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f1/f2 Similarity Factor

FDA-recommended statistical test for comparing dissolution profiles. Establishes similarity between reference and test products.

FDA Guidance SUPAC Generic Drug
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Industry Use

Profile Comparison and Biowaiver Strategy

The f1/f2 similarity factor is the FDA-recommended mathematical approach for comparing two dissolution profiles (typically a reference/brand product and a generic/test product). This test was introduced in the FDA's 1997 Guidance for Industry and is now standard in regulatory submissions worldwide. The f2 factor is particularly important for establishing bioequivalence waivers and post-approval changes.

Key Applications:

FDA Guidance and EMA guidelines both accept f2 ≥ 50 as proof of profile similarity. f2 = 100 indicates identical profiles.

FDA 1997 Guidance EMA Guideline f2 ≥ 50
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Calculation Explanation

Difference and Similarity Factors

Two factors are calculated: the difference factor (f1) measures the percent absolute difference between profiles, while the similarity factor (f2) measures the logarithmic reciprocal square root of the sum of squared differences. f2 is the primary criterion for establishing similarity.

f1 (Difference Factor) — Measures Absolute Difference:

Difference Factor Formula
f1 = (Σ|Rₜ − Tₜ| / ΣRₜ) × 100

Where Rₜ = dissolution at time t for reference product, Tₜ = dissolution at time t for test product.

Interpretation: f1 ranges from 0 to 100. f1 = 0 indicates identical profiles. Values closer to 0 indicate greater similarity.

f2 (Similarity Factor) — Primary Acceptance Criterion:

Similarity Factor Formula
f2 = 50 × log₁₀{[1 + (1/n)Σ(Rₜ − Tₜ)²]⁻⁰·⁵ × 100}

Where n = number of time points, Rₜ and Tₜ as above.

Acceptance Criteria:

Prerequisites for f2 Calculation:

FDA 1997 f2 ≥ 50 4+ Time Points
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Variable Definitions

f1/f2 Calculation Parameters

Symbol Parameter Name Units Description
n Number of Time Points time points Count of dissolution measurements. Must be ≥ 3; typical is 4–6. Same time points used for both reference and test.
Rₜ Reference Dissolution % Released Dissolution value (% API released) for the reference/brand product at time t. Usually average of 6 or 12 units.
Tₜ Test Dissolution % Released Dissolution value (% API released) for the test/generic product at time t. Usually average of 6 or 12 units.
f1 Difference Factor 0–100 Measure of absolute percent difference. f1 = 0 = identical; larger values = greater difference. Typically < 15 for similar profiles.
f2 Similarity Factor 0–100 Primary acceptance criterion. f2 ≥ 50 = SIMILAR (acceptable). f2 = 100 = identical. f2 < 50 = NOT SIMILAR.
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Step-by-Step Tutorial

Worked Example with Four Time Points

Scenario: A generic manufacturer is developing an immediate release tablet formulation to match a reference brand product. Dissolution testing is performed at four time points. The applicant compares the generic (test) profile to the brand (reference) profile using f1/f2 analysis to support a biowaiver for in vivo bioequivalence testing.

Dissolution Profiles: Reference vs. Test (n=4 time points)
Time (min) Reference (%) Test (%) Difference |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
  1. Calculate f1 (Difference Factor):
    f1 = (Σ|Rₜ − Tₜ| / ΣRₜ) × 100
    Σ|Rₜ − Tₜ| = 2 + 3 + 3 + 2 = 10
    ΣRₜ = 25 + 55 + 75 + 85 = 240
    f1 = (10 / 240) × 100 = 4.17
  2. Calculate Mean Squared Difference:
    Σ(Rₜ − Tₜ)² = 4 + 9 + 9 + 4 = 26
    Mean = 26 / n = 26 / 4 = 6.5
  3. Calculate f2 (Similarity Factor):
    f2 = 50 × log₁₀{[1 + (1/n)Σ(Rₜ − Tₜ)²]⁻⁰·⁵ × 100}
    Step A: 1 + (1/4) × 26 = 1 + 6.5 = 7.5
    Step B: (7.5)⁻⁰·⁵ = 1/√7.5 = 1/2.739 = 0.3651
    Step C: 0.3651 × 100 = 36.51
    Step D: log₁₀(36.51) = 1.5623
    f2 = 50 × 1.5623 = 78.12
  4. Apply Acceptance Criteria:
    f1 = 4.17 (typically < 15 for similar profiles) ✓
    f2 = 78.12
    Criterion: f2 ≥ 50
    Result: 78.12 ≥ 50 ✓
✓ PROFILES ARE SIMILAR
f1 = 4.17 | f2 = 78.12 (Limit: ≥50)
Biowaiver eligible. In vivo BE not required (subject to BCS classification).

Interpretation: The test product's dissolution profile is highly similar to the reference product (f2 = 78.12, well above the 50 threshold). The low f1 value (4.17) confirms minimal absolute difference between the profiles. The products exhibit comparable release kinetics at all four time points, supporting the assumption of equivalent bioavailability and qualifying for a biowaiver from in vivo bioequivalence testing.

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