Serial Dilution Calculator

Plan serial dilutions from a dilution factor or a concentration range.

Supports nine molarity units and twenty-one volume units, for one to ten solutions.

Updated September 11, 2026

CreatorFrank Zhao

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What is serial dilution?

Serial dilution is a stepwise dilution technique used to systematically reduce the concentration of a substance in a solution. At each step, a measured volume of the previous solution is transferred into a fixed volume of diluent, producing a new solution with a known, lower concentration.

This method is fundamental across chemistry, biology, pharmacology, and environmental science. It allows researchers to create a range of precisely known concentrations from a single stock solution — essential for dose-response curves, microbial counting, and standard curve preparation.

This calculator handles the full planning workflow: from determining how much solution you need at each concentration level, to calculating exact volumes of stock solution and diluent required. It accounts for pipetting error and supports both forward planning (known dilution factor) and reverse planning (known target concentration range).

How to use this calculator

Choose a calculation mode, then fill in the values you know — the calculator will automatically solve for the remaining fields. You can start from any point in the workflow.

1Choose your method

Select Dilution factor if you know the ratio between each step (e.g., a 1:4 dilution means the dilution factor is 4). Select Concentration range if you know your starting and final concentrations and want the calculator to determine the dilution factor.

2Set the dilution parameters

Enter the number of dilutions (1–10), the dilution factor or concentration range, and the starting solution concentration. The calculator will display the concentration of each solution in the series.

3Enter your volume requirements

Specify the volume you need per concentration level and how many times each dilution will be used. Choose an error type — Percentage adds a percentage buffer (default 10%), or Volume adds a fixed pipetting error amount. The calculator computes the minimum volume you should prepare.

4Review the starting solution and repeat volumes

For multi-step dilutions (n > 1), the calculator shows how to prepare the starting solution from your stock, plus the volume to transfer and diluent to add at each step. If you set 1 dilution, only the starting solution composition is shown.

Worked example — Dilution factor mode

Suppose you need 5 serial dilutions with a dilution factor of 4, starting from a $10\ \mathrm{M}$ stock. Each concentration level requires 5 mL used 3 times, with 10% error margin.

Step 1: Minimum volume per dilution:

V_{\min} = V_{\text{use}} \times N_{\text{use}} \times \left(1 + \frac{E}{100}\right)

V_{\min} = 5 \times 3 \times (1 + 0.10)

=

16.5\ \mathrm{mL}

Step 2: Volume to transfer at each step:

V_{\text{move}} = \frac{V_{\min}}{DF - 1}

=

\frac{16.5}{4 - 1}

=

5.5\ \mathrm{mL}

Step 3: Diluent to add at each step:

V_{\text{added}} = V_{\text{move}} \times (DF - 1)

=

5.5 \times 3

=

16.5\ \mathrm{mL}

Result: The concentration of each solution follows:

C_k = \frac{C_0}{DF^{\,k-1}}

For this example: $10 \rightarrow 2.5 \rightarrow 0.625 \rightarrow 0.15625 \rightarrow 0.0390625 \rightarrow 0.009765625\ \mathrm{M}$ .

Worked example — Concentration range mode

You need 5 solutions ranging from $1\ \mathrm{M}$ down to $0.001\ \mathrm{M}$ . The calculator derives the dilution factor:

DF = \left(\frac{C_{\text{start}}}{C_{\text{final}}}\right)^{\frac{1}{n-1}}

=

\left(\frac{1}{0.001}\right)^{\frac{1}{4}}

=

5.623

The resulting concentrations are approximately $1 \rightarrow 0.178 \rightarrow 0.0316 \rightarrow 0.00562 \rightarrow 0.001\ \mathrm{M}$ , evenly spaced on a logarithmic scale.

Calculation formulas explained

The calculator uses a chain of connected formulas. Each formula can be solved in multiple directions — you provide the known values and it computes the unknown.

Minimum volume required

This is the minimum amount of solution you should prepare at each concentration level, accounting for your usage needs and pipetting error.

Percentage error mode:

V_{\min} = V_{\text{use}} \times N_{\text{use}} \times \left(1 + \frac{E}{100}\right)

Pipette error mode:

V_{\min} = (V_{\text{use}} + E_{\text{pip}}) \times N_{\text{use}}

where $V_{\text{use}}$ = volume per use, $N_{\text{use}}$ = number of uses, $E$ = percentage error, $E_{\text{pip}}$ = pipette error volume.

Volume to transfer at each step

V_{\text{move}} = \frac{V_{\min}}{DF - 1}

This is the volume of solution you transfer from one tube to the next. The diluent already in the tube brings the total up to $V_{\min}$ at the new concentration.

Starting volume needed

V_{\text{start}} = V_{\min} + V_{\text{move}}

The first tube in the series needs extra volume because you will be withdrawing $V_{\text{move}}$ from it. All subsequent tubes need only $V_{\min}$ .

Starting solution composition

The starting solution is prepared from a concentrated stock solution using the dilution equation:

V_{\text{stock}} = \frac{C_{\text{start}} \times V_{\text{start}}}{C_{\text{stock}}}

where $C_{\text{start}}$ is the starting solution concentration, $V_{\text{start}}$ is the total starting volume, and $C_{\text{stock}}$ is the stock solution concentration. The remaining volume is diluent:

V_{\text{diluent}} = V_{\text{start}} - V_{\text{stock}}

Concentration of each solution

In a uniform serial dilution, each solution has a concentration that is the previous solution divided by the dilution factor:

C_k = \frac{C_{\text{start}}}{DF^{\,k-1}}

The final (last) solution concentration is:

C_{\text{final}} = \frac{C_{\text{start}}}{DF^{\,n-1}}

In Concentration range mode, this is rearranged to solve for the dilution factor:

DF = \left(\frac{C_{\text{start}}}{C_{\text{final}}}\right)^{\frac{1}{n-1}}

Total diluent needed

V_{\text{total}} = V_{\text{added}} \times n + V_{\text{diluent}}

This sums the diluent added at each transfer step plus the diluent used to prepare the starting solution, giving you the total amount of diluent to measure out before beginning.

Real-world examples

Here are practical scenarios where serial dilution planning is essential.

Antibiotic susceptibility testing (MIC determination)

A microbiologist needs to determine the minimum inhibitory concentration (MIC) of an antibiotic. The standard approach uses 8 two-fold dilutions (DF = 2) starting from 128 µg/mL, yielding: 128, 64, 32, 16, 8, 4, 2, 1 µg/mL. Each well requires 100 µL with 2 replicates.

Using this calculator: Enter 8 dilutions, DF = 2, starting concentration = 128 µM, volume per use = 100 µL, 2 repeats, 10% error. The calculator will determine the minimum volume per well, the transfer volume (100 µL between tubes), and the total diluent needed.

Drug dose-response curve preparation

A pharmacology lab is testing a new compound across a concentration range from 100 µM to 0.1 µM. Using the Concentration range mode with 6 solutions, the calculator determines the required dilution factor of approximately 6.31 and the exact volumes needed to prepare enough solution for a 96-well plate.

By entering the pipette error volume instead of a percentage, you can account for the systematic error of your specific multichannel pipette, ensuring enough solution is prepared for accurate results.

Environmental water quality testing

When testing water samples for contaminants, lab technicians often dilute the original sample multiple times to bring concentrations within the detection range of analytical instruments. If a river water sample is expected to have a contaminant around 50 mg/L and the instrument's linear range is 0.5–5 mg/L, a 5-step dilution with DF ≈ 2.19 brings the final concentration to approximately 0.5 mg/L.

The calculator helps plan exactly how much of the original sample and diluent to prepare, factoring in the number of aliquots needed for replicate measurements.

Tips and best practices

Account for pipetting variability

Always include an error margin. The default 10% percentage error provides a reasonable buffer for manual pipetting. If you use a calibrated electronic pipette, you can switch to the volume error mode and enter the manufacturer-specified tolerance for tighter margins.

Match your units to the task

For microscale experiments, use µL or mL. For bulk preparation, liters or gallons may be more practical. The calculator supports 21 volume units and 9 molarity units — switch freely and the conversions happen automatically.

Use bidirectional solving

You don't have to start from the top. If you know the minimum volume you have available and the dilution factor, enter those first — the calculator will work out the volume per use. Any field in a formula group can be the starting point.

Plan for the first tube separately

The first solution in a multi-step series needs more volume than the rest — it is the source for the first transfer. The calculator automatically accounts for this in the starting volume and stock solution composition sections.

Limitations and disclaimers

Planning tool, not a substitute for verification. All volumes and concentrations are calculated from mathematical formulas. Actual results in the lab depend on pipette calibration, temperature, solution density, and operator technique.
Error models are simplified. The percentage and pipette error options provide a uniform buffer but do not capture the full distribution of random pipetting errors, meniscus effects, or residual liquid in tips.
Up to 10 dilution steps. The calculator supports a maximum of 10 dilutions. For longer series, you can run the calculation in segments.
Uniform dilution factor assumed. All steps in a series use the same dilution factor. If your protocol requires variable dilution ratios between steps, calculate each transition separately.
Concentration range mode requires at least 2 dilutions. With only 1 solution, the dilution factor is not meaningful because there is no range to span.

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