Serial Dilution Calculator
A serial dilution repeats the same dilution step over a row of tubes, so the concentration falls geometrically instead of in one jump. Enter a stock concentration, a per-step factor and a number of steps to get the concentration in the last tube plus every tube in between, or enter a target concentration to find how many steps you need. Because each step multiplies the previous one, the overall factor is the per-step factor raised to the number of steps — a 1:10 series run for four steps is an overall 1:10,000, not 1:40.
Serial dilution is what you reach for when the total factor is too large to pipette accurately in a single step. A 1:10,000 dilution done at once means 1 µL into 10 mL, which sits at the ragged bottom of most pipettes' reliable range; the same dilution done as four successive 1:10 steps keeps every transfer in a comfortable volume. The cost is that each step carries its own small error, and those errors compound, so the series has to be planned, not improvised. This calculator is part of our laboratory calculator set and it is the multi-step sibling of the single-step dilution calculator.
The defining idea is geometric decay. After one step the tube holds C₀ / DF; after two it holds C₀ / DF²; after n steps it holds C₀ / DFⁿ. That exponent is why a modest-looking 1:10 factor run for six steps already spans a million-fold range, and it is the reason a standard curve or a microbial titre is laid out as a row of tubes rather than one brave jump. When you also care about the molarity of the result, the molarity calculator converts the final concentration into moles per litre.
Two directions matter at the bench. Sometimes you know the series you intend to run and want the endpoint concentration — that is the "final concentration" mode. Sometimes you know the concentration you must reach and want to know how many steps it takes — that is the "steps required" mode, which rounds up, because a partial step is not something you can pipette.
Serial Dilution Calculator
How to use the serial dilution calculator
Pick the direction in the Solve for dropdown. "Final concentration" starts from a stock, a per-step factor and a number of steps; "Steps required" starts from a stock, a per-step factor and the target concentration you want to reach.
Enter the stock concentration (tube 0) and choose its unit — M, mM, µM or nM. The engine normalises to mol/L internally, so the unit you pick is the unit the answer is reported in for steps mode and the basis of the comparison in both modes.
Set the per-step dilution factor. A value of 10 means each tube is one tenth of the one before it; 2 means a two-fold series, which is common for MIC and titration work.
In final mode enter the number of steps (whole tubes after the stock). In steps mode enter the target concentration; the calculator returns the smallest whole number of steps that reaches or goes below it, and the concentration actually achieved after that many steps.
Optionally enter the volume per tube and its unit. The tool then reports how much of the previous tube to transfer (V_tube ÷ DF) and how much diluent to add to make each tube up to that volume.
Press Calculate. The primary card answers your question; the step table lists the concentration in every tube so you can label them before you start.
Serial Dilution formula
Variables and units
| Symbol | Meaning | Unit |
|---|---|---|
| C₀ | Stock concentration (tube 0) | any (M, mM, µM…) |
| Cₙ | Concentration after n steps | same as C₀ |
| DF | Per-step dilution factor | × |
| n | Number of dilution steps | count |
| DF_overall | Cumulative factor after the series | × |
| V_transfer | Aliquot carried into each tube | L |
| V_diluent | Diluent added to each tube | L |
How serial dilution is calculated
- Normalise the stock concentration to mol/L so any input unit behaves consistently.
- For an endpoint, raise the per-step factor to the number of steps and divide: Cₙ = C₀ / DFⁿ.
- For a step count, take the logarithm: n = ⌈log(C₀ / C_target) ÷ log(DF)⌉, rounding up so the achieved concentration is at or below the target.
- Build the step table by applying the factor one tube at a time — tube i holds C₀ / DFⁱ.
- If a volume per tube is given, transfer V_tube ÷ DF from the previous tube and add diluent to V_tube.
Worked laboratory examples
Example 1 — A four-step 1:10 series from 1 M
Given: stock 1 M · per-step factor 10 · 4 steps · 1 mL per tube
- C₄ = 1 M ÷ 10⁴ = 1 × 10⁻⁴ M = 0.1 mM
- overall factor = 10⁴ = 10,000
- transfer = 1 mL ÷ 10 = 0.1 mL into 0.9 mL diluent per tube
- tubes: 0.1 M, 0.01 M, 0.001 M, 0.0001 M
Result: final tube 1 × 10⁻⁴ M (0.1 mM) after an overall 1:10,000 dilution
Example 2 — A two-fold series over four steps
Given: stock 100 mM · per-step factor 2 · 4 steps
- C₄ = 100 mM ÷ 2⁴ = 100 ÷ 16 = 6.25 mM
- overall factor = 16
- tubes: 50, 25, 12.5, 6.25 mM
Result: final tube 6.25 mM — the spacing a titration or MIC series wants
Example 3 — Steps needed to reach a target
Given: stock 1 M · per-step factor 10 · target 1 × 10⁻⁴ M
- exact = log(1 ÷ 10⁻⁴) ÷ log(10) = 4
- round up → 4 steps
- achieved = 1 M ÷ 10⁴ = 1 × 10⁻⁴ M
Result: 4 steps, landing exactly on the 1 × 10⁻⁴ M target
Example 4 — When the target does not divide evenly
Given: stock 1 M · per-step factor 10 · target 5 × 10⁻⁴ M
- exact = log(1 ÷ 5 × 10⁻⁴) ÷ log(10) ≈ 3.30
- round up → 4 steps
- achieved = 1 M ÷ 10⁴ = 1 × 10⁻⁴ M, below the 5 × 10⁻⁴ M target
Result: 4 steps — you overshoot downward, because you cannot run a third of a tube
Want the reasoning behind the numbers? Read How to Make a Serial Dilution and How to Calculate a Dilution.
How to interpret the result
The primary card answers the question you asked; the step table is what you actually work from, because you label and pipette tube by tube. Read the overall factor as the cumulative dilution from stock to final tube: a per-step factor of 10 over four steps is 10,000-fold, which is the number you quote when someone asks "how dilute is the last tube".
In steps mode the achieved concentration is almost always slightly below your target, because the step count rounds up. That is the correct behaviour — you would rather land at or under a limit than a hair above it. If the overshoot is large, a smaller per-step factor gives finer control at the cost of more tubes.
Watch the warnings. A per-step factor below 1 means each tube is stronger than the last, which is a sign the factor was entered inverted. A series longer than about twelve steps accumulates enough pipetting error that the nominal endpoint and the real one drift apart; a larger factor or a fresh stock is the better answer.
Assumptions
- Every step uses the same per-step dilution factor; mixed factors are not modelled.
- Volumes are additive and each tube is made up to the same final volume.
- The solute is conserved and fully mixed at each transfer — nothing adsorbs to the tube wall or reacts.
- Concentration is normalised to mol/L, so the input unit must be a molar unit (M, mM, µM, nM).
Limitations
- Pipetting error compounds down the series; the calculator reports nominal concentrations, not the real spread you would measure.
- It plans an evenly spaced geometric series only — irregular or back-filled schemes are out of scope.
- Carryover volume and mixing efficiency are assumed ideal; at very small transfer volumes these assumptions weaken.
- The step count rounds up in steps mode, so the achieved concentration can sit meaningfully below a target that falls between tube values.
Common mistakes
- Treating four 1:10 steps as an overall 1:40 dilution instead of 1:10,000 — the factor is raised to the number of steps, not multiplied by it.
- Using the same tip for every transfer, which drags the previous tube forward and flattens the whole series.
- Running too many steps with a tiny factor when a larger factor and fewer tubes would be more accurate.
- Forgetting to make each tube up to a fixed final volume, so the per-step factor is not what you think it is.
- Rounding the step count down in steps mode, which leaves the final tube above the target concentration.
FAQ
What is a serial dilution?
How do I calculate the final concentration of a serial dilution?
How do I find the number of steps for a target concentration?
What is the overall dilution factor of a series?
Why use a serial dilution instead of one big dilution?
Does the concentration unit matter?
How much do I transfer into each tube?
Scientific Sources
- Promega Biomath — Dilution Calculator · Tier 2 source
- NEB NEBioCalculator · Tier 2 source
- NIST Chemistry WebBook · Tier 1 source
External links open in a new tab and carry rel="nofollow". We cite primary references (NIST, NIH/NCBI, peer-reviewed papers) and established manufacturer technical documentation (NEB, Thermo Fisher, Promega, IDT). Calculated results are estimates; your protocol and manufacturer guidance take precedence.
Last reviewed: 2026-09 · Method version: 1.0