Assay DF Ratio — Concept & Beginner Guide

The calculator uses one formula. It looks long, but it is just four ratios multiplied and turned into a percentage:

Why it is built this way. Peak area follows concentration. The standard's concentration is its weight (corrected for purity) divided by its total DF. The sample's concentration, if it were exactly 100% pure, would be its weight divided by its total DF. The assay is simply how much the sample really gave, compared with how much it would have given at 100%. Work through the algebra and you land on the formula above.

What the calculator checks before it runs

• Every area reading and every other field must be a number greater than zero. Zero, negative or empty values are rejected.
• An empty extra area row counts as a problem. Fill it or remove it with the × button. Each solution always keeps at least one row.
• When something is wrong, the first bad field is outlined, scrolled into view and the cursor is placed in it, with a message above the results. Fix that one and press calculate again.
• If you enter more than one reading for a solution, the average of those readings goes into the formula.
• Clear All empties every field and returns each area list to a single row.

The formula treats weight ÷ total DF as concentration. That only works if both solutions are counted on the same basis. The simplest way is to count everything the weighed material was dissolved in: the first flask and every later dilution.

Counting only the later dilution steps would give 10 for both, and the first-flask difference (50 mL against 100 mL) would be lost. If you prefer to count only the later steps, make sure the first flasks were the same volume. For how to work out a DF from an aliquot and a final volume, see the Dilution Factor guide.

Using the two preparations above, with standard purity 99.8%, label claim 100%, and two readings for each solution:

1. Average the readings. Standard = (1254320 + 1256780) ÷ 2 = 1255550. Sample = (1249870 + 1252310) ÷ 2 = 1251090.
2. Area Ratio. 1251090 ÷ 1255550 = 0.996448
3. DF Ratio. 1000 ÷ 500 = 2
4. Weight Ratio. 25.20 ÷ 50.30 = 0.500994
5. Put it together. 0.996448 × 0.500994 × 2 × 0.9980 × 100 = 99.6432%

That is inside 98.0% to 102.0%, so the result card shows the green pass style. The three ratios are shown the same way in the math log on the page and on the printed sheet.

• Assay % to four decimal places, with the DF Ratio and Area Ratio shown beside it. The panel also repeats the two DFs, the Weight Ratio, the label claim and the purity you used.
• The coloured banner. The heading always reads "Assay Calculation Complete". What changes is the colour and icon: green (98.0% to 102.0%), yellow (95.0% to 105.0% but outside the green range), or grey with an info icon (outside 95.0% to 105.0%).
• Math log, 7 steps. Inputs collected, readings averaged, Area Ratio, DF Ratio, Weight Ratio, the full formula with your numbers in it, and a last step that compares the result with the typical 98.0% to 102.0% range for finished product and API.

Those ranges are the tool's typical ones. The banner is a quick signal, not a pass or fail ruling. Check the number against the specification in your own method.

Copying and printing

The copy button puts the run into the clipboard as text: date, the readings (with the average when there is more than one), both DFs, both weights, purity, label claim, DF Ratio, Area Ratio and the assay. The assay line is wrapped in asterisks so it appears bold in WhatsApp, Telegram or Slack.

The print report opens from the results after a calculation. It lists the raw data in a table, the formula, the Area Ratio, DF Ratio and Weight Ratio working, and the final assay. You can add a logo to the sheet: PNG, JPG or WebP, under 1 MB and no larger than 512 × 512 px (square or rectangular). Esc closes the preview.

• Swapping the two DFs. With the example numbers, putting 500 in the sample box and 1000 in the standard box gives 24.91% instead of 99.64%.
• Leaving out a dilution step in the total DF. If the sample DF is entered as 100 instead of 1000, the result drops to 9.96%, exactly a tenth.
• Typing purity as a fraction. 0.998 instead of 99.8 gives 0.9964%.
• Counting DF on a different basis for each solution. One includes the first flask, the other does not, and the ratio is wrong even though each number looks reasonable alone.
• Mixing up the weights. The ratio is standard over sample. Reversing them inverts that ratio and the result goes well off.
• Using readings from different injections of different preparations. Only put readings in the same list if they come from the same solution.

Do I have to enter weights and purity?

Yes. The calculator will not run until every field is filled: all peak area readings, both total DFs, both weights, the label claim and the standard purity. Each one has to be a number above zero. There is no shortened formula for the case where you leave weights out.

Is the label claim part of the calculation?

No. The assay is worked out from areas, weights, DFs and purity only. The label claim is carried along so it shows in the results, the copy text, the math log and the report, but it does not change the number.

What happens if I enter more than one reading for the standard or the sample?

The calculator takes the plain average of the readings you entered for that solution and uses the average in the formula. With one reading it uses that reading as it is. Every row you add must be filled, otherwise the calculator stops and points at the empty box; remove the row if you do not need it.

What do the green, yellow and grey result colours mean?

Green means the assay is between 98.0% and 102.0%. Yellow means it is outside that range but still between 95.0% and 105.0%. Grey, with an info icon, means it is outside 95.0% to 105.0%. These are typical ranges built into the tool. Your own specification is what counts, so compare the number with your method.

Should purity be typed as 99.8 or 0.998?

Type it as a percentage, 99.8. The formula divides purity by 100 itself. If you type 0.998 the result comes out roughly a hundred times too small.

Does this work out assay for tablets or capsules?

It compares one sample preparation with one standard preparation using the weights you give it. It does not take average tablet weight, content per unit or any other finished product factor. Use it for the ratio part of the working and apply any other factors your method needs separately.