The dosing interval for a drug is calculated using the drug’s half-life, the elimination rate constant derived from it, and the desired peak and trough concentrations you want to maintain. The core formula is: dosing interval (τ) = (ln(desired peak / desired trough) / elimination rate constant) + infusion time. For a quick rule of thumb, setting the dosing interval equal to the half-life keeps blood levels within a roughly two-fold fluctuation between peak and trough at steady state.
The Elimination Rate Constant
Before you can calculate a dosing interval, you need to convert the half-life into something more mathematically useful: the elimination rate constant, abbreviated as k. The relationship is straightforward.
k = 0.693 / half-life
The 0.693 comes from the natural logarithm of 2, which reflects the fact that a half-life is the time it takes for exactly half the drug to be cleared. If a drug has a half-life of 6 hours, its elimination rate constant is 0.693 / 6 = 0.1155 per hour. This number tells you the fraction of the drug eliminated per unit of time and feeds directly into the dosing interval formula.
The Dosing Interval Formula
The standard pharmacokinetic equation for the recommended dosing interval (τ, or “tau”) is:
τ = (ln(Cmax desired / Cmin desired) / k) + T
Here’s what each piece means:
- Cmax desired: the highest blood concentration you want to reach after a dose (the peak)
- Cmin desired: the lowest acceptable concentration right before the next dose (the trough)
- k: the elimination rate constant you calculated from the half-life
- T: the infusion time, meaning how long it takes to administer the dose (for an oral dose or a rapid injection, this is often treated as zero or near-zero)
The “ln” is the natural logarithm. What the formula really asks is: how long does it take for the drug concentration to fall from your target peak down to your target trough, given the rate at which the body eliminates it? That decay time, plus however long the infusion takes, gives you the interval between doses.
A Worked Example
Say you’re working with a drug that has a half-life of 8 hours. You want a peak concentration of 10 mg/L and a trough no lower than 2 mg/L, and the drug is given as a rapid injection (T ≈ 0).
First, find k: 0.693 / 8 = 0.0866 per hour.
Then plug into the formula: τ = ln(10 / 2) / 0.0866 = ln(5) / 0.0866 = 1.609 / 0.0866 ≈ 18.6 hours.
You’d round this to a practical schedule, likely every 18 or 24 hours depending on clinical context and convenience. Dosing intervals are almost always rounded to numbers that fit real life: every 6, 8, 12, or 24 hours.
The Simple Rule: Interval Equals Half-Life
When the dosing interval is set equal to the drug’s half-life, the concentration drops by exactly half between doses. At steady state, this means the peak will be roughly twice the trough. A drug with a 12-hour half-life dosed every 12 hours will fluctuate within that two-fold range once levels stabilize.
This is a useful baseline. When you need the interval equal to the half-life, the loading dose is simply twice the maintenance dose, and steady state is achieved immediately. For drugs with a wide safety margin between effective and toxic concentrations, this two-fold fluctuation is perfectly acceptable, and it simplifies dosing considerably.
How Steady State Fits In
Regardless of the interval you choose, the drug needs time to build up to its stable, repeating pattern of peaks and troughs. This buildup follows a predictable timeline measured in half-lives:
- 1 half-life: 50% of steady-state concentration
- 2 half-lives: 75%
- 3 half-lives: 87.5%
- 5 half-lives: greater than 95%
Five half-lives is the standard benchmark for reaching steady state. For a drug with a 6-hour half-life, that’s 30 hours. For a drug with a 24-hour half-life, it’s 5 days. This matters because checking blood levels or judging whether a dosing regimen is working before steady state is reached will give misleading results. If any part of the regimen changes (dose size, interval, or both), the five-half-life clock resets.
This is also why loading doses exist. For drugs with long half-lives, waiting days to reach effective levels isn’t practical. A loading dose, calculated as the target concentration multiplied by the volume of distribution, jumps you to therapeutic levels right away, and the maintenance doses keep you there.
Narrow Therapeutic Index Drugs
The ratio between your desired peak and trough determines how much flexibility you have with the interval. For drugs where the toxic concentration is only slightly above the effective concentration (a narrow therapeutic index), you need to keep fluctuations small. That means shorter dosing intervals relative to the half-life, so the concentration stays within a tight band.
In the formula, this shows up as a small ratio of Cmax to Cmin. If you can only tolerate a peak-to-trough ratio of 1.5 instead of 5, the calculated interval shrinks significantly. These drugs often require blood level monitoring and individualized dosing because even modest changes in how quickly someone eliminates the drug can push levels into the toxic range.
Adjusting for Organ Impairment
The half-life your formula uses should reflect the actual patient, not just the textbook value. Kidney or liver disease can slow elimination dramatically, effectively lengthening the half-life and lowering the elimination rate constant. A drug with a normal half-life of 8 hours might stretch to 40 hours or more in someone with severe kidney impairment.
There are two standard ways to adjust:
- Keep the interval, reduce the dose. You give less drug each time but on the same schedule. This keeps the timing simple but changes the peak-to-trough pattern.
- Keep the dose, extend the interval. You give the full dose less frequently, matching the slower elimination. This preserves the original peak concentration but allows more time between doses.
In practice, clinicians often use a combination of both to land on a regimen that’s both effective and practical. The adjustment factor is based on the patient’s remaining elimination capacity, estimated from measures like creatinine clearance for kidney function. For a drug that’s 70% eliminated by the kidneys, a patient with half-normal kidney function would need roughly a 35% dose reduction or a proportionally longer interval to avoid accumulation.
Putting It All Together
The sequence for calculating a dosing interval works like this. Start with the drug’s known half-life and convert it to the elimination rate constant (0.693 / half-life). Identify your target peak and trough concentrations based on the drug’s therapeutic range. Plug those values into the formula: τ = ln(Cmax / Cmin) / k, adding infusion time if applicable. Round the result to a clinically practical interval. Then confirm that steady state will be reached within an acceptable timeframe (five half-lives), and decide whether a loading dose is needed to bridge the gap.
If the patient has impaired elimination, recalculate k using the adjusted half-life before running the formula. The math stays the same; only the inputs change.