Dilution Factor Calculators

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A dilution factor describes how much a solution has been diluted — the ratio of the original concentration to the final concentration. In microbiology, serial dilutions are used to reduce bacterial concentrations to a countable range for colony counting. In analytical chemistry, dilutions are used to bring samples into the linear range of an instrument. Understanding how to calculate dilution factors, work with serial dilutions, and back-calculate original concentrations from diluted measurements are essential practical skills in any quantitative laboratory.

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Dilution Factor Formula

Dilution factor = Volume of sample / Total volume (sample + diluent)

Example: add 1 mL sample to 9 mL diluent → Dilution factor = 1/10 = 10⁻¹

Original concentration = Measured concentration × Dilution factor⁻¹ = Measured × 10

Serial Dilutions

Each successive tube is diluted by the same factor. After n steps with factor f per step:

Total dilution = f^n

Example: 6 × 10-fold dilutions → Total dilution = 10⁻⁶

If 5 μL is plated from the 10⁻⁶ tube and 47 colonies counted:

CFU/mL = colonies / (volume plated × dilution factor) = 47 / (0.005 mL × 10⁻⁶) = 47 / 5 × 10⁻⁹ = 9.4 × 10⁹ CFU/mL

CFU Back-Calculation

CFU/mL = Colony count / (Volume plated in mL × Dilution factor)

Countable range for agar plates: 30–300 colonies per plate (below 30: statistically unreliable; above 300: colonies merge and become uncountable).

C₁V₁ = C₂V₂ for Single Dilutions

For preparing a specific concentration from stock:
V₁ = (C₂ × V₂) / C₁
Example: prepare 50 mL of 0.1 M from 2 M stock:
V₁ = (0.1 × 50) / 2 = 2.5 mL stock diluted to 50 mL total

Working with Log Dilutions

Serial dilutions in microbiology are usually logged:
log₁₀(10⁻⁶) = −6. Each 10-fold dilution step changes the log by −1. Used to construct dilution series across many decades of concentration.

Glossary

Dilution Factor
The ratio of sample volume to total volume: DF = Vsample/Vtotal. Indicates how much the original sample has been diluted. Original concentration = Measured concentration / DF.
Serial Dilution
Stepwise dilution where each tube is diluted by the same factor from the previous one. Total dilution after n steps = (individual factor)^n. Used in microbiology to dilute samples to a countable range for colony counting.
CFU (Colony-Forming Unit)
A single bacterial cell or clump capable of forming a visible colony on an agar plate. CFU/mL = colony count / (volume plated × dilution factor). Countable range: 30–300 colonies per plate for accurate estimates.

Frequently Asked Questions

Dilution factor = volume of sample / total volume (sample + diluent). Example: 1 mL into 9 mL = 1/10 = 10⁻¹. The dilution factor tells you how much the original sample has been diluted. To find the original concentration: Original = Measured concentration / Dilution factor = Measured × (1/DF). For serial dilutions, multiply individual factors: 1/10 × 1/10 × 1/10 = 10⁻³ total dilution.

CFU/mL = Colony count / (Volume plated in mL × Dilution factor of that tube). Example: 52 colonies on a plate inoculated with 0.1 mL from a 10⁻⁵ dilution: CFU/mL = 52 / (0.1 × 10⁻⁵) = 52 / 10⁻⁶ = 5.2 × 10⁷ CFU/mL. Always use plates with 30–300 colonies for reliable counts — below 30 is statistically imprecise; above 300 colonies merge.

A serial dilution is a stepwise dilution where each tube is diluted by the same factor (usually 10-fold or 2-fold) from the previous one. Used when the original sample concentration spans many orders of magnitude — too concentrated to plate or measure directly. After n steps of 10-fold dilution, the total dilution = 10⁻ⁿ. This allows plating of bacteria at a concentration that produces countable colonies (30–300 per plate), enabling accurate CFU/mL calculation.

C₁V₁ = C₂V₂ (conservation of moles) rearranges for laboratory dilutions: V₁ = (C₂ × V₂)/C₁, where V₁ = volume of stock needed and V₂ = final target volume. The dilution factor DF = C₂/C₁ = V₁/V₂. Example: C₁ = 10 M, C₂ = 0.5 M, V₂ = 100 mL → V₁ = (0.5 × 100)/10 = 5 mL stock in 100 mL total → DF = 0.5/10 = 0.05 (1:20 dilution).