Calculator
Accumulation Index Calculator
How much a drug builds up when the next dose arrives before the last has cleared.
Accumulation index (R)
2.00×
Moderate accumulation — consider a dose adjustment.
Dosing parameters
Time for the concentration to fall by half.
24 for once daily, 12 for twice daily, 8 for three times daily.
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Working
Accumulation scale
k = 0.693 / t½
R = 1 / (1 − e^(−k · τ))
The exponential term is the fraction of drug still present when the next dose is given. If half remains, the next dose lands on top of it, then the one after lands on top of that — and the series converges on R times the single-dose concentration.
Dose an interval equal to the half-life and R is 2. Dose every half-life for a drug with a long half-life and R grows quickly, which is why a long-half-life drug given frequently is the classic recipe for delayed toxicity.
Keep learning
References
- Rowland and Tozer's Clinical Pharmacokinetics and Pharmacodynamics: Concepts and Applications. 5th ed. Philadelphia: Wolters Kluwer; 2019.
- Ducharme MP, Shargel L, editors. Shargel and Yu's Applied Biopharmaceutics & Pharmacokinetics. 8th ed. New York: McGraw Hill; 2022.
Common questions
No. R depends only on the half-life and the interval. A bigger dose raises every concentration proportionally, but the ratio of steady state to first dose is unchanged.
About 4 half-lives gets you to 94% and 5 half-lives to 97%, whatever the interval. This is why a loading dose exists: for a drug with a 72-hour half-life, waiting for steady state means waiting the better part of a fortnight.
There is no universal threshold — it depends on the therapeutic index. R of 5 for a drug with a wide margin may be fine; R of 2 for digoxin or lithium is worth planning around. Use the value to decide whether monitoring is needed, not as a pass/fail.
Not meaningfully. R is set by τ relative to t½, so lengthening the interval lowers R but also lowers the average concentration unless each dose is made larger. The trade is between a flat profile with more frequent dosing and bigger peaks and troughs with less frequent dosing.
It is the natural logarithm of 2. First-order elimination is exponential, so the constant that turns a half-life into a rate constant is ln 2.
Prepared by the PharmaWallah student team. Verify results with your textbook or instructor. Report an error · Editorial policy