Drug Half-Life Calculator

How to use this half-life calculator

1. Choose a drug or enter its half-life. Choosing from the list in the name field, which you can search by generic or brand name, fills in a typical half-life. For any other drug, type its name and enter the half-life in minutes, hours or days.
2. Add the doses. Give each dose a time in hours and an amount. Add dose continues the schedule, and Repeat dose adds a series.
3. Choose the absorption. Instant puts each dose in the body at once. Cmax / Tmax lets the level rise to a peak first.
4. Read the results. Point at or tap a chart to read the level at any hour. The summary shows the peak, when it happens, and when the level stays below 5% of the peak.

What is a drug's half-life?

A drug's half-life (t½) is the time it takes for the amount of the drug in the body to fall by half. With a half-life of 6 hours, a 100 mg dose leaves 50 mg after 6 hours, 25 mg after 12 hours and 12.5 mg after 18 hours. The same share is removed in each half-life, so the level falls quickly at first and more slowly later.

How do you calculate how much of a drug is left?

Amount left = dose × (1/2)^{t ÷ t½}

Here t is the time since the dose and t½ is the half-life, both in the same unit. For example, take 200 mg of a drug with a 6-hour half-life. After 15 hours, 2.5 half-lives have passed, so 200 × (1/2)^2.5 ≈ 35.4 mg is left. With several doses, work this out for each dose and add the results. That is what the calculator does.

How long does a drug stay in the body?

A common rule of thumb is that a drug is essentially gone after about five half-lives, when roughly 97% has been eliminated. That is about 30 hours for a 6-hour half-life and about 20 days for a 4-day half-life.

Treat that as a rough guide. Half-lives vary from person to person, and liver or kidney problems can change them. Some drugs also break down into active metabolites that last longer than the drug itself. The calculator cannot tell you when a drug's effects have worn off, or whether a drug test would still detect it.

What happens with repeated doses?

If a new dose arrives before the last one has cleared, it adds to what is left, so the level climbs with each dose. On a regular schedule it levels off at a steady state after about four to five half-lives. A larger dose raises the level but does not change how long that takes.

For example, with an instant dose taken once every half-life, the level settles between one and two times the dose. To see this, use Repeat dose on any drug and set the interval to its half-life.

What are Tmax and Cmax?

Tablets and other oral forms are absorbed over time, so the level rises to a peak before it falls. Tmax is the time from a dose to that peak, and Cmax is the concentration at the peak. In Cmax / Tmax mode the calculator works out the absorption rate from Tmax and the half-life. Add Cmax and the dose that produced it to chart a concentration, such as mg/L, instead of an amount.

Which formulas does the calculator use?

It uses a one-compartment model with first-order absorption and elimination and linear kinetics, and each dose adds its own curve to the total. The elimination rate is k_e = ln 2 ÷ t½, and k_a is the absorption rate. For a dose A taken at time 0, the amount at time t is:

Instant absorption:
A · e^−k_et
Gradual absorption:
A · k_a ÷ (k_a − k_e) · (e^−k_et − e^−k_at)

Where can I find a drug's half-life?

The prescribing information usually lists it in the pharmacokinetics section. In the United States, DailyMed publishes current FDA drug labels. Published values are averages, so ask a doctor or pharmacist what applies to you.

The list in the name field holds 46 entries for common drugs and everyday substances, and you can search it by generic or brand name. Choosing one fills in the typical or mean half-life that its source states. If the source gives only a range, the calculator uses the midpoint, and if it gives only an upper limit, it uses that limit. The source and any caveats, such as active metabolites, appear below the field. Choosing a drug also fills in its Tmax, where a source gives one. Extended-release forms have their own entries and start in Cmax / Tmax mode, so their curves rise gradually. A brand name only helps you find the drug: the half-life comes from the cited source and may not apply to that product, and a combination product contains other drugs as well.

These are typical values for healthy adults, as stated in FDA documents, NIH-hosted reviews or published human studies. Age, liver and kidney function, genetics and interacting drugs can change them substantially. They are a general reference only, not medical advice.

When does this model not apply?

This page is an illustration, not medical advice. Do not use it to decide, change or time your doses. The model also leaves out several things:

• Alcohol and other drugs with saturable elimination. These are removed at a roughly constant rate, not by half over a fixed time, so a single half-life does not describe them.
• Drugs with several phases of elimination. One compartment cannot draw a drug that spreads slowly into tissues and returns later.
• Interactions. Each drug is calculated on its own, so the effect of one drug on another is not included.

Sources

• Elimination Half-Life of Drugs, StatPearls, NCBI Bookshelf
• Steady State Concentration, StatPearls, NCBI Bookshelf
• Physiology, Zero- and First-Order Kinetics, StatPearls, NCBI Bookshelf

Half-lives in the drug list:

• Acetaminophen: FDA label (Ofirmev, IV)
• Ibuprofen: FDA label (Motrin)
• Naproxen: FDA label (Naprosyn)
• Aspirin (acetylsalicylic acid): FDA label (Soma Compound, carisoprodol and aspirin)
• Diphenhydramine: NIH StatPearls
• Cetirizine: FDA label (Zyrtec)
• Loratadine: NIH StatPearls (loratadine); FDA label (Clarinex, desloratadine)
• Omeprazole: FDA label (Prilosec)
• Sertraline: FDA label (Zoloft)
• Citalopram: FDA label (Celexa)
• Escitalopram: FDA label (Lexapro)
• Paroxetine: FDA label (Paxil)
• Fluoxetine: FDA label (Prozac)
• Venlafaxine: FDA label (Effexor)
• Venlafaxine XR: FDA label (Effexor XR, DailyMed)
• Duloxetine: FDA label (Cymbalta)
• Alprazolam: FDA label (alprazolam tablets, DailyMed)
• Alprazolam XR: FDA label (Xanax XR, DailyMed)
• Lorazepam: FDA label (Ativan)
• Lorazepam XR: FDA label (Loreev XR, DailyMed)
• Clonazepam: FDA label (Klonopin)
• Diazepam: FDA label (Valium)
• Midazolam: FDA label (midazolam injection)
• Morphine: FDA label (morphine sulfate tablets)
• Morphine ER tablets: FDA label (MS Contin, DailyMed)
• Morphine ER capsules: FDA label (morphine sulfate extended-release capsules, DailyMed)
• Codeine: FDA label (codeine sulfate)
• Oxycodone: FDA label (oxycodone HCl tablets, DailyMed)
• Oxycodone ER: FDA label (OxyContin, DailyMed)
• Tramadol: FDA label (Ultram)
• Tramadol ER tablets: FDA label (tramadol hydrochloride extended-release tablets, DailyMed)
• Tramadol ER capsules: FDA label (ConZip, DailyMed)
• Amlodipine: FDA label (Norvasc)
• Lisinopril: FDA label (Zestril)
• Metoprolol (tartrate): FDA label (Lopressor)
• Atorvastatin: FDA label (Lipitor)
• Rosuvastatin: FDA label (Crestor)
• Pravastatin: FDA label (Pravachol)
• Simvastatin: Human pharmacokinetic study (Die Pharmazie 2013, PubMed)
• Metformin: FDA label (Glucophage)
• Metformin ER: FDA label (Glumetza, DailyMed)
• Levothyroxine (T4): FDA label (Synthroid)
• Warfarin: FDA label (Jantoven, DailyMed)
• Caffeine: FDA memorandum summarising human studies
• Nicotine: NIH-hosted pharmacology review (Benowitz)
• Alcohol (ethanol): NIH-hosted review (Alcohol Metabolism)

Where a note cites a second source, such as for Tmax, the link is in the note.