Dilution Calculations Guide

Dilution Factor Calculation
Single Dilution Using C₁V₁ = C₂V₂
Serial Dilution Calculation
Practical Examples
Key Formulas Summary

Dilution Factor Calculation

Basic Formula

The dilution factor (DF) represents how many times a solution has been diluted:

$$\text{Dilution Factor} = \frac{\text{Final Volume}}{\text{Sample Volume}}$$

Notation Types

S:D notation (Stock to Diluent)

Format: Stock Volume : Diluent Volume

S:T notation (Stock to Total)

Format: Stock Volume : Total Volume

Example

If you add 10 mL of stock solution to 90 mL of solvent:

Total volume = 100 mL
DF = 100 mL ÷ 10 mL = 10 (represents a 1:10 dilution)

Single Dilution Using C₁V₁ = C₂V₂

The Dilution Equation

$$C_1V_1 = C_2V_2$$

Variables

C₁ = initial (starting) concentration
V₁ = initial (starting) volume
C₂ = final concentration
V₂ = final volume

Solving for Unknown Variables

To find initial volume (V₁): $$V_1 = \frac{C_2 \times V_2}{C_1}$$

To find final concentration (C₂): $$C_2 = \frac{C_1 \times V_1}{V_2}$$

To find final volume (V₂): $$V_2 = \frac{C_1 \times V_1}{C_2}$$

Step-by-Step Process

Identify all known values (C₁, V₁, C₂, or V₂)
Determine which variable you need to solve for
Rearrange the equation accordingly
Substitute values and calculate
Verify units match before calculation

Serial Dilution Calculation

Definition

A serial dilution is a step-wise series of dilutions where the dilution factor remains constant for each step. Common dilution factors are 2-fold (1:2) and 10-fold (1:10).

Common Serial Dilution Setup

For a 10-fold serial dilution:

Combine 1 mL of sample (or previous dilution) with 9 mL of fresh diluent
Dilution factor per step = 10⁻¹ (or 1/10)

Total Dilution Factor Formula

When performing multiple sequential dilutions:

$$\text{Total Dilution Factor} = \text{DF}1 \times \text{DF}2 \times \text{DF}_3 \times \ldots$$

Example: 7-Step 10-Fold Serial Dilution

$$\text{Total DF} = 10^{-1} \times 10^{-1} \times 10^{-1} \times 10^{-1} \times 10^{-1} \times 10^{-1} \times 10^{-1} = 10^{-7}$$

The final concentration = 1/10,000,000 of the original

Required Volume Calculations

Transfer Volume (amount to move to next tube): $$\text{Transfer Volume} = \frac{\text{Final Volume}}{\text{Dilution Factor}}$$

Diluent Volume (amount of fresh diluent): $$\text{Diluent Volume} = \text{Final Volume} - \text{Transfer Volume}$$

Practical Examples

Example 1: Basic Dilution Calculation

Question: What volume of a 10 mM stock solution is required to make 20 mL of a 50 μM solution?

Given:

C₁ = 10 mM (starting concentration)
C₂ = 50 μM = 0.05 mM (final concentration)
V₂ = 20 mL (final volume)

Solution: $$V_1 = \frac{C_2 \times V_2}{C_1} = \frac{0.05 \text{ mM} \times 20 \text{ mL}}{10 \text{ mM}} = \frac{1}{10} = 0.1 \text{ mL}$$

Answer: Use 0.1 mL (100 μL) of stock solution + 19.9 mL of diluent = 20 mL total

Example 2: Serial Dilution Planning

Question: Plan a 10-fold serial dilution with 10 mL per tube for 5 steps.

Calculations for each tube:

Transfer volume = 10 mL ÷ 10 = 1 mL
Diluent volume = 10 mL - 1 mL = 9 mL

Procedure:

Tube 1 (10⁻¹): Transfer 1 mL of original sample to 9 mL diluent
Tube 2 (10⁻²): Transfer 1 mL from Tube 1 to 9 mL fresh diluent
Tube 3 (10⁻³): Transfer 1 mL from Tube 2 to 9 mL fresh diluent
Tube 4 (10⁻⁴): Transfer 1 mL from Tube 3 to 9 mL fresh diluent
Tube 5 (10⁻⁵): Transfer 1 mL from Tube 4 to 9 mL fresh diluent

Example 3: Finding Initial Concentration After Serial Dilution

Question: You measure a bacterial count of 100 cells/mL in a sample that was diluted 10⁻⁶. What is the original concentration?

Given:

Measured concentration = 100 cells/mL
Final dilution factor = 10⁻⁶

Solution: $$\text{Initial Concentration} = 100 \text{ cells/mL} \times 10^6 = 100,000,000 \text{ cells/mL} = 10^8 \text{ cells/mL}$$

Answer: The original concentration was 10⁸ cells/mL or 100 million cells/mL

Key Formulas Summary

Dilution Factor

$$\text{DF} = \frac{\text{Final Volume}}{\text{Sample Volume}}$$

Single Dilution (C₁V₁ = C₂V₂)

Stock Volume: $V_1 = \frac{C_2 \times V_2}{C_1}$
Final Concentration: $C_2 = \frac{C_1 \times V_1}{V_2}$

Serial Dilution

Transfer Volume: $\frac{\text{Final Volume}}{\text{Dilution Factor}}$
Diluent Volume: $\text{Final Volume} - \text{Transfer Volume}$
Total DF: $\text{DF}1 \times \text{DF}2 \times \text{DF}_3 \times \ldots$

Back-Calculating Original Concentration

$$\text{Original Concentration} = \text{Measured Concentration} \times \text{Total Dilution Factor}$$

Quick Reference Tips

Always ensure units are consistent before performing calculations
Mix thoroughly at each dilution step, especially in serial dilutions
Use sterile techniques when preparing dilutions
Label all tubes clearly with the dilution factor (e.g., 10⁻³, 10⁻⁶)
For 10-fold dilutions: 1 mL sample + 9 mL diluent = 10 mL total
For 2-fold dilutions: 1 mL sample + 1 mL diluent = 2 mL total
Verify calculations by working backwards from the final solution

Dilution Calculator