Hong Life CalculatorsUnderstanding the drug half-life calculator — concept and principle
This calculator shows how much of a single dose of a medicine or other substance is still in the body after a given number of hours, based on its elimination half-life. People use it to understand why a drug wears off, when a medicine is "practically gone", or how long to wait before a test or another medicine.
How it is calculated
Fraction left = 0.5^(t ÷ t½)
Amount left = starting amount × fraction left
Time to reach a fraction f = t½ × log₂(1 ÷ f)
- t½ is the elimination half-life in hours, taken from the leaflet or a pharmacology reference.
- t is the time since the dose in hours.
- The starting amount can be in any unit (mg, µg, tablets); the amount left uses the same unit.
- The calculator also shows the time to fall below 10%, to about 3% (5 half-lives) and below 1%.
The principle
Most substances are eliminated by first-order kinetics: the body removes the same fraction in each equal step of time, not the same amount. If half leaves in 6 hours, half of what is left leaves in the next 6 hours, and so on. That gives the halving pattern 50%, 25%, 12.5%, 6.25%. After five half-lives about 3% remains, which is why five half-lives is widely used as the point where a single dose is practically gone.
Worked example
Default inputs: half-life 6 h, 24 h since the dose, starting amount 100.
- Half-lives passed = 24 ÷ 6 = 4.
- Fraction left = 0.5⁴ = 0.0625 = 6.3% (shown rounded); eliminated 93.8%.
- Amount left = 100 × 0.0625 = 6.25.
- Time below 10% = 6 × log₂(10) = 6 × 3.322 = 19.9 h.
- Time to about 3% = 5 × 6 = 30 h; below 1% = 6 × log₂(100) = 39.9 h.
| Hours since it was taken | Still in the body |
|---|---|
| 6 | 50% |
| 12 | 25% |
| 18 | 12.5% |
| 24 | 6.3% |
| 30 | 3.1% |
| 36 | 1.6% |
| 48 | 0.4% |
How to read the result
A low percentage left means the drug's direct effect has mostly faded, though some effects (for example on enzymes or receptors) can outlast the drug. With regular dosing, levels build up and reach a steady state after about four to five half-lives, which this single-dose picture does not show.
Common mistakes
- Assuming the drug is gone after one half-life. Half is still there.
- Ignoring absorption. The clock really starts once the drug is absorbed, so peak levels come later than the dose.
- Using it for alcohol, which is removed at a roughly constant amount per hour, not a constant fraction.
- Forgetting that kidney or liver disease, age and other medicines can lengthen the half-life a lot.
Frequently asked questions
What does "five half-lives" mean?
After five half-lives about 3% of a single dose remains, so the drug is usually considered cleared for practical purposes.
Why do some drugs have a long half-life?
They may be stored in fat or tissues, bind strongly to proteins, or be removed slowly by the liver or kidneys.
Do active metabolites matter?
Yes. Some drugs turn into active compounds with their own, sometimes longer, half-lives.
Where do I find a drug's half-life?
The product leaflet or summary of product characteristics usually lists it under pharmacokinetics.
Sources: Rowland M, Tozer TN, Clinical Pharmacokinetics and Pharmacodynamics: Concepts and Applications, 4th ed., Lippincott Williams & Wilkins, 2011, ch. 3