Serial Dilution Calculator

Background.

Six tubes, each holding 0.9 mL of buffer, and a pipette set to 100 µL: that is all it takes to divide a sample's concentration by a million. Doing the same thing in one step would mean putting 1 µL of sample into almost a litre of diluent, a volume few pipettes deliver accurately and a dilution few benches have room for. A serial dilution reaches the same place through a chain of modest steps, each one diluting the tube before it, and because each step divides by the same factor, the factors multiply. Six ten-fold steps give 10⁶.

The calculator plans that chain in either direction. Given a stock concentration, a factor per step and a number of steps, it lists the concentration in every tube and the two volumes you pipette at each step: how much to carry forward and how much diluent to put in each tube first. Given a target instead, it works out how many steps a chosen factor needs, or what factor reaches the target in a fixed number of tubes.

One convention decides whether the result is right. A 1:10 or 1-in-10 dilution means one part of sample in ten parts total, one part sample plus nine of diluent, so the factor is 10. The FDA's Bacteriological Analytical Manual describes its decimal dilutions as 10 mL of the previous dilution into 90 mL of diluent, and the WHO semen-analysis manual writes dilutions as "1 + 19 (1:20)", spelling out both volumes so nobody has to guess. Read 1:10 as one part into ten parts of diluent and each step is really 11-fold; over six steps a tube meant to hold 100 CFU/mL holds about 56.4.

Any concentration unit works, from CFU/mL to mol/L, ppm or genome copies per µL, because the arithmetic only divides; the answers come back in the unit you typed. Volumes are in millilitres.

What is serial dilution calculator?

A serial dilution is a series of dilutions in which each one is made from the previous dilution rather than from the original stock. Every step is an ordinary dilution: carrying a volume V_transfer from a tube at concentration C into a total volume V_final leaves C × V_transfer ÷ V_final, which is C ÷ D if the per-step dilution factor D is V_final ÷ V_transfer. Repeating the same step n times gives a geometric series, Cₙ = C₀ ÷ Dⁿ, and the total dilution factor relative to the stock is Dⁿ. Ten-fold steps are the standard for plate counts, where they span the many orders of magnitude between a culture and a countable plate. Two-fold steps are the standard for antibody titres and for broth-microdilution minimum inhibitory concentration testing of antibiotics, where finer spacing matters more than range. Chemists use both to build calibration standards from a single stock.

How to use this calculator.

1. 01Choose the mode: plan the series if you already know the factor and the number of steps, or one of the two target modes to work backwards.
2. 02Enter the stock concentration in whatever unit you use. The target, in the target modes, must be in the same unit and lower than the stock.
3. 03Enter the factor per step as total parts: 10 for 1 + 9, 2 for equal volumes of sample and diluent, 5 for 1 + 4. If your protocol really is one part into ten parts of diluent, enter 11.
4. 04Enter the number of transfers, from 1 to 20, and the volume each tube holds once the transfer has arrived, in millilitres: 1 for a standard tube, 0.2 for a 200 µL microplate well. Once you take the next aliquot out, each earlier tube is left with the diluent volume.
5. 05Fill every tube with the diluent volume before starting, then move the transfer volume from the stock into tube 1, mix, change the tip, and repeat down the rack.
6. 06Use the tube-by-tube plan to decide which tubes to plate or measure, and the total diluent figure to prepare enough buffer, saline or medium beforehand.

The formula.

Concentration is amount divided by volume, and moving liquid between tubes neither creates nor destroys the solute or the cells in it. Carry V_transfer from a tube at concentration C and you carry C × V_transfer of material; spread it through V_final and the new concentration is C × V_transfer ÷ V_final. Writing D = V_final ÷ V_transfer, one step is C ÷ D. That is the familiar C₁V₁ = C₂V₂ rule with the factor made explicit.

The second tube is made from the first, so it holds (C₀ ÷ D) ÷ D = C₀ ÷ D², and after n steps Cₙ = C₀ ÷ Dⁿ. The pipetting volumes come from the same definition: V_transfer = V_final ÷ D, and the diluent placed in each tube beforehand is V_final − V_transfer. The total diluent for the series is n times that.

The two target modes solve the same relation for a different unknown. For the number of steps, n = ln(C₀ ÷ C_target) ÷ ln(D). That is rarely a whole number, and a transfer cannot be split, so it is rounded up and the last tube lands at or below the target; a value that is a whole number to nine decimal places is kept as it is, so an exactly six-step problem stays at six. For the factor, D = (C₀ ÷ C_target)^(1/n), which reaches the target exactly but can give awkward volumes. The step count is limited to 20, and the factor must be above 1, since a factor of 1 changes nothing and adding diluent cannot concentrate anything.

Because dilution series exist to make small numbers, results are kept to twelve significant figures rather than a fixed number of decimal places. A 1 mol/L stock taken through twelve ten-fold steps therefore shows 1 × 10⁻¹² mol/L, one picomolar, instead of zero.

A worked example.

Frequently asked questions.

References& sources.

1. [1]US Food and Drug Administration, Bacteriological Analytical Manual (BAM), Chapter 3 'Aerobic Plate Count', January 2001 Edition (original source: BAM 8th ed., Revision A, 1998). Section B specifies decimal dilutions prepared 'by transferring 10 ml of previous dilution to 90 ml of diluent' — 10 + 90 = 100 total parts, i.e. a dilution factor of 10 per step applied to the previous dilution. Public, free, not paywalled. Retrieved 2026-07-29.
2. [2]World Health Organization, WHO Laboratory Manual for the Examination and Processing of Human Semen, Table 2.3 and §2.8.4. Independent second authority consulted for the dilution convention: WHO writes every dilution in the unambiguous two-volume form — '1 + 4 (1:5)', '1 + 19 (1:20)', '1:50 (1 + 49)' — and recovers the original concentration by multiplying the measured value by the dilution factor. Agrees with the D = V_final ÷ V_transfer convention used here. Public PDF. Retrieved 2026-07-29.
3. [3]International Union of Pure and Applied Chemistry, IUPAC Compendium of Chemical Terminology (Gold Book), 'amount-of-substance concentration, c' = n/V. The definition of concentration on which the per-step conservation argument rests. Definitional reference, independent of the arithmetic. Retrieved 2026-07-29.
4. [4]ISO 6887-1:2017, Microbiology of the food chain — Preparation of test samples, initial suspension and decimal dilutions for microbiological examination — Part 1: General rules for the preparation of the initial suspension and decimal dilutions. The governing international standard for preparing decimal dilution series. PAYWALLED — cited bibliographically; title, scope and edition confirmed from the ISO catalogue entry, retrieved 2026-07-29.
5. [5]ISO/TC 34/SC 9 (Food products — Microbiology), 'Excel tool to implement the calculations of the colony-count technique according to ISO 7218 — Verification Report', S. Grosz, 28 August 2020. A free ISO committee document reproducing the ISO 7218:2007/Amd 1:2013 §11.2.6 calculation examples, which confirm that consecutive decimal (ten-fold) dilutions are the assumed chain in plate-count work. Retrieved 2026-07-29.
6. [6]Strober, W. (2015). 'Trypan Blue Exclusion Test of Cell Viability.' Current Protocols in Immunology, 111, A3.B.1–A3.B.3. DOI 10.1002/0471142735.ima03bs111 (PMID 26529666). Peer-reviewed protocol describing the routine dilution-then-count workflow that a serial dilution feeds. Publisher paywall on the full text; abstract and bibliographic record are open.