Half-Life Time of Medicine Calculator

Determine the Medicine Half-Life

Half-Life Time Formula

Formula

\[ k = \frac{\ln(A_0 / K_0)}{t} \\ t_{1/2} = \frac{\ln 2}{k} = \frac{0.693 \times t}{\ln(A_0 / K_0)} \]

Where:

\(t_{1/2}\) — half-life time (hrs), the time for the concentration to fall by 50%
\(A_0\) — initial peak concentration (mcg/mL)
\(K_0\) — trough concentration measured after time \(t\) (mcg/mL)
\(t\) — time interval between the two measurements (hrs)
\(k\) — elimination rate constant (1/hrs)

The formula assumes first-order elimination: the concentration decays exponentially, so \(k\) is found from the ratio of the two measured concentrations, and the half-life follows from \(\ln 2 \approx 0.693\).

Half-Life Time – Calculation Example

Example: a drug reaches a peak concentration of 10 mcg/mL, and 8 hours later its concentration has fallen to 2.5 mcg/mL.

\[ k = \frac{\ln(10 / 2.5)}{8} = \frac{\ln 4}{8} = \frac{1.3863}{8} = 0.1733 \ \text{hrs}^{-1} \]

\[ t_{1/2} = \frac{0.693}{0.1733} = 4 \ \text{hrs} \]

Result: the half-life time is 4 hrs — every 4 hours the concentration drops by half (from 10 to 5 to 2.5 mcg/mL, which matches the measured trough).

How to Use the Calculator

Enter the Initial peak concentration in mcg/mL — the higher of the two measured concentrations (e.g. a peak level drawn after dosing).
Enter the Trough concentration after time in mcg/mL — the lower concentration measured later, just before the next dose.
Enter the Time interval in hours between the two measurements.
Read the Half-life time in hours, which tells you how long it takes for the drug concentration to halve.

What Is the Half-Life of a Medicine?

The half-life \(t_{1/2}\) of a drug is the time required for its concentration in the blood (or plasma) to decrease by one half. For most drugs, elimination follows first-order kinetics: a constant fraction of the drug is cleared per unit time, so the concentration falls along an exponential curve rather than a straight line. The half-life is the natural way to describe how fast that decay happens.

Half-life directly drives dosing decisions. A drug with a half-life of 4 hours loses about 94% of a dose after 16 hours (four half-lives), so it typically needs dosing three or four times a day to keep levels in the therapeutic range. A drug with a half-life of 24 hours or more can often be given once daily. Half-life also determines the accumulation time: after about 4–5 half-lives of repeated dosing, the drug reaches steady state, and the same rule applies to washout after stopping the drug.

This calculator estimates the half-life from two real measurements — a peak and a trough separated by a known time. That is exactly how clinicians think about drugs with narrow therapeutic windows, such as vancomycin or aminoglycosides, where levels are monitored and doses adjusted. Once you know \(t_{1/2}\), you can predict the concentration at any future moment or work backwards to a suitable dosing interval. For planning the infusion rate itself, see the Dosage Infusion calculator, and for weight-based tablet dosing see the Tablet Dose calculator.

Interpreting the Result

Short half-life (under ~6 hrs): rapid clearance; frequent dosing or an extended-release formulation is usually needed.
Long half-life (over ~24 hrs): slow clearance; once-daily dosing may suffice, but accumulation and delayed washout deserve attention.
Concentration after \(n\) half-lives: the remaining fraction is \( (1/2)^n \) — e.g. 25% after 2 half-lives, 6.25% after 4.

Assumptions and Limitations

The calculation assumes first-order elimination (exponential decay). Some drugs — ethanol, phenytoin at high levels, aspirin at toxic doses — follow zero-order (constant-rate) kinetics, for which a half-life does not exist and this formula does not apply.
It assumes no further absorption is occurring between the two measurements; the trough should be taken when levels are falling, not while the drug is still being absorbed or distributed.
Half-life depends on both clearance and volume of distribution. In renal or hepatic impairment, heart failure, or dehydration, the half-life can be much longer than in a healthy patient — measured levels beat textbook values. For renal function-related dose adjustments, the Dialysis Dose (Kt/V) calculator may be relevant.
Both concentrations must be in the same units, and the trough must be lower than the peak; otherwise the elimination constant \(k\) would be negative or undefined.
Use this tool for education and estimation, not as a substitute for therapeutic drug monitoring guided by a pharmacist or physician.

Frequently Asked Questions

How do I calculate drug half-life by hand with two concentration levels?

Divide the peak concentration by the trough concentration, take the natural logarithm of that ratio, and divide by the time between the two measurements. This gives the elimination rate constant \(k\). Then divide 0.693 by \(k\) to get the half-life. For example, from 10 to 2.5 mcg/mL over 8 hours: \(k = \ln(4)/8 \approx 0.173\), so \(t_{1/2} = 0.693/0.173 = 4\) hours.

How many half-lives does it take for a drug to be fully eliminated?

A drug is never mathematically fully eliminated, but practically it is considered cleared after about 5 half-lives, when roughly 97% is gone. After 1 half-life 50% remains, after 2 half-lives 25%, after 3 half-lives 12.5%, and after 4 half-lives 6.25%. The same 4–5 half-life rule applies to reaching steady state with repeated dosing and to washout after stopping a medication.

Can I use this calculator with concentrations in mg/L or other units?

Yes. The formula only uses the ratio of the two concentrations, so any consistent unit works — mcg/mL, mg/L, ng/mL, or even ng/dL — because the units cancel out. What matters is that both concentrations are expressed in the same unit. The time interval, however, must be in hours if you want the half-life in hours; if you enter minutes or days, the result will be in those same time units.

What is a normal half-life for a medication?

There is no single normal value — half-lives range from minutes (nitroglycerin) to weeks (amiodarone). Many common drugs fall between 2 and 12 hours, requiring dosing two to four times daily, while drugs with half-lives over 24 hours (e.g., fluoxetine, amlodipine) can often be taken once a day. Textbook values apply to healthy adults; kidney or liver disease can extend a half-life considerably, so measured levels are more reliable.

Why is my calculated half-life negative or undefined?

This happens when the trough concentration is equal to or higher than the peak. The ratio \(A_0/K_0\) is then 1 or less, making the logarithm zero or negative and the half-life meaningless. Check that you entered the larger concentration as the peak and the smaller one as the trough, and that both are measured while levels are falling — a trough drawn too early, during absorption, can be misleading.

Does half-life change with the dose taken?

For drugs with first-order kinetics — the vast majority — no: half-life stays the same whether you take a small or large dose, because a constant fraction is cleared per hour. However, some drugs saturate their elimination pathways at high concentrations and switch to zero-order kinetics (ethanol, phenytoin at toxic levels, high-dose aspirin). For those, elimination proceeds at a fixed rate and a true half-life does not exist, so this formula should not be used.

How is half-life used to set a dosing interval?

The goal is usually to keep concentrations within the therapeutic window between doses. Knowing the half-life, you can predict the trough before the next dose: after one half-life the level halves, after two it quarters, and so on. Drugs with short half-lives need frequent dosing or extended-release forms, while long-half-life drugs are suited to once-daily schedules. Actual dosing decisions should always be made with a physician or pharmacist.

Half-Life Time of Medicine