Drug Accumulation Ratio Calculator
When a drug is administered repeatedly before it is fully eliminated, plasma concentrations build up (accumulate) until steady state is reached. The accumulation ratio (R) quantifies this buildup: R = 1 / (1 - e^(-ke x tau)), where ke is the elimination rate constant (hr-1) and tau is the dosing interval (hr). R is always 1 or greater. An R of 2 means steady-state concentrations are twice those after a single dose. Knowing R allows clinicians to predict steady-state levels from single-dose data, an important concept in dose-ranging studies and drug information.
Drug accumulation ratio formula
R = 1 / (1 - e^(-ke x tau))
ke = elimination rate constant (hr-1) = 0.693 / t1/2; tau = dosing interval (hr). When tau equals t1/2 (ke x tau = 0.693), R = 1/(1 - 0.5) = 2. Longer tau relative to t1/2 reduces R toward 1.
Interpreting drug accumulation
- R = 1: no accumulation (dosing interval very long relative to half-life).
- R = 2: tau equals one half-life; steady-state Cmax is twice that of a single dose.
- R greater than 5: dosing interval is short relative to half-life; substantial accumulation occurs.
- Examples: fluoxetine (t1/2 1 to 4 days, once daily dosing) accumulates significantly over weeks; aspirin (t1/2 15 min) does not accumulate with 4-hourly dosing.
- Accumulation ratio is also used to estimate how long a loading-dose period lasts before steady state is reached.
Drug accumulation ratio: frequently asked questions
What is drug accumulation ratio?
The accumulation ratio (R) is the ratio of the steady-state AUC (or Cmax or Cmin) to the AUC after a single dose. It indicates how much drug accumulates with repeated dosing relative to a single dose. R = 1 means no accumulation; R greater than 1 means accumulation.
What does a high accumulation ratio mean?
A high R means drug plasma levels are substantially higher at steady state than after a single dose. This occurs when the dosing interval is short relative to the half-life, causing residual drug from previous doses to add to each new dose. Drugs with long half-lives and short dosing intervals have high R values.
How does the dosing interval affect accumulation?
A shorter dosing interval relative to half-life leads to greater accumulation (higher R). If tau equals one half-life, R = 2. If tau is much longer than the half-life, R approaches 1 (essentially no accumulation between doses).
What is the relationship between accumulation ratio and peak-to-trough ratio?
The accumulation ratio R applies to average concentration or AUC. The peak-to-trough ratio depends on both R and the fraction eliminated during each interval. Drugs with high R have relatively stable plasma levels; drugs with low R show large swings between peaks and troughs.
Can this calculator be used for clinical decisions?
This tool is for educational and pharmacokinetic learning purposes only. Clinical dosing decisions require patient-specific assessment by qualified healthcare professionals using therapeutic drug monitoring and institutional protocols.
Official sources
- U.S. Food and Drug Administration: FDA Pharmacokinetics Guidance.
- NIH National Library of Medicine: Pharmacokinetics (StatPearls).
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.