Serial Dilution Calculator: Molar Concentration After n Steps

This calculator follows a serial dilution, where each tube is diluted from the one before by the same factor. Enter the starting concentration in millimolar, the dilution factor of each step and the number of steps; you get the concentration in the last tube in mM and µM, and the total dilution factor.

Formula

C_n = C₀ ÷ fⁿ, and the total dilution factor is fⁿ.

• C₀: starting concentration (mM here)
• f: dilution factor of each step, for example 3 for 1 part in 3 parts total
• n: number of dilution steps
• C_n: concentration after step n; 1 mM = 1000 µM

Worked Example

A 5 mM solution diluted 1:3 five times in a row (for example 100 µL into 300 µL total at each step).

1. Total dilution factor: 3⁵ = 243
2. C₅ = 5 ÷ 243 = 0.020576 mM, shown as 0.0206 mM
3. In micromolar: 0.020576 × 1000 = 20.58 µM

Assumptions

• Every step uses the same factor and is mixed fully before the next transfer.
• The number of steps is a whole number; tube 0 is the starting solution, so tube n has been diluted n times.
• Volumes are measured accurately at every step; pipetting errors compound along the series.

How to read the result

Each step multiplies the dilution, so the concentration falls fast: five 1:3 steps make the solution 243 times weaker, and five 1:10 steps make it 100,000 times weaker. The concentration in any intermediate tube k is C₀ ÷ f^k. Serial dilutions are used to cover a wide range of concentrations, as in a standard curve, without having to measure very small volumes. For a single step, use the dilution factor calculator.

Limits and common mistakes

• Adding the factors instead of multiplying them: three 1:10 steps are 1:1000, not 1:30.
• Confusing transfer to diluent (1:2 as 1 + 2) with transfer to total volume changes f in every step.
• A small systematic pipetting error of 2% per step becomes about 10% after five steps.

Frequently Asked Questions

What is the concentration after five 1:3 dilutions of 5 mM?

About 0.0206 mM, or 20.58 µM; the total dilution is 243-fold.

What is the formula for serial dilution?

C_n = C₀ ÷ fⁿ, where f is the factor per step and n the number of steps.

How do I find the total dilution factor?

Multiply the factors of all steps; with equal steps it is fⁿ.

Can the steps have different factors?

Yes, but then multiply the individual factors yourself; this calculator assumes equal steps.

in c0 | Starting concentration | mM | 5 | 0
in fct | Dilution factor per step | - | 3 | 1
sel k | Number of steps | 5=5, 1=1, 2=2, 3=3, 4=4, 6=6, 7=7, 8=8, 9=9, 10=10, 11=11, 12=12
out cn | Concentration after the last step | mM | c0 / fct ^ k | 4
out cnu | Concentration after the last step in micromolar | µM | cn * 1000 | 2
out tdf | Total dilution factor | - | fct ^ k | 0