f₂ Similarity Factor — Concept & Beginner Guide

The standalone calculator has one table and nothing else to set up. Each row is one time point, with three boxes: the time in minutes, the mean % dissolved for the Reference product (Rt), and the mean % dissolved for the Test product (Tt). The Reference column comes first and the Test column second, and the (Rt − Tt) column is always Reference minus Test.

• Starting rows. The page opens with the IR template already loaded: 5, 10, 15, 20, 30, 45 and 60 minutes, with the time filled in and the two % columns empty.
• Templates. The IR button loads those seven rows. The SR button loads six rows at 60, 120, 240, 360, 480 and 720 minutes (1 to 12 hours). Loading a template clears whatever rows were there before.
• Add Row adds an empty row and the ✕ button removes one. Clear All removes every row and hides the results.
• Row counter. A line under the table shows how many time points you have, and warns you while there are fewer than 3.
• Order does not matter. The input table keeps the order you typed. The results table and the chart are sorted by time.

The (Rt − Tt) and (Rt − Tt)² columns in the input table stay empty until you calculate, and a sum row appears under the table afterwards.

Above the table is a drop-down labelled Decimal Precision (required before calculating), with options from 0 digits to 5 digits. Nothing is selected when the page opens. If you press calculate without choosing, the calculator stops with a message and moves the cursor to the drop-down. Changing the precision after you have results re-runs the calculation straight away.

The setting changes only what you see. The sum, the square root and the logarithm are worked out with full precision whatever you choose, so f₂ does not move when you change the display. See the question about 0 digits in the FAQs below, because at low precision the visible rows may not add up to the visible total.

The calculator does not check that time points are unique. Two rows at the same time are both used in the sum and both counted in n, so keep each time to one row.

Here are mean results for a Reference and a Test tablet. Choose 2 digits of precision and enter the rows below:

The calculation table under the results then shows these rows, followed by the working rows:

The medium-calc line under the result card reads f₂ = 50 × log₁₀[100 / 2.84] = 50 × 1.55 = 77.33. Because 77.33 is between 50 and 100 and n is 5, the banner reads Dissolution Profiles: SIMILAR, and the result card shows SIMILAR with the note "FDA/EMA criterion (f₂ ≥ 50)".

There is no 15-minute row in this data, so the note under the table says no 15-minute time point was found and the 85% check could not be performed. f₂ was calculated from all five rows.

To see the other outcome, replace the Test column with 22.0, 38.5, 52.0, 70.1 and 81.4. The squared differences now add up to 874.10 and f₂ drops to 43.87, so the banner turns red and reads NOT SIMILAR.

After every calculation the calculator looks for a row at exactly 15 minutes and shows one of three notes:

• 85% rule satisfied. A 15-minute row exists and both Test and Reference are at or above 85%. The row is highlighted in green in both tables, and the note explains that f₂ may not be needed in that case. The f₂ value is still calculated.
• 85% rule not met. A 15-minute row exists, but at least one product is below 85%. The note shows both values.
• No 15-minute time point. The check cannot be made. This is what the worked example above shows.

None of these notes removes or changes any row. The calculator uses every time point you entered.

• Summary cards: the f₂ value, the verdict, the number of time points (n) and the total squared difference.
• Math Log: four numbered steps. Step 1 lists each time point's squared difference and their sum, step 2 divides by n, step 3 adds 1 and takes the square root, and step 4 applies the logarithm and the factor of 50.
• Chart: time in minutes along the bottom and % result up the side. The Reference is a purple line with square markers and the Test is a blue line with diamond markers. The value is printed under every marker, using your chosen decimals, and a small table beneath the chart repeats the numbers.

Both buttons need a completed calculation. If you press them before calculating, a message asks you to calculate first.

Copy Full Report copies a text report: a title line, the table (time, Reference, Test, difference, squared difference, separated by tabs so it pastes neatly into Excel), then the f₂ value with its tag and the verdict text.

Print Report opens an editable A4 preview that fits on one page. It carries the calculation table with its working rows, the verdict banner with the f₂ value and the formula, and the chart as an image. You type these details directly on the sheet before printing: company name, dissolution medium (buffer), Reference brand and batch, Test brand and batch, analysis date, instrument, and the Analyzed by and Checked by lines.

The logo box accepts a PNG, JPG or WebP image of up to 1 MB, between 30 × 30 and 512 × 512 px on each side. HEIC photos from phones are not accepted. Choose Save as PDF in the print dialog and switch off Headers and footers for the cleanest file. Esc or the Close button leaves the preview.

• Typing one vessel's result instead of the mean. The calculator treats whatever you enter as the mean.
• Including too many points near full release. Rows after the profile has levelled off pull the differences towards zero and push f₂ up. The calculator will not stop you, so follow your guidance on how many points at or above 85% to use.
• Mixing time units. Everything is in minutes. A 2-hour point is 120, not 2.
• Entering fractions. Type 92.6, not 0.926. The range check would not catch a fraction because it is between 0 and 120.
• Leaving a template row empty. The IR template loads seven rows. If you only have five time points, remove the two extra rows, or the calculation stops.
• Duplicate time rows. They are not rejected, but they are both counted.
• Relying on 0 digits for hand-checking. Use 2 or more digits when you want the rows and total to match.

Do I enter individual unit values or the mean for each time point?

Enter the mean % dissolved for each product at each time point, for example the average of 6 or 12 units. The standalone calculator does not average anything for you. If you only have unit-level data and want the calculator to work out the means and the %RSD first, use the Comparative Dissolution Profile calculator instead.

Why do I have to choose decimal precision before I can calculate?

The calculate button is always clickable, but if no precision is chosen the calculator stops and shows a message asking you to select 0 to 5 digits. The choice controls how every number is displayed: the table, the sum, the verdict text, the math log, the chart labels, the copied text and the printed report. The calculation itself keeps full precision.

Why do the rows not add up exactly when I choose 0 digits?

Because only the display is rounded. With the example in this guide, the true differences are 2.4, 3.2, 2.4, 2.8 and 2.4, but at 0 digits the rows show 2, 3, 2, 3 and 2, while the sum of squares is still calculated from the real values (35.36, shown as 35). Choose 2 or more digits when you want to check the arithmetic by hand.

Does swapping the Reference and Test columns change f₂?

No. The differences change sign, but they are squared before they are added, so f₂ is identical. Only the colour and sign shown in the (Rt − Tt) column change. It is still worth entering the products in the right columns so the report is correct.

Can f₂ be greater than 100?

No. Identical profiles give exactly 100, and every difference between them pulls the value down. If you ever see a number above 100 somewhere else, check the data or the formula used.

What does the calculator do with fewer than 3 time points?

It still calculates f₂, but the verdict banner says there are not enough time points for regulatory use, the result card shows Inconclusive, and a note under the table asks you to add more points. The row counter on the data-entry table also reminds you when you have fewer than 3 rows.

Which template should I use for an extended-release product?

The SR template loads six rows at 60, 120, 240, 360, 480 and 720 minutes, which is 1 to 12 hours. Time is always entered in minutes, so convert hours before typing if you build your own rows.

Does the calculator remove time points after 85% dissolution?

No. Every row you enter goes into the calculation. If your guidance allows only one mean at or above 85% for each product, leave out the extra points yourself.

Is the data I type sent anywhere?

The calculation, chart, copy text and print preview all run in your browser, and the calculator script does not send your entries to a server.

Educational use only. This guide explains how the standalone f₂ calculator on this site works. It is not a validated system, and it does not replace your SOPs or the guidance your regulator expects you to follow. Please read the disclaimer for how this site should be used.