PharmaCalc

The f1 (difference) and f2 (similarity) factors are model-independent metrics for comparing two dissolution profiles — typically a test (post-change or generic) product against a reference. The method was published by Moore and Flanner (1996) and adopted by FDA in its 1997 guidance on dissolution testing of immediate-release solid oral dosage forms; EMA applies materially the same approach in its 2010 bioequivalence guideline. FDA's stated basis: “f1 values up to 15 (0–15) and f2 values greater than 50 (50–100) ensure sameness or equivalence of the two curves.”

Where this is used:

• Post-approval manufacturing changes (SUPAC).
• Generic development and BCS-based biowaivers.
• Site transfers, scale-up, and equipment changes.
• Comparing profiles across strengths or stability time points.

f2 similarity supports, but does not by itself establish, bioequivalence.

Preconditions for a valid f2 comparison (FDA 1997; EMA 2010 Appendix I): 12 units per product at each time point · at least three time points (zero excluded), identical for both products · %CV not more than 20% at the earlier time points (e.g. 15 minutes) and not more than 10% at other time points — high variability invalidates f2; use a multivariate or bootstrap approach instead · the 85% rule: “Only one measurement should be considered after 85% dissolution of both the products” (FDA 1997; EMA's formulation: not more than one mean value > 85% dissolved for any formulation). Including multiple post-plateau points inflates f2 artificially. PharmaCalc enforces the EMA form — not more than one mean value > 85% dissolved for either product — which is at least as strict as the FDA wording.

Scenario: an immediate-release tablet is compared before and after a manufacturing change. Four shared time points; each value is the mean of 12 units per product.

1. Tabulate the profiles and differences.
   Example Data

   Time (min)	Rₜ (%)	Tₜ (%)	|R−T|	(R−T)²
   15	25	27	2	4
   30	55	52	3	9
   45	75	72	3	9
   60	85	83	2	4

2. Check the preconditions: 12 units per point, four shared time points, CVs within 20%/10%, and no mean value exceeds 85% dissolved for either product — so all four points are validly included.
3. Compute f1.
   Calculation

   Σ|R−T| = 10; ΣR = 240
   f1 = (10/240) × 100 = 4.17
4. Compute f2.
   Calculation

   Σ(R−T)² = 26; 26/4 = 6.5
   100/√7.5 = 36.51
   f2 = 50 × log₁₀(36.51) = 78.12
5. Conclude.
   Interpretation

   f1 = 4.17 ≤ 15 and f2 = 78.12 ≥ 50 → the profiles are similar.

• Acceptance: f2 ≥ 50 → profiles similar; f2 < 50 → not similar by this metric. PharmaCalc's verdict is governed by f2 alone: f1 ≤ 15 supports sameness (FDA states both ranges together) and is reported as a supporting metric, flagged when it exceeds 15, but it does not overturn an f2 pass.
• Preconditions gate the verdict: it applies only if the unit counts, time-point, CV, and 85% conditions are met. If both products dissolve ≥ 85% within 15 minutes, EMA regards profiles as similar without an f2 calculation.
• Mean profiles only: f1 and f2 compare means; with high variability, f2 is not appropriate.
• Time-point sensitivity: f2 is sensitive to the number and placement of time points; post-plateau points inflate it — that is what the 85% rule prevents.
• Asymmetry: f1 normalises by the reference; swapping test and reference changes f1 but not f2.
• Scope of the conclusion: similarity by f2 is a formulation-performance conclusion, not a standalone bioequivalence conclusion.

• Moore, J.W. and Flanner, H.H. (1996). Mathematical Comparison of Dissolution Profiles. Pharmaceutical Technology 20(6):64–74.
• FDA, Dissolution Testing of Immediate Release Solid Oral Dosage Forms, August 1997. fda.gov/media/70936/download
• EMA, Guideline on the Investigation of Bioequivalence, CPMP/EWP/QWP/1401/98 Rev. 1 (2010), Appendix I. ema.europa.eu