Not for clinical use. This calculator supports clinical decisions (dosing, a risk score, an obstetric or laboratory assessment) and has not been reviewed by a named qualified clinician. It is published for reference and education only, it is excluded from search indexing for that reason, and it must not be used to guide the care of any patient. Verify every figure against the primary source and your own professional judgement.
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).
This content is provided for educational purposes only and has not been reviewed by a qualified specialist in this field. See our methodology and review panel.