Drug half-life is calculated using the formula t½ = 0.693 / k, where k is the elimination rate constant. The number 0.693 is the natural logarithm of 2, and it appears because half-life literally measures the time it takes for a drug’s concentration to drop by half. If you know how quickly a drug is being cleared from the body, this formula gives you the half-life directly.
The Core Half-Life Formula
The standard equation for first-order drug elimination is:
t½ = 0.693 / k
Here, t½ is the half-life in hours (or minutes, depending on the drug), and k is the elimination rate constant, expressed as a fraction per unit of time. If k = 0.1 per hour, the drug’s half-life is 0.693 / 0.1 = 6.93 hours. The constant 0.693 comes from ln(2), which is baked into any process where something decays by exactly half.
Most drugs follow first-order kinetics, meaning a fixed percentage of the drug is eliminated per unit of time rather than a fixed amount. This is what makes the half-life constant regardless of dose: whether you start with 500 mg or 50 mg in the bloodstream, it still takes the same amount of time for the concentration to halve.
How to Find the Elimination Rate Constant
To use the formula above, you first need k. The standard method is to measure blood drug concentrations at multiple time points after dosing, then plot those concentrations on a logarithmic scale against time. During the terminal elimination phase (after the drug has fully distributed through the body), this plot forms a straight line. The slope of that line is the negative value of k.
In practice, this means you need at least two concentration measurements taken during the elimination phase. If you know the concentration drops from 80 mcg/mL to 20 mcg/mL over 10 hours, you can calculate k using the natural log of the ratio:
k = ln(80/20) / 10 = ln(4) / 10 = 1.386 / 10 = 0.1386 per hour
Then plug that into the half-life formula: t½ = 0.693 / 0.1386 = 5 hours.
The Clearance and Volume Formula
There’s a second half-life equation that’s useful when you don’t have concentration-time data but do know a drug’s pharmacokinetic parameters:
t½ = 0.693 × Vd / CL
Vd is the volume of distribution, which reflects how widely a drug spreads through body tissues. CL is clearance, the volume of blood completely cleared of the drug per unit of time. This formula shows why half-life isn’t purely about how fast the body eliminates a drug. A drug that distributes into a huge “virtual volume” of tissue will have a longer half-life even if clearance is efficient, because there’s simply more drug tucked away in tissues for the body to work through.
This version of the formula is especially helpful for understanding why the same drug can have different half-lives in different patients. Anything that changes clearance (like kidney disease reducing elimination) or volume of distribution (like obesity increasing fat-soluble drug storage) will shift the half-life.
Tracking Drug Levels Over Multiple Half-Lives
Once you know the half-life, you can predict how much drug remains at any point. The math is simple: the concentration halves with each half-life that passes.
- After 1 half-life: 50% remains
- After 2 half-lives: 25% remains
- After 3 half-lives: 12.5% remains
- After 4 half-lives: 6.25% remains
- After 5 half-lives: 3.125% remains
This pattern works in reverse too. When you take repeated doses, the drug accumulates until it reaches a steady state, which takes approximately five half-lives. At that point, the amount entering the body per dose equals the amount being eliminated between doses.
A Worked Example
Say a drug has a half-life of 9 hours, and you want to know how long until only about 6% of the original steady-state level remains after stopping the medication. Using the table above, 6.25% remains after four half-lives. Four half-lives at 9 hours each gives you 36 hours.
You can also work backward. If you know a drug drops from 100 mg to 25 mg in 6 hours, it went through two half-lives in that window (100 → 50 → 25), so each half-life is 3 hours. From there, k = 0.693 / 3 = 0.231 per hour.
When the Standard Formula Doesn’t Apply
The formulas above assume first-order kinetics, where elimination rate depends on concentration. A small number of drugs, most notably alcohol, follow zero-order kinetics instead. In zero-order elimination, the body removes a fixed amount per hour regardless of how much drug is present (because the enzymes responsible are completely saturated). The zero-order half-life formula is:
t½ = initial concentration / (2 × k)
The critical difference is that this half-life changes depending on the starting concentration. A higher blood alcohol level doesn’t just mean more alcohol to clear; it means each “half” takes longer. This is why alcohol elimination is often described as a flat rate (roughly one standard drink per hour) rather than a half-life.
What Changes a Drug’s Half-Life
Half-life is not a fixed property of a molecule in the way that molecular weight is. It depends on the interaction between the drug and the body eliminating it, so several physiological factors can shift it significantly.
Kidney function is the most common variable. Drugs eliminated primarily through the kidneys will have a longer half-life when kidney filtration declines, whether from aging, disease, or dehydration. Liver function matters for drugs that are metabolized before excretion. Reduced liver enzyme activity slows clearance and extends half-life.
Drug interactions also play a role. Some medications speed up liver enzyme activity (a process called enzyme induction), which increases clearance and shortens half-life. The result can be a loss of effectiveness for the affected drug, because it’s being broken down faster than expected. Other medications inhibit those same enzymes, slowing metabolism, extending half-life, and potentially causing toxicity from drug accumulation.
Body composition matters as well. Fat-soluble drugs may have a larger volume of distribution in people with higher body fat, extending the half-life. Age-related changes in both body composition and organ function mean that half-life values listed in drug references represent population averages, not guarantees for any individual patient.