Serial Dilution Calculator
Plan a constant-factor dilution series, the transfer volume between tubes, and the stock-and-diluent volumes needed for the starting solution.
Dilution setup
Live results
Concentration across the series
The line uses a logarithmic concentration axis because each step changes by the same multiplicative factor.
Dilution plan
| Solution | Concentration (M) | Cumulative factor | Transfer in (mL) | Diluent added (mL) | Prepared volume (mL) |
|---|
Tube 1 is prepared from stock and diluent. Each later tube receives the same transfer volume from the preceding tube plus the listed diluent.
How to use this serial dilution calculator
What this calculator does
This tool plans a constant-factor serial dilution. It calculates the concentration in every tube, the liquid volume that must remain available for experimental uses, the transfer volume between adjacent tubes, and the stock and diluent volumes needed to prepare tube 1. It assumes ideal volume additivity and the same dilution factor at every step. It does not verify chemical compatibility, solubility, pipette performance, sterility, or whether a particular concentration is safe for a biological or clinical procedure.
When to use it
Use it to prepare calibration standards, dose-response plates, microbiology dilution series, or screening concentrations for spectroscopy and analytical chemistry. The underlying concentration-volume relationship is the same dilution principle described in OpenStax Chemistry's section on molarity and dilution.
How to calculate
- The calculator opens with a complete demonstration: six solutions, a 4× step factor, 10 M starting concentration, 9 mL per use, three uses, a 3 mL fixed allowance, and 50 M stock. The example workbook is immediately available.
- Choose Method. Use “Dilution factor” when the step factor is known. Use “Concentration range” when the starting and final concentrations are known; the calculator derives the constant factor as (start ÷ final)1/(n – 1).
- Replace the demonstration values, read the live results and dilution plan, then select Download Excel to export the current validated model.
- Select Reset to clear all data. Reset does not restore the demonstration and disables export until a complete valid setup is entered again.
Input guide
Number of dilutions is a required whole-number tube count from 2 to 96; 6 is a practical example. Increasing it extends the concentration series. Dilution factor is a required decimal greater than 1 in factor mode; 4 means each tube has one quarter of the previous concentration. Starting solution concentration (M) is required and must be positive; it is the concentration of tube 1, not the stock. Final solution concentration (M) appears in range mode and must be positive and below the start.
Volume per use (mL) is the amount consumed by one assay or measurement; 9 mL is used in the example. Number of uses per dilution is the required replicate count. Error allowance determines whether reserve volume is a fixed pipette allowance or a percentage. A fixed value such as 3 mL is added directly; a percentage such as 10 means the required use volume is multiplied by 1.10. Stock solution concentration (M) must be at least the starting concentration; 50 M is used only as a numerical demonstration. Do not enter grouping commas, scientific notation, units, or symbols in numeric boxes.
Output guide and worked example
Minimum volume retained is the volume required for all planned uses plus the allowance. Transfer volume each step is minimum volume ÷ (factor – 1). Starting solution volume needed is minimum plus transfer volume. Stock volume for tube 1 follows C₁V₁ = C₂V₂, while Diluent for tube 1 is the balance. Diluent per later tube equals transfer volume × (factor – 1), and Total diluent required adds tube 1's diluent to all later tubes.
For the startup example, 9 mL × 3 uses + 3 mL allowance gives 30 mL retained. With a factor of 4, the transfer is 30 ÷ 3 = 10 mL, so tube 1 needs 40 mL total. Preparing 40 mL at 10 M from 50 M stock requires 8 mL stock and 32 mL diluent. Five later tubes each receive 10 mL transferred solution and 30 mL diluent. The final concentration is 10 ÷ 4⁵ = 0.009765625 M.
Concentrations in the table and chart are exact model identities subject only to display rounding. Volumes are planning estimates and should be checked against vessel capacity and instrument tolerances. Consult the NIOSH school chemistry laboratory safety guide for general chemical-handling principles and use a validated protocol for regulated work.
Formula and practical interpretation
Concentration at step i = starting concentration ÷ factori – 1
A serial dilution is multiplicative, not subtractive. A 4× factor does not remove 4 M each time; it divides the current concentration by four. This is why a logarithmic chart is appropriate: equal horizontal steps represent equal multiplicative changes. The stock calculation uses the standard C₁V₁ = C₂V₂ dilution identity. OpenStax also summarizes the relevant concentration units in its guide to solution concentration units.
Practical accuracy is limited by pipette calibration, mixing, carryover, adsorption, evaporation, and cumulative transfer error. Use clean tips or pipettes, mix each tube thoroughly before transferring, and select equipment whose operating range comfortably includes the calculated transfer volume. For assay design context, the NCBI Assay Guidance Manual chapter on assay validation explains why repeatability and controlled liquid handling matter.