How this calculation works
The Solution Dilution Calculator uses the conservation of mass equation (C₁V₁ = C₂V₂) to calculate the exact volume of concentrated stock solution (V₁) required and the volume of solvent diluent to add for preparing precise working reagents.
Mathematical formula and logic
V₁ = (C₂ × V₂) / C₁. Volume of Solvent to Add = V₂ - V₁. Dilution Factor = C₁ / C₂.
Worked example
To make 500 mL of 1.0 M solution from a 10.0 M stock: V₁ = (1.0 × 500) / 10.0 = 50 mL of stock solution. Add 450 mL of solvent (500 - 50 = 450 mL) for a 10x dilution.
Calculation assumptions
- Concentration and volume units must be consistent on both sides of the equation.
- Assumes ideal additive fluid volumes (no significant volumetric contraction upon mixing).
Frequently asked questions
What is the C1V1 = C2V2 formula?
The dilution equation (C₁V₁ = C₂V₂) is based on the principle that the total moles/mass of solute remains constant when diluting a concentrated stock solution with additional solvent.
What is a dilution factor?
The dilution factor (DF = C₁ / C₂ = V₂ / V₁) describes the ratio of the initial concentrated stock strength to the final diluted strength (e.g. a 1:10 dilution has a DF of 10).
Why should you always add acid to water ('Do as you oughta, add acid to water')?
Diluting concentrated acids is highly exothermic. Adding acid slowly to a large volume of water allows the water to absorb heat safely. Adding water to concentrated acid can cause violent boiling, acid splatter, and flash boiling.
What units can be used in C1V1 = C2V2?
Any concentration unit (Molar, mM, %, mg/mL, ppm) and volume unit (mL, L, µL) can be used as long as C₁/C₂ and V₁/V₂ share the same respective units.
What is serial dilution?
Serial dilution is a stepwise series of sequential dilutions (often 10-fold or 2-fold) used in microbiology and pharmacology to create exponentially decreasing concentrations across test wells.
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