Drug Half Life Calculator - Time, Amount, Steady State

A drug half life is the time for the amount of active drug in the body to fall to half of its previous value, and it is the central number in first-order pharmacokinetics. The drug half life calculator applies the first-order elimination formula to a half-life, an initial dose, an elapsed time, and an optional target percent, and returns the percent still in the body, the mg in circulation, the number of half-lives elapsed, and the hours needed to reach a target percent or about 97 percent of steady state.

• • Estimate a re-dose interval: See how much of an earlier dose is still on board at a given elapsed time, which is the same arithmetic that drives an every-4-hour or every-24-hour dose label.
• • Estimate a washout: See how long it takes for the percent remaining to fall to a small target percent, which is the same arithmetic used in coursework and licensing-exam washout problems.
• • Reason about steady state: Check how many days a regular dose needs to build up to its full effect, which is about 4 to 5 half-lives for most drugs.

The phrase half life shows up on drug labels and in pharmacology textbooks, and it usually refers to the plasma elimination half life under first-order kinetics. The half life stays the same no matter how much is in the body, which is what makes the math work.

When the question is how often to redose a stimulant with a short half-life, Adderall Dosage Calculator lines up the morning and afternoon schedule with the elimination curve the calculator describes.

The calculator applies the first-order formula C(t) = C0 times 0.5^(t / t1/2) and rearranges the same equation to compute the time needed to reach any target percent remaining.

• t1/2: Elimination half-life in hours, the time for plasma concentration to fall to half of its previous value. Source: FDA pharmacokinetics guidance.
• C0: Initial dose or peak plasma concentration in mg.
• t: Elapsed time in hours since the dose was taken, on the same time scale as the half-life.
• target percent: Optional target percent remaining, used to compute the time needed to reach that level.

The FDA Pharmacokinetics guidance defines the half-life as 0.693 divided by the elimination rate constant k, which is the same relationship this formula is built on.

According to FDA Guidance for Industry: Population Pharmacokinetics, the elimination half-life is the time for plasma concentration to fall by half under first-order kinetics and is calculated as t1/2 = 0.693 divided by the elimination rate constant k.

The first-order formula C(t) = C0 * 0.5^(t / t1/2) is the same one used for radioactive decay, so Half-Life Calculator shows the same exponential curve for isotope work.

Four ideas show up in almost every half-life question and explain why the same formula describes caffeine and warfarin alike.

The half-life is the single most useful number in the first-order elimination arithmetic on this page.

Paracetamol's roughly 2.5 hour half-life makes it a clean short-half-life example, and Paracetamol Dosage Calculator applies the same idea to set a safe 4 to 6 hour re-dose interval under the daily cap.

Enter the half-life, dose, elapsed time, and target percent, and the calculator fills in the rest.

1. 1 Look up the half-life: Look up the plasma elimination half-life in hours from the FDA label, the British National Formulary, or a trusted pharmacology source. Common examples are 5 hours for caffeine, 1.7 hours for amoxicillin, 2 hours for ibuprofen, and 36 hours for warfarin.
2. 2 Enter the dose: Type the starting dose in mg, the same number on the prescription label or pill bottle, so the mg remaining output is in the same unit.
3. 3 Enter the elapsed time: Use the number of hours that have passed since the dose. Zero means at the moment of the dose, and any other value is the time since the peak.
4. 4 Set a target percent: Pick a target percent of the original dose to compute the time for. Ten percent is a common target in washout problems, 50 percent is one half-life, and 5 percent is a stricter target used in some drug-switching examples.
5. 5 Read the results: Use the percent remaining and mg remaining to compare dose strengths, and use the time-to-target row to compare a target percent against the half-life you entered. The half-lives elapsed row is a quick sanity check.

A worked example: amoxicillin 500 mg taken at hour 0, half-life 1.7 hours. At hour 8 the percent remaining is about 3.83, the mg in the body is 19.16, half-lives elapsed is 4.71, and the time to 10 percent is 5.64 hours.

Ibuprofen's 2 hour half-life is the canonical short half-life example, and Ibuprofen Dosage Calculator uses the same 0.5^(t / t1/2) curve to plan a 6 to 8 hour re-dose interval under the daily maximum.

Half-life arithmetic can be done with pen and paper, but a calculator keeps the constants, rounding, and multiple outputs in one place, which matters when a small mistake would otherwise change the answer.

• • Standardised percent remaining: Returns the percent of the dose still in the body for any half-life, dose, and elapsed time, so the user does not have to compute 0.5 to the n by hand.
• • Built-in target percent search: Computes the hours needed to reach any custom target percent, which is the same arithmetic used to compare how long different drugs take to fall to a chosen level.
• • Steady-state sanity check: Shows the time to 5 half-lives, which is the common 'almost at steady state' rule and is more reliable than a single rule-of-thumb number.
• • Mg and percent in the same panel: Lists the percent remaining and the mg remaining side by side, so a reader can see how much of the original dose is still on the books in absolute and relative terms.
• • Reusable for many drugs: Works for any drug that follows first-order elimination, from short half-lives like ibuprofen to long half-lives like warfarin.

The calculator is a teaching and planning aid, not a prescription.

Several things can move the half-life of a drug up or down, so the calculator works best when the entered value is the half-life the user actually wants to model.

• • The calculator assumes first-order elimination, so it is not a fit for drugs that follow zero-order kinetics such as ethanol, high-dose aspirin, or phenytoin at toxic concentrations. For those drugs the half-life grows as the concentration falls.
• • It is a planning and teaching tool, not a clinical decision support system. Narrow-window drugs like digoxin, lithium, and warfarin should be guided by measured drug levels, because real half-lives can differ by 30 to 50 percent from the label.
• • The model treats the body as a single compartment. Two-compartment drugs show a fast distribution phase and a slower terminal half-life, and the calculator reflects the terminal half-life the user enters.

Real-world half-lives are a range, not a single number, so the time to steady state and the time to a custom target percent should be read as estimates with a meaningful error bar rather than exact values.

According to Merck Manual Professional Edition: Overview of Pharmacokinetics, the fraction of drug remaining in the body after n elimination half-lives is 0.5 to the n, and four to five half-lives is the conventional interval over which a regularly dosed drug reaches about 94 to 97 percent of its steady-state plasma level under first-order kinetics.

Children can have longer or shorter half-lives than adults for the same drug, so Pediatric Dose Calculator pairs the half-life arithmetic on this page with the weight-based dose that pediatric labels actually call for.