Dilution Calculators

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A dilution reduces the concentration of a solute in a solution by adding more solvent. The fundamental relationship is conservation of moles: C₁V₁ = C₂V₂, where C = concentration and V = volume (subscripts 1 and 2 represent before and after dilution). Serial dilutions apply a fixed dilution ratio (commonly 1:10) repeatedly to achieve very large dilution factors — essential for plate counting, antibody titration, and drug dose-response curves. The dilution factor = C₁/C₂ = V₂/V₁, and log-scale dilution series are standard in microbiology and analytical chemistry.

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C₁V₁ = C₂V₂ Formula

Moles of solute are conserved during dilution: C₁ × V₁ = C₂ × V₂. Solve for any unknown: V₁ = (C₂ × V₂) / C₁ (volume of stock needed). C₂ = (C₁ × V₁) / V₂ (final concentration after dilution). Example: Prepare 500 mL of 0.1 M HCl from 12 M stock: V₁ = (0.1 × 500) / 12 = 4.17 mL of 12 M HCl, diluted to 500 mL total.

Dilution Factor (DF)

DF = C₁/C₂ = V₂/V₁ = (solute volume + diluent volume) / solute volume. A 1:10 dilution: take 1 part sample, add 9 parts diluent → DF = 10. A 1:100 dilution: 1 part in 100 total → DF = 100. In plate counting: dilution factor = product of all individual dilution factors: 10⁻¹ × 10⁻¹ × 10⁻¹ = 10⁻³ (three sequential 1:10 dilutions).

Serial Dilution

Transfer a fixed volume into the same volume of diluent (1:2 serial) or 1/10 of the diluent volume (1:10 serial): Tube 1: 1 mL sample + 9 mL diluent = 10⁻¹. Tube 2: 1 mL from Tube 1 + 9 mL = 10⁻². Continue to 10⁻³, 10⁻⁴, 10⁻⁵. In plate counting, plate 0.1 mL from each dilution; count plates with 30–300 colonies for CFU/mL calculation.

Parts Notation

1:10 means 1 part sample in 10 total (9 parts diluent + 1 part sample) → DF = 10. Sometimes written as 1/10 dilution. Confusing: 1:10 can also mean 1 part to 10 parts (11 total) in some contexts — always clarify which convention is being used.

Glossary

Dilution
Reduction of solute concentration by adding solvent; governed by C₁V₁ = C₂V₂ (mole conservation); expressed as dilution factor (C_initial/C_final) or as ratio (1:10 = 10-fold dilution).
Serial Dilution
Sequential dilutions each applying the same factor (usually 1:10); used in plate counting and antibody titration; total DF = product of individual DFs; 3×1:10 dilutions = 10⁻³.
Dilution Factor
C_initial/C_final = V_final/V_initial; for a 1:10 dilution, DF = 10; total DF of serial dilutions = product of all individual DFs.

Frequently Asked Questions

C₁V₁ = C₂V₂ states that moles of solute are conserved when a solution is diluted (no solute added or removed). Solve for the unknown: V₁ = (C₂ × V₂) / C₁ (volume of stock). C₂ = (C₁ × V₁) / V₂ (final concentration). Examples: Make 100 mL of 10 mM from 1 M stock: V₁ = (0.01 M × 0.1 L) / 1 M = 0.001 L = 1 mL. Take 1 mL of 1 M stock, add 99 mL buffer = 100 mL of 10 mM solution. Works for any consistent concentration units (M, mM, μg/mL, %): just ensure both C values use the same units.

Serial dilution reduces bacterial concentration stepwise to a countable range for plate counting. Standard 1:10 serial: transfer 1 mL into 9 mL diluent (sterile water, PBS, or broth); mix vigorously; repeat. After n steps: dilution factor = 10⁻ⁿ. To plate: use 0.1 mL from several consecutive dilutions onto agar plates. After incubation: count plates with 30–300 colonies. CFU/mL = colonies / (dilution × 0.1 mL plated). Critical: mix each tube thoroughly before transferring (vortex 5–10 sec) — poor mixing is a leading cause of plate count errors.

Dilution factor (DF) = final volume / initial volume = C_initial / C_final = 1 / (sample fraction). For a 1:10 dilution (1 mL sample in 9 mL diluent = 10 mL total): DF = 10 (or 10⁻¹ as a fraction). For multiple sequential dilutions: multiply all individual DFs: three 1:10 dilutions: DF = 10 × 10 × 10 = 1000 = 10³ (or concentration = 10⁻³ of original). Example: 1 mL into 9 mL = 10⁻¹; then 1 mL of that into 9 mL = 10⁻²; then 1 mL into 9 mL = 10⁻³. Concentration at 10⁻³ is 1/1000 of the original.

This notation can be ambiguous: In most biological laboratory contexts: 1:10 means 1 part sample in 10 parts TOTAL (9 parts diluent + 1 part sample) → dilution factor = 10. In chemistry (particularly older conventions): 1:10 may mean 1 part to 10 parts diluent (11 parts total) → dilution factor = 11. The WHO/IUPAC recommended notation to avoid ambiguity: '1 in 10' or '1/10' = one part in 10 total = dilution factor 10. Always verify with a colleague or protocol when the context is unclear — using the wrong convention introduces a 10% error in concentration that may matter in precise work. For plate counting, the distinction is minor; for preparing drug stocks, it could be clinically significant.