How to calculate the f2 similarity factor: a worked example

The formula

f2 is calculated from the mean percentage dissolved for the reference (R) and test (T) products at each time point:

where n is the number of time points and R_t, T_t are the mean percentages dissolved at time t.

Conditions before you calculate

Regulatory guidance (US FDA guidance on dissolution testing of immediate-release oral dosage forms, and the EMA guideline on the investigation of bioequivalence) expects the following:

• At least 12 units of each product, tested under identical conditions.
• At least 3 time points, excluding zero, at the same times for both products.
• No more than one time point after both products have reached 85% dissolved.
• Low variability: coefficient of variation not more than 20% at the earlier time points and not more than 10% at later time points.
• If both products dissolve 85% or more within 15 minutes, the profiles are generally accepted as similar without calculating f2.

If variability is too high, f2 on the means is not reliable. Use a bootstrap f2 or a model-independent multivariate approach instead.

Worked example

Mean percentage dissolved for a reference tablet and a test formulation (12 units each):

1. Mean squared difference: 46 ÷ 5 = 9.2
2. Add 1: 1 + 9.2 = 10.2
3. Raise to the power −0.5: 10.2^−0.5 = 0.3131
4. Multiply by 100: 31.31
5. Take log₁₀: 1.4957
6. Multiply by 50: f2 = 74.8

Only the 45-minute point is above 85% for both products, so the conditions are met. An f2 of 74.8 lies between 50 and 100, so the profiles are similar.

Common mistakes

• Including several time points after 85% dissolution, which inflates f2.
• Using individual unit values instead of means.
• Ignoring high variability at early time points.
• Comparing profiles run in different media, apparatus or speeds.
• Reporting f2 without the underlying profiles and variability.