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Serial Dilution Calculator

Find the concentration after a serial dilution.

How it is calculated

In a serial dilution each step dilutes the previous tube by the same factor. After n steps the total dilution is DFn and the final concentration is Cfinal = C0 / DFn. The factor means 1 part sample into DF parts total, so a factor of 10 is a 1 : 10 dilution, not 1 : 9 with diluent only. The result is shown in scientific notation in the same unit as the starting concentration. The step count is cut to a whole number; the concentration cannot be negative and the factor must be above zero.

Worked example

Starting concentration 1 (any unit), tenfold dilution, 6 steps. Total dilution = 106 = 1 : 1,000,000. Final concentration = 1 / 1,000,000 = 1.0000 × 10⁻⁶, so one millionth of the starting amount remains. Each step cuts the previous tube by a factor of ten: 0.1, 0.01, 0.001, and so on.

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Common mistakes

  • Confusing the dilution factor (total volume / sample volume) with the diluent volume; a 1 : 10 dilution uses 1 part sample plus 9 parts diluent.
  • Multiplying the factor by the number of steps instead of raising it to that power.
  • Including the neat stock as a step; the count is how many dilutions are made.
  • Mixing units between the starting concentration and the reading, such as mg/mL and µg/mL.

About this calculator

Serial dilution repeatedly dilutes a solution by the same factor at each step (e.g. 1:10) so the total dilution after n steps is the per-step factor raised to the nth power, and the final concentration equals the starting concentration divided by that total dilution factor. Doubling or halving errors compound quickly, which is exactly why the geometric progression matters.

Microbiologists rely on serial dilution to bring bacterial or viral samples into a countable range for colony-forming unit (CFU) plating; pharmacologists use it to prepare a range of drug concentrations for dose-response curves; and analytical chemists use it to build calibration standards for assays like ELISA.

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Comments (1)

  • Editorial team

    Plate counts are the usual reason for running a series. Pick the tube whose plate lands in the commonly used 30 to 300 colony range, then multiply the colonies by the total dilution shown here and divide by the volume you plated to get the count per millilitre of the original sample. The tool assumes the same factor at every step, so a series that mixes, say, a tenfold and a twofold step needs the factors multiplied by hand. Which factor does your protocol use?

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