🧪 Pharmaceutical QC Calculator

f₂ Similarity Factor Calculator

Compare a Test and Reference dissolution profile using the FDA/EMA f₂ similarity factor. Enter the mean % API dissolved for each product at every time point — the f₂ value, regulatory verdict, a step-by-step calculation log, and a graphical profile overlay are generated automatically.

📐 f₂ Similarity Factor 📋 IR & SR Templates ✅ 85% @ 15 min Waiver Check 📈 Profile Chart Overlay 🧮 Step-by-Step Math Log

📐

✓

📘

Beginner Guide

Concept, formula & how to use

📐 f₂ Formula Reference

Similarity Factor Formula & Step-by-Step Logic

f₂ Similarity Factor Formula (FDA / EMA / ICH)

f₂ = 50 × log { 100 / √[ 1 + (1/n) × Σᵢ(Rt − Tt)² ] }

Where: Rt = mean % Reference dissolved at time t | Tt = mean % Test dissolved at time t | n = number of time points

Step-by-Step Calculation

For each time point: calculate (Rt − Tt)²
Sum all squared differences: Σ(Rt − Tt)²
Divide by n: Σ(Rt − Tt)² / n
Add 1: 1 + Σ(Rt − Tt)² / n
Take square root: √[1 + ...]
Divide 100 by that: 100 / √[...]
Apply log₁₀ and multiply by 50: f₂ = 50 × log₁₀(...)

Acceptance Criteria

🟢 f₂ = 50–100 → Profiles are SIMILAR

🔴 f₂ < 50 → Profiles are NOT SIMILAR

⚠️ f₂ > 100 → Mathematically impossible — check data

📋 Min. 3 time points required for regulatory validity

🏃 85% at 15 min → f₂ may be waived (both products)

⚙️ Data Entry

Enter Mean % Dissolved per Time Point

Instructions: Enter the mean % drug dissolved for Reference (Rt) and Test (Tt) products at each time point. (Rt − Tt) and (Rt − Tt)² columns are calculated after you click Calculate.

🎯 Decimal Precision (required before calculating): ⚠️ Please select decimal precision to enable Calculate

Time Point (min)	% API Dissolved		Calculation
Time Point (min)	Reference Product (Rt)	Test Product (Tt)	( Rt − Tt )	( Rt − Tt )²
Sum of ( Rt − Tt )²					—

0 time points entered

📐

f₂ Calculated

See details below.

f₂ Value

—

50–100 = Similar

Verdict

—

FDA/EMA criterion

Time Points (n)

—

≥ 3 required for regulatory use

Sum (Rt − Tt)²

—

Total squared difference

📊 Calculation Table

Test vs Reference — Per Time Point Breakdown

Time Point (min)	Mean % Dissolved		Calculation
Time Point (min)	Reference Product (Rt)	Test Product (Tt)	(Rt − Tt)	(Rt − Tt)²

📈 Dissolution Profile Chart

Graphical Overlay — Test vs Reference

🧮 Math Log

Step-by-Step f₂ Calculation

Step 1 — Per Time Point: (Rt − Tt)²

For each time point, subtract the Reference mean from the Test mean, then square the result.

—

Step 2 — Sum of (Rt − Tt)² / n

Sum all squared differences, then divide by n (number of time points).

—

Step 3 — 1 + Sum(Rt − Tt)²/n, then √

Add 1 to the result from Step 2, then take its square root.

—

Step 4 — f₂ = 50 × log [100 / √(...)]

Divide 100 by the square root from Step 3, take log₁₀, then multiply by 50.

—

f2 Similarity Factor Calculator

Similarity Factor Formula & Step-by-Step Logic

Enter Mean % Dissolved per Time Point

Test vs Reference — Per Time Point Breakdown

Graphical Overlay — Test vs Reference

Step-by-Step f2 Calculation

f₂ Similarity Factor Calculator

Step-by-Step f₂ Calculation