Half-life and steady state calculator

Half-life is 0.693 multiplied by the volume of distribution, divided by clearance. Steady state is reached after roughly four to five half-lives regardless of the dose given, which is exactly why a loading dose exists: it fills the volume immediately instead of waiting.

When to use the half-life calculator

Use to judge how long a drug takes to reach a stable concentration, how long it lingers after stopping, and whether a loading dose is needed to avoid waiting.

The half-life formula

Half-life = 0.693 × Vd ÷ CL. Steady state is reached after roughly five half-lives, and the same interval governs washout after stopping.

Worked example

A drug has a volume of distribution of 50 L and clearance of 5 L/hr. Half-life = (0.693 × 50) ÷ 5 = 6.93 hours, so steady state arrives at roughly 35 hours.

The mistake that costs marks

Steady state depends only on half-life, never on dose. Increasing the dose raises the concentration at steady state but does not reach it any sooner, which is precisely why loading doses exist. Questions offering a higher dose as a way to reach steady state faster are testing this.

Study aid, not a clinical tool

This calculator exists so you can learn the method and check your working for an examination. It is not medical advice and not clinical decision support, and it must not be used to make a decision about a real patient. Verify any result against your local formulary, the product literature and a qualified pharmacist. Our medical disclaimer sets out the full position.

Calculators you will usually need alongside this

Most questions that reach for one of these reach for another a step later, so these are the three that most often pair with it.

• Loading dose calculator — Loading dose
• Creatinine clearance calculator (Cockcroft-Gault) — Creatinine clearance
• Infusion rate converter (mcg/kg/min to mL/hr) — mcg/kg/min to mL/hr

Keep going

Calculations are only half of what examinations test. The other half is knowing why a drug does what it does, which is what decides whether a number you calculated is even the right number to be calculating. Start with CYP450 inducers and inhibitors. The drug class pages cover the mechanism behind the number, or browse the rest of the free calculators and try the practice questions.