A serial dilution is a stepwise reduction in the concentration of a solution, produced by diluting a sample by the same factor at each of several successive stages rather than in a single dilution. It is one of the most common quantitative techniques in a research lab, used to prepare standard curves, count colony-forming units, titer viruses and antibodies, and bring concentrated stock reagents into a usable working range. Getting the math and the pipetting technique right matters: a single mislabeled tube or transposed factor propagates through every subsequent step and can silently invalidate an entire assay.
What a serial dilution is (and why not just dilute once)
A single, one-step dilution works fine when the required dilution factor is small — say, 1:10 or 1:20. But many lab applications need much larger dilution factors (1:1,000,000 or more, as in phage titering or bacterial colony counts) or need a whole series of intermediate concentrations at once (as in a standard curve for an ELISA or a spectrophotometric assay). Trying to measure out, for example, 1 microliter of stock into 999,999 microliters of diluent in a single transfer is not practical or accurate with standard lab pipettes, which are calibrated for a limited volume range and lose accuracy at their extremes.
A serial dilution solves this by breaking one large dilution into a chain of smaller, more pipettable steps. Each tube in the series becomes the source for the next, and the dilution factors multiply together to reach the overall target.
The core formula: C₁V₁ = C₂V₂
Every individual dilution step in a serial dilution — and every single dilution generally — is governed by the conservation-of-mass relationship:
C₁V₁ = C₂V₂
- C₁ = concentration of the stock (starting) solution
- V₁ = volume of stock solution you need to use
- C₂ = concentration you want to end up with
- V₂ = total final volume you want to make
This works because the total amount of solute (moles, or mass, or particles — whatever unit C is expressed in) doesn’t change when you add diluent; only the volume it’s dissolved in changes, so concentration and volume are inversely related and their product (the total quantity of solute) stays constant.
Worked example: preparing one dilution
Suppose you have a 1 M stock solution of NaCl and you need 50 mL of a 0.1 M working solution. Solve for V₁, the volume of stock you need:
C₁V₁ = C₂V₂
(1 M)(V₁) = (0.1 M)(50 mL)
V₁ = (0.1 M × 50 mL) / 1 M
V₁ = 5 mL
You would pipette 5 mL of the 1 M stock into a container and add diluent (typically water or buffer) to bring the total volume to 50 mL — not add 45 mL of diluent to the 5 mL, which would only be correct if the diluent volume itself totaled 50 mL after mixing. Always add stock first, then bring the total volume up to the target with diluent (often using a graduated cylinder or volumetric flask, or by adding diluent up to a calibration mark), rather than assuming stock-plus-diluent volumes sum without correction for solution non-ideality in more precise chemistry work.
How to perform a serial dilution, step by step
- Decide your dilution factor (DF) per step. The most common is a twofold (1:2) or tenfold (1:10) serial dilution, but any consistent ratio works. A 1:10 dilution means each tube is 1/10th the concentration of the tube before it.
- Label every tube with its dilution (e.g., 10⁻¹, 10⁻², 10⁻³ for a tenfold series, or 1:2, 1:4, 1:8 for a twofold series) before you start pipetting. This is the single most common source of downstream error — unlabeled or ambiguously labeled tubes.
- Aliquot diluent into every tube first. For a 1:10 series, put 900 µL of diluent in each tube if you’ll be transferring 100 µL; for a 1:2 series, put an equal volume of diluent in each tube as the transfer volume.
- Transfer from the stock into tube 1, mix thoroughly (pipette up and down or vortex — do not just tap), and change your pipette tip.
- Transfer the same volume from tube 1 into tube 2, mix, change tip, and repeat down the series. Always use a fresh tip between transfers; reusing a tip carries over concentrated solution and silently skews every downstream dilution, an error that is very difficult to detect after the fact because the results still look plausible.
- Stop at the dilution(s) you actually need and use those tubes for your assay, plate, or measurement.
Worked example: a tenfold serial dilution
You have a bacterial culture and want dilutions of 10⁻¹ through 10⁻&sup6; for a colony-count assay.
- Label six tubes 10⁻¹ through 10⁻&sup6;, each containing 9 mL of sterile diluent.
- Transfer 1 mL of the original culture into tube 10⁻¹ (1 mL into 9 mL = 1:10 total, i.e. 10⁻¹). Mix well.
- Transfer 1 mL from tube 10⁻¹ into tube 10⁻² (another 1:10 dilution of an already-1:10 solution = 10⁻² overall, or 1:100). Mix well, fresh tip.
- Repeat the same 1 mL transfer down the chain through 10⁻&sup6;.
The overall dilution factor at any tube in the chain is the product of each individual step’s factor: after six consecutive 1:10 transfers, the cumulative dilution is 10⁻¹ × 10⁻¹ × 10⁻¹ × 10⁻¹ × 10⁻¹ × 10⁻¹ = 10⁻&sup6;, i.e. the culture in tube 6 is one-millionth the concentration of the original.
Calculating back to the original concentration
Serial dilutions are frequently used in reverse: you measure something in a diluted tube (for example, count colonies on an agar plate spread from a diluted sample) and need to back-calculate the concentration in the original, undiluted sample. The general relationship is:
Original concentration = (measured value in diluted sample) ÷ (dilution factor) ÷ (volume plated, if applicable)
Worked example: You plate 0.1 mL of the 10⁻&sup4; dilution from the series above and count 85 colonies after incubation.
Colony-forming units per mL (CFU/mL) = colonies counted ÷ (dilution factor × volume plated)
CFU/mL = 85 ÷ (10⁻&sup4; × 0.1 mL)
CFU/mL = 85 ÷ 0.00001
CFU/mL = 8.5 × 10⁶
In colony-count work, only plates with a countable range (typically 30–300 colonies) are used for this back-calculation; plates with too many or too few colonies are discarded because both very sparse and overcrowded plates introduce disproportionate counting error.
Serial dilution vs. a single dilution: when to use each
| Situation | Single dilution | Serial dilution |
|---|---|---|
| Dilution factor needed | Small (roughly up to 1:20–1:100) | Large (1:1,000+) or multiple concentrations needed at once |
| Pipetting accuracy | Good, if within pipette’s calibrated range | Good at every step, because each transfer stays within a practical pipette range |
| Error propagation | Limited to one step | Compounds at every step — an error in an early tube affects every tube after it |
| Typical use | Making a single working reagent from a concentrated stock | Standard curves, titers, colony counts, viral/antibody dilution series |
Common sources of error
- Reusing pipette tips between tubes. Carryover of even a small volume of the more concentrated preceding tube skews every subsequent dilution in the series, and the resulting error looks like normal experimental noise rather than an obvious mistake.
- Inadequate mixing. If a tube isn’t thoroughly mixed before the next transfer is taken, the aliquot won’t reflect the tube’s true average concentration.
- Pipetting outside a pipette’s rated volume range. Micropipettes are least accurate near the bottom of their rated range; where possible, choose a pipette (or a transfer volume) so the volume being measured falls comfortably within the mid-to-upper portion of the instrument’s range.
- Confusing “dilution factor” with “dilution ratio.” A “1:10 dilution” (1 part sample to 9 parts diluent, total 10 parts) is not the same statement as a “dilution factor of 10” applied loosely — be explicit about whether a ratio describes parts-of-sample-to-parts-of-diluent or sample-to-total-volume, and keep the convention consistent across a protocol.
- Losing track of the cumulative dilution. Especially past four or five steps, it’s easy to mis-multiply the per-step factors. Writing the cumulative dilution on each tube’s label, not just the per-step factor, reduces this risk.
- Not accounting for the diluent’s contribution to final volume precisely. For work that requires precise final concentrations (rather than approximate lab dilutions), use volumetric glassware and bring the total solution up to volume with diluent, rather than simply adding a diluent volume to a stock volume and assuming the sum is exact, since mixing certain solutions is not strictly additive in volume.
Frequently asked questions
What is a serial dilution?
A serial dilution is a series of sequential dilutions where each dilution uses the previous dilution as its starting material, applying the same (or a defined) dilution factor at each step. It’s used to reach very high dilution factors accurately, or to generate a range of concentrations for a standard curve or titer, without pipetting impractically small or large single-step volumes.
How do you calculate a serial dilution?
Decide the per-step dilution factor (for example, 1:10), then calculate the volume of the previous tube’s solution and the volume of diluent needed at each step using C₁V₁ = C₂V₂. The overall dilution at any point in the series is the product of all the individual step factors up to that point (for example, three consecutive 1:10 steps give an overall 1:1,000 dilution).
What is a dilution factor?
The dilution factor is the ratio of the final total volume to the volume of the original sample used — equivalently, how many times more dilute the new solution is than the source. A 1 mL sample brought to a 10 mL final volume has a dilution factor of 10 (often written 1:10).
Why is serial dilution used instead of one large dilution?
Because standard lab pipettes and volumetric equipment are only accurate within a defined volume range, extremely large single-step dilution factors (1:1,000,000 or more) would require measuring volumes too small to pipette accurately. Breaking the dilution into several smaller, accurately pipettable steps avoids this problem and also naturally produces the intermediate concentrations needed for a standard curve or titer.
What is the difference between a twofold and a tenfold serial dilution?
The difference is the per-step dilution factor: a twofold (1:2) series halves the concentration at each step (useful for generating a finely spaced titer, such as antibody or virus titers), while a tenfold (1:10) series reduces concentration by an order of magnitude at each step (useful for reaching very large overall dilution factors quickly, as in bacterial colony counts).
Related concepts
Serial dilution results are only as trustworthy as the documentation behind them — recording exact dilution factors, lot numbers, and calculation steps at the bench is part of what makes an experiment reproducible rather than a one-off result nobody can retrace. Labs that log dilution series and calculations in an electronic lab notebook rather than loose paper worksheets make that retracing far easier, particularly in regulated or GxP environments where the calculation chain itself may need to be auditable.
