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Chemistry & Materials Science

Serial Dilution Calculator

Calculate the exact final concentration of a solution after a specific number of repeated, sequential serial dilutions in the laboratory.

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mL
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Calculate the exact final concentration of a solution after performing a sequence of repeated dilutions. Serial dilution is a critical technique in microbiology, biochemistry, and analytical chemistry for creating highly dilute, accurate solutions.

The Serial Process

In a serial dilution, a small amount of a previous solution is transferred to a new tube containing fresh diluent. This process is repeated nn times. The total dilution factor compounds exponentially with each step.

Cn=C0×(VtVt+Vd)n\begin{aligned} C_n = C_0 \times \left( \frac{V_t}{V_t + V_d} \right)^n \end{aligned}

Where:
CnC_n=
Final Concentration after n steps
C0C_0=
Initial Stock Concentration
VtV_t=
Transfer Volume
VdV_d=
Diluent Volume
n=
Number of Dilutions

Precision at Scale

If you need to reach parts-per-billion (ppb) concentrations or create standard curves for spectrophotometry, performing a 1:10 dilution three times is far more accurate than trying to measure a single 1:1000 dilution directly.

Frequently Asked Questions

The dilution factor is the ratio of the final volume to the initial (transfer) volume. For example, transferring 1 mL into 9 mL of diluent gives a total volume of 10 mL. The dilution factor is 1/10, or 10^-1.

Microbiologists use serial dilutions to reduce the concentration of bacteria in a sample to a countable level. Plating a highly concentrated sample would result in a solid 'lawn' of bacteria, whereas a diluted sample allows individual colonies to form and be counted.

Multiply the individual dilution factors together. If you do three 1:10 dilutions, the total dilution factor is 1/10 × 1/10 × 1/10 = 1/1000 (or 10^-3).

A simple dilution is a one-time reduction in concentration. A serial dilution is a stepwise, geometric progression of dilutions that allows for massive reductions in concentration with high precision.

This calculator assumes a uniform serial dilution where the transfer and diluent volumes remain constant at each step. If you change volumes, you must calculate each step's M1V1=M2V2M_1V_1=M_2V_2 individually.

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