Pharmacokinetics
Bioequivalence Calculator
Checks whether a test product's AUC and Cmax 90% confidence intervals fall inside the 80–125% acceptance range against a reference product.
Bioequivalence verdict
Fail
Not bioequivalent — AUC and Cmax outside 80–125%. AUC 90% CI 77.8–92.2% · Cmax 90% CI 75.6–91.1%.
Study design
Typically 18–24 subjects in a crossover study.
The interval is always computed with z = 1.645 (the 90% CI), whichever alpha is chosen.
AUC — primary endpoint
Mean and standard deviation (SD). Any unit (e.g. ng·h/mL), as long as test and reference use the same one.
Cmax — secondary endpoint
Peak concentration, mean and SD, in the same unit for both products (e.g. ng/mL).
Try an example study
90% confidence intervals
Shaded band = 80–125% acceptance range.
Working
Ratio = mean(Test) ÷ mean(Reference)
SE = √[(SD_T ÷ mean_T)² + (SD_R ÷ mean_R)²] ÷ √N
90% CI = Ratio ± 1.645 × SE
Power ≈ 100 − 2 × CV, where CV = √(SD_T² + SD_R²) ÷ [(mean_T + mean_R) ÷ 2] × 100
Each SD is turned into a coefficient of variation (SD ÷ mean), the two are combined, and dividing by √N shrinks the uncertainty as more subjects are studied. The product passes when the whole interval — not just the ratio — sits inside 80–125% for both AUC and Cmax.
Formal studies log-transform the data, run an ANOVA on the crossover design and use a t-value with the study's degrees of freedom. This tool is an approximation for learning how N, variability and the ratio drive the result.
Keep learning
References
- Ducharme MP, Shargel L, editors. Shargel and Yu's Applied Biopharmaceutics & Pharmacokinetics. 8th ed. New York: McGraw Hill; 2022.
Common questions
The limits are symmetric on a log scale: ln(0.8) = −0.223 and ln(1.25) = +0.223. A test product 20% lower than the reference is as far from equivalence as one 25% higher.
The verdict depends on the whole confidence interval, not the ratio. High variability (large SDs) or too few subjects widen the interval until one end crosses 80% or 125%. Try increasing N to see the interval narrow.
Any — the calculation only uses ratios, so units cancel. What matters is that the test and reference values are in the same unit.
No. The calculation always uses z = 1.645, which corresponds to the 90% interval that regulators require (two one-sided tests at α = 0.05).
The interval is so wide that it runs below 80% and above 125% at the same time. The study cannot say whether the products differ — usually a sign of high variability or too few subjects.
Prepared by the PharmaWallah student team. Verify results with your textbook or instructor. Report an error · Editorial policy