Serial Dilution Calculator

Background.

A serial dilution calculator plans a chain of repeated dilutions — the workhorse technique for turning something far too concentrated to measure into something you can actually count, read or pipette. Instead of trying to make a single enormous dilution in one impossible step, you make the same modest dilution several times in a row, each one performed on the product of the last. Enter your stock concentration, the factor you want at each step, how many steps you plan and how much liquid you want in each tube, and this calculator returns the concentration in every tube, the volume to transfer between tubes, the volume of diluent to put in each tube first, and the overall dilution factor relative to the stock.

The reason serial dilution exists is arithmetic. Suppose an overnight bacterial culture sits somewhere near 10⁸ colony-forming units per millilitre and you need roughly 100 CFU/mL to get a countable agar plate. That is a million-fold dilution. Doing it in one step would mean pipetting one microlitre of culture into a litre of diluent — a volume no ordinary pipette measures accurately and a container no bench has room for. Doing it as six consecutive ten-fold steps means six easy transfers of 100 µL into 900 µL, in six 1 mL tubes, using the same pipette every time. The concentrations multiply down the chain: each step divides by ten, and six steps divide by 10⁶. That multiplicative chaining is the whole trick, and it is why every microbiology, virology, immunology and analytical-chemistry bench in the world has a rack of dilution tubes on it.

This calculator is deliberately unit-agnostic. The equation behind it, C_n = C₀ ÷ Dⁿ, is a pure ratio, so it does not care whether your concentration is colony-forming units per millilitre, moles per litre, milligrams per millilitre, percent weight-by-volume, parts per million, or viral genome copies per microlitre. It also does not depend on temperature, pressure or any reference state; there is no STP-versus-SATP question to answer here, because nothing in the derivation involves a gas, an activity coefficient or an equilibrium. The one thing the calculator cannot do is guess your units for you, so C₀ and your target concentration must be expressed in the same unit as each other, and the volume fields are millilitres throughout.

One convention matters enormously and is the single most common source of a wrong answer, so it belongs here rather than buried in an FAQ. **A '1:10' or '1-in-10' dilution means one part of stock brought to ten TOTAL parts — one part sample plus nine parts diluent — giving a dilution factor of 10.** It does not mean one part sample plus ten parts diluent, which would be eleven total parts and a factor of 11. The US FDA's Bacteriological Analytical Manual writes this as '10 ml of previous dilution to 90 ml of diluent'; the WHO laboratory manual writes it as '1 + 19 (1:20)'. Both spell out the two volumes explicitly, precisely because the colon notation is ambiguous in casual use. This calculator always uses the factor D = final volume ÷ transfer volume, so entering 10 gives you 1 part into 9, and the tube-by-tube plan states both volumes so there is nothing left to interpret.

The calculator also runs the question backwards. If you know where you are starting and where you need to end up but not how many steps that takes, the 'how many steps' mode solves n = ln(C₀ ÷ C_target) ÷ ln(D) and rounds up to a whole transfer, because you cannot perform three-fifths of a pipetting step. If instead your protocol fixes the number of tubes — a 96-well plate row, say, or a fixed eight-point standard curve — the 'what factor' mode solves D = (C₀ ÷ C_target)^(1/n) and tells you what per-step dilution hits the target in exactly that many tubes.

Where the model stops being exact is worth knowing before you trust a number from it. The equation assumes perfect mixing at every step, additive volumes, and no loss of solute to the tube. Real serial dilutions accumulate pipetting error multiplicatively — a systematic 2% error per step becomes roughly 13% over six steps — which is why calibrated pipettes and vortexing between steps matter more than they look like they should. At the far end of a long chain, where only a handful of discrete cells or molecules remain in each aliquot, the deterministic C₀ ÷ Dⁿ stops describing what is in any individual tube at all: Poisson sampling takes over, and this is the real reason plate counts are only trusted inside a countable range rather than extrapolated from a single very dilute plate.

What is serial dilution calculator?

A serial dilution is a sequence of dilutions in which each step is performed on the product of the previous step rather than on the original stock. Each individual step is an ordinary dilution and obeys the same conservation law as any other: taking a volume V_transfer from a solution at concentration C and bringing it to a total volume V_final leaves a concentration C × V_transfer ÷ V_final. Writing D for the per-step dilution factor V_final ÷ V_transfer, that single step is simply C ÷ D. Applying an identical step n times in a row gives a geometric progression, C_n = C₀ ÷ Dⁿ, and the overall or total dilution factor relative to the original stock is Dⁿ.

Two practical volumes fall straight out of the choice of D and the tube volume. The transfer volume is V_final ÷ D — the aliquot you carry forward, and also the amount of stock that starts the series. The diluent volume is V_final − V_transfer, which is what you pre-load into each empty tube. For the ubiquitous ten-fold step in a 1 mL tube that is 100 µL transferred into 900 µL of diluent. For a two-fold step, common in antibiotic minimum-inhibitory-concentration testing and in antibody titration, it is 500 µL into 500 µL. Because the tubes are all identical, one pipette setting does the entire rack.

Serial dilutions appear far beyond microbiology. Analytical chemists build calibration curves from them; immunologists titrate antisera in two-fold steps down a microplate row; pharmacologists generate the concentration range for a dose–response curve; water utilities and food laboratories use decimal dilution series as the mandated preparatory step before plating. The mathematics is identical in every case, which is why this calculator does not ask what you are diluting.

How to use this calculator.

1. 01Pick a mode. 'Plan the series' is the normal case: you know the per-step factor and how many steps you want. The other two modes work backwards from a target concentration.
2. 02Enter the stock concentration in whatever unit you actually use — CFU/mL, mol/L, mg/mL, % w/v, ppm, copies/µL. Every result comes back in that same unit; the calculator never converts.
3. 03Enter the dilution factor per step. Use 10 for a 1-in-10 (1 part + 9 parts) step, 2 for a two-fold step, 5 for 1-in-5. Remember that '1:10' means ten TOTAL parts, so the factor is 10 and not 11.
4. 04Enter the number of transfer steps as a whole number, and the final volume you want in each tube in millilitres (1 mL for a standard dilution tube, 0.2 for a 200 µL microplate well).
5. 05Read 'Diluent per tube' and pre-load that volume of sterile buffer, saline or medium into every tube in the rack BEFORE you start transferring.
6. 06Read 'Transfer volume per step' and use it for every transfer, including the first one out of the stock. Vortex or pipette-mix thoroughly after each addition, and change the tip between steps — carry-over on the outside of a tip is the largest avoidable error in a dilution series.
7. 07Check the tube-by-tube plan against what you need. For plate counts, aim for the tube whose predicted concentration lands your plated volume inside the countable range of your method.
8. 08For the two 'reach a target' modes, enter the target concentration in the same unit as the stock. The step count always rounds UP, so the last tube sits at or below your target rather than above it.

The formula.

Start from a single step. Concentration is amount of solute divided by volume, and moving an aliquot into a fresh tube does not create or destroy solute. So if you take V_transfer from a solution at concentration C, you have carried C × V_transfer units of solute; bringing that to a total volume V_final spreads the same amount through the larger volume, giving C × V_transfer ÷ V_final. Defining the per-step dilution factor as D = V_final ÷ V_transfer, one step is exactly C ÷ D. This is the same conservation argument as the ordinary C₁V₁ = C₂V₂ dilution law, just written so the factor is explicit.

Now apply that step to its own output, n times. The first tube holds C₀ ÷ D, the second holds (C₀ ÷ D) ÷ D = C₀ ÷ D², and after n transfers the concentration is C₀ ÷ Dⁿ. Because each step divides by the same factor, the effects multiply rather than add, and the total dilution factor across the whole chain is Dⁿ. That is why six ten-fold steps give a million-fold dilution and not a sixty-fold one — the single most common error in reading a dilution series.

The pipetting volumes follow from the definition of D. Rearranging D = V_final ÷ V_transfer gives V_transfer = V_final ÷ D, and since each tube ends at V_final made up of the incoming aliquot plus whatever was already there, the diluent to pre-load is V_diluent = V_final − V_transfer = V_final × (1 − 1 ⁄ D). For the worked example below — a 1.0 mL tube at D = 10 — that is 1.0 ÷ 10 = 0.1 mL transferred into 1.0 − 0.1 = 0.9 mL of diluent, and 6 × 0.9 = 5.4 mL of diluent for the whole six-tube series.

The two inverse modes invert the same geometric relation. Solving C₀ ÷ Dⁿ = C_target for n gives n = ln(C₀ ÷ C_target) ÷ ln(D); solving it for D gives D = (C₀ ÷ C_target)^(1/n). Step counts must be whole numbers, so the first of those is rounded up — three ten-fold steps from 1000 to a target of 3 land you at 1, below the target, which is the safe direction.

Rounding stage: every intermediate value is carried at full Decimal.js working precision and nothing is rounded until the result is returned. The returned numbers are rounded to twelve significant digits rather than to a fixed number of decimal places, because a serial dilution routinely produces answers spanning many orders of magnitude and a fixed-decimal-place rounding would flush small final concentrations to zero. The one exception is the step count in the 'how many steps' mode, which must be an integer: n is computed in full precision, snapped to an exact integer when it agrees to nine decimal places, and otherwise rounded up. Without that snap, a mathematically exact six-step problem can be reported as seven because ln(10⁶) ÷ ln(10) lands a fraction of a quintillionth below 6.

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.