue that it is a ratio rather than a compartment.

Read that way, Vd tells you where the drug is:

That last row is why dialysis is ineffective for some overdoses. If the drug is sitting in tissue rather than circulating, filtering the blood filters a compartment that holds hardly any of it.

Clearance Sets the Maintenance Dose

Clearance is the volume of plasma completely cleared of drug per unit time. It is the parameter that determines how much drug has to be replaced to hold a concentration steady.

Cl = k × Vd

The relationship between the three parameters is the most useful thing on this page. Half-life is not an independent property — it is what falls out of clearance and volume of distribution together:

t½ = 0.693 × Vd ÷ Cl

This explains results that otherwise look contradictory. A drug with poor clearance can still have a short half-life if its Vd is small. A drug with excellent clearance can have a very long half-life if it is extensively distributed into tissue, because clearance can only act on the fraction currently in plasma. Half-life alone therefore says little about how efficiently the body is eliminating a drug.

Loading and Maintenance Answer Different Questions

The two dose calculations use different parameters because they solve different problems. The loading dose fills the distribution space; the maintenance dose replaces what is cleared.

Loading dose = (Target concentration × Vd) ÷ F
Maintenance dose = (Target concentration × Cl × Dosing interval) ÷ F

Notice that the loading dose depends on Vd and not at all on clearance, while the maintenance dose depends on clearance and not at all on Vd. A patient with impaired renal function needs the same loading dose as anyone else — their distribution space has not changed — but a reduced maintenance dose, because the drug they are given now leaves more slowly. Reducing the loading dose in renal impairment is a common error that simply delays reaching a therapeutic concentration.

F is bioavailability, the fraction of an administered dose reaching systemic circulation. It is 1 for intravenous administration and less for every other route. Dividing by F is what converts an intravenous dose into the larger oral dose that produces equivalent exposure.

When First-Order Assumptions Break

Everything above assumes first-order kinetics, where a constant fraction of drug is eliminated per unit time and the elimination machinery is nowhere near saturated. Most drugs at therapeutic concentrations behave this way.

Zero-order kinetics is what happens when the enzymes are saturated: a constant amount is eliminated per unit time rather than a constant fraction, and half-life ceases to be a fixed number at all. Alcohol is the familiar example. The clinically dangerous cases are drugs that behave in first-order fashion through most of their therapeutic range and cross into saturation near the top of it — a modest dose increase then produces a disproportionate rise in concentration rather than a proportional one.

A practical signal is worth watching for: if a small dose increase produces a much larger rise in measured level than expected, the assumption of first-order kinetics is probably no longer safe, and extrapolating with these formulas will underestimate the next concentration.

What Renal Impairment Actually Changes

Impaired renal function reduces clearance for renally eliminated drugs. Vd is largely unaffected. Since half-life is 0.693 × Vd ÷ Cl, a fall in clearance with unchanged Vd lengthens half-life proportionally, and time to steady state lengthens with it. How far that function has fallen is the figure a creatinine clearance calculator puts a number on, and it is the number most renal dosing tables are written against.

Two adjustments follow, and they are not equivalent. Reducing the dose while keeping the interval lowers both peak and trough. Extending the interval while keeping the dose preserves the peak and lowers the trough. For drugs whose effect depends on achieving a high peak, the second is preferred; for drugs where toxicity tracks the trough, extending the interval is what gives the concentration time to fall. Which applies is a property of the drug.

For the arithmetic of turning a calculated dose into an administered one, see the dosage calculator for weight-based orders and the IV calculator for infusion rates. The pharmacodynamics calculator covers the other half of the relationship — what the drug does once it is there.

Immunoglobulin is the awkward case for all of this. Its half-life is measured in weeks rather than hours, so the interval between doses is set by trough levels over a month instead of by the clearance arithmetic above, and the rate-limiting number during administration is tolerance rather than kinetics. The IVIG calculator covers the administration side of it.

Pharmacokinetics Questions, Worked Through

Educational reference only. Confirm any clinical calculation independently before acting on it. How this page is reviewed