A drug's half-life determines how quickly it leaves the body, how long a single dose keeps working, and how long it takes for repeated dosing to reach a stable blood level. This calculator converts between the underlying rate constant and half-life, projects the remaining amount over time, and reverse-solves for the time to any percent cleared.
Why 0.693 shows up in the formula
Most drugs are eliminated by first-order kinetics: the rate of removal is proportional to how much drug is currently present, so a constant fraction — not a constant amount — leaves the body per unit time. This produces an exponential decay curve, C(t) = C0 × e−ke·t, where ke is the elimination rate constant.
Half-life is defined as the time at which exactly half the starting amount remains. Solving e−ke·t½ = 0.5 for t½ gives t½ = ln(2) / ke, and ln(2) ≈ 0.693 — that's where the familiar 0.693 constant comes from.
What the three tabs compute
The Half-Life tab converts between ke and t½ — enter either one and the other updates instantly. The Remaining Concentration tab applies C(t) = C0 × 0.5(t/t½) to project how much of a starting dose is left after any elapsed time, plotted as a decay curve. The Time to Clearance tab reverses that equation to answer 'how long until X% is gone' — useful for questions like how long before a drug interaction risk passes, or how long until a substance falls below a detection threshold.
All three tabs share the same half-life value, so changing it on one tab updates the others.
Limits and how to use the result
This calculator assumes simple one-compartment, first-order elimination — accurate for many drugs at typical doses, but not universal. Some drugs (notably ethanol and phenytoin at higher doses) follow zero-order kinetics, where a constant amount is eliminated per unit time rather than a constant fraction; the half-life concept does not apply the same way to those. A published half-life is also a population average — an individual's true elimination rate varies with renal and hepatic function, age, body composition, genetics, and interacting medications. This tool is for education and general reference only; it does not replace consulting a pharmacist or the current prescribing information before making any dosing decision.