Dilution Factor — Concept & Beginner Guide

This is the one thing that surprises most first-time users, so it is worth reading before you enter any numbers.

For either one, the total over several steps is the product of the step values. A Standard total is always at most 1. A Sample total is always at least 1. The results panel also shows the Standard the other way up as Std as Multiplier (1/DF), so you can compare it directly with the Sample.

When you run both together, the calculator multiplies the two totals. That is the same as dividing the Sample DF by the Standard multiplier, and the result is the number the panel labels Dilution Factor (Sample × Std), with the note "correction factor for assay". Calculators that ask for a Dilution Factor, such as the CDP calculator, point you to this tool for it.

No mode is selected when the page opens. Until you pick one, the entry sections stay hidden and the calculate button is not shown. Clear All also puts the page back in this unselected state.

Each dilution step is one row. The page starts with two rows for the Standard and two for the Sample, and you add one row per volumetric step with Add Dilution Step. The × button removes a row and the rows renumber themselves.

• Step Description is only a label. It starts as Stock preparation, Second dilution, Third dilution and so on, and you can type your own. It appears in the tables, the copy text and the printed sheet.
• Step 1 is the stock preparation. Its aliquot is fixed at 1 (shown as the weight, "suppose 1 mg") and is read-only, with a reminder not to count weighing. You enter only the final volume of the first flask.
• Later steps need an aliquot volume and a final volume, both in mL.
• Live preview. Under each aliquot box the step's own DF appears as you type, for example DF = 5 ÷ 50 = 0.1.

What stops the calculation

• No calculation mode chosen.
• A row left empty, or with zero or a negative number. Every row you have added must be complete, so fill it in or remove it.
• A final volume smaller than its aliquot. Equal volumes are accepted and give a DF of 1.

When any of these happens, a red message appears above the results and nothing is calculated.

Standard: the stock is made up in a 50 mL flask, then 5 mL is made up to 50 mL, then 5 mL is made up to 25 mL. Sample: the stock is made up in a 100 mL flask, then 5 mL is made up to 50 mL.

1. Total Standard DF = 0.0200 × 0.1000 × 0.2000 = 0.0004. As a multiplier, 1 ÷ 0.0004 = 2500.
2. Total Sample DF = 100 × 10 = 1000.
3. Dilution Factor = 1000 × 0.0004 = 0.4000. Check: 1000 ÷ 2500 gives the same 0.4.

The DF Match Status reads Different, and the Ratio Interpretation reads Standard 2.5000× more diluted, because the Standard multiplier (2500) is 2.5 times the Sample DF (1000). The log₁₀ cards show 3.3979 for the Standard multiplier and 3.0000 for the Sample, and the Sample inverted (1/DF) card shows 1.0000e-3.

• Dilution Factor (Sample × Std) appears in combined mode only, with the note "correction factor for assay".
• Total Standard DF, Total Sample DF, and the number of steps in each (Std Steps (n), Spl Steps (n)).
• Std as Multiplier (1/DF) and Spl Inverted (1/DF). The second one is shown in exponent notation, such as 1.0000e-3.
• DF Match Status and Ratio Interpretation in combined mode. Equal means the final Dilution Factor is 1 within 0.0001.
• Std Log₁₀ and Spl Log₁₀. The base-10 logarithm of the Standard multiplier and of the Sample DF, to four decimals. Handy for comparing very different dilution levels.
• Visual scale. Bars comparing the Standard multiplier and Sample DF, scaled to the larger of the two.
• Step tables. One for each preparation, with a cumulative column and a total row showing the product of all steps.
• Calculation log. The same working written out in plain steps, with your numbers filled in.

Numbers are displayed with a sensible number of decimals: whole numbers as they are, 4 decimals below 10, 2 decimals from 10 to 99, 1 decimal from 100 to 999, and none from 1000 up. The maths underneath uses the full value. For a long Standard chain the total can be a very small fraction, so read the Std as Multiplier card as well.

Copy Results copies a short report with the date, each step line (for example Step 2 (Second dilution): 5 ÷ 50 = DF 0.1000), the totals and, in combined mode, the Dilution Factor. It includes only the sections you calculated. The headline numbers are bold when you paste into Word, Gmail or Google Docs, and are wrapped in asterisks so they show bold in WhatsApp, Telegram or Slack.

Print Report opens only after a calculation. It shows an editable A4 sheet where each step appears as a fraction with its value, followed by a total row. Combined mode puts "Total Sample DF × Total Standard DF" on one highlighted line, and single modes finish with an Answer row. You type the company, product and batch details directly on the sheet before printing. Long combined calculations (more than 8 steps in total) switch to tighter spacing so the sheet stays on one page.

To add a logo, use a PNG, JPG or WebP file of 1 MB or less and between 30 × 30 and 512 × 512 px. HEIC photos are not accepted. Esc closes the preview.

• Entering the diluent volume as the final volume. If you take 5 mL and add 45 mL of diluent, the final volume is 50 mL, not 45.
• Skipping the stock flask. Step 1 is the first flask. If you leave it out, the totals are off by that flask's volume.
• Reading a Standard total as a multiplier. A Total Standard DF of 0.0004 does not mean "0.0004 times diluted". Use the multiplier card, 2500, for that.
• Slipping a decimal point. The fields are in mL. An aliquot of 0.2 mL typed as 2 makes that step ten times too small, and every total after it with it.
• Counting non-dilution steps. Sonication, shaking, filtering and centrifuging do not change the concentration, so they get no row.
• Leaving an extra empty row. One blank row stops the whole calculation. Remove it or fill it.

Why is the Standard dilution factor a fraction and the Sample one a whole number?

The calculator deliberately writes the two the opposite way round. A Standard step is aliquot ÷ final, so 5 mL made up to 50 mL is 0.1. A Sample step is final ÷ aliquot, so the same 5 mL into 50 mL is 10. Multiplying the Total Sample DF by the Total Standard DF then gives one number, the Dilution Factor, which the results panel labels as a correction factor for assay.

Why is the aliquot in Step 1 fixed at 1?

Step 1 is the stock preparation, where you weigh the material and make it up in the first flask. The weight is treated as 1 mg and cannot be edited, so only the flask volume matters. The first step's DF is therefore 1 ÷ final volume for a Standard, or final volume ÷ 1 for a Sample. The weighing itself is not counted as a dilution.

Do I have to use all three calculation modes?

No. Choose the one you need: Standard Only, Sample Only, or Standard + Sample (Combined). Nothing is selected when the page loads, and calculating is blocked until you choose. Only the combined mode returns the final Dilution Factor, because it needs both preparations.

What does the DF Match Status mean?

In combined mode, the calculator checks whether the final Dilution Factor is 1, within a tolerance of 0.0001. If it is, the status reads Equal, meaning the Sample and Standard are diluted to the same extent. Otherwise it reads Different, and the Ratio Interpretation card says which preparation is more diluted and by how many times.

Can I enter volumes in other units?

The fields are in mL. If your record uses another unit, convert it to mL before you type. Every volume in a calculation must be in the same unit, otherwise the ratio is wrong.

What if the final volume is smaller than the aliquot?

The calculator rejects the row. A flask cannot hold less than what you put into it. If the aliquot and final volume are equal, the step is accepted and its DF is 1.

Is the data I enter sent anywhere?

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