Solution Dilution Calculator
Finds the final concentration of a solution after adding solvent, using the dilution equation C₁V₁ = C₂V₂. Essential for lab prep when making working solutions from concentrated stock.
About this calculator
When you dilute a solution, the number of moles of solute stays constant — only the volume increases. This gives the dilution equation: C₁V₁ = C₂V₂, where C₁ is the initial (stock) concentration in molarity (M), V₁ is the initial volume, C₂ is the final concentration, and V₂ is the final volume. Rearranging for the final concentration: C₂ = (C₁ × V₁) / V₂. Both volumes must be in the same units (liters in this calculator). The equation holds for any concentration unit as long as C₁ and C₂ share the same unit. It is valid for ideal solutions and is a cornerstone of analytical chemistry, biochemistry, and pharmaceutical compounding.
How to use
You have a 6.0 M hydrochloric acid stock solution and need 500 mL of a 0.5 M working solution. Enter Initial Concentration = 6.0 M, Initial Volume = 0.0417 L (the volume of stock you will take), and Final Volume = 0.500 L. C₂ = (6.0 × 0.0417) / 0.500 = 0.250 / 0.500 = 0.50 M. Alternatively, enter the known initial and final volumes with the stock concentration to find C₂ directly. Always add acid to water — never water to acid — for safe dilution practice.
Frequently asked questions
What does the dilution equation C₁V₁ = C₂V₂ actually mean chemically?
The equation expresses conservation of solute moles. Moles = concentration × volume, so C₁V₁ gives the moles in your stock aliquot and C₂V₂ gives the moles in your final solution. Because you only add solvent (which contains no solute), those mole counts must be equal. This makes the formula universally applicable regardless of the solute or solvent, as long as the solution behaves ideally and no chemical reaction occurs during mixing.
How do I calculate how much stock solution to use when preparing a diluted sample?
Rearrange C₁V₁ = C₂V₂ to solve for V₁: V₁ = (C₂ × V₂) / C₁. For example, to make 1 L of 0.1 M NaOH from a 2 M stock, V₁ = (0.1 × 1) / 2 = 0.05 L = 50 mL. Measure out 50 mL of the 2 M stock, then add water to a total volume of 1 L in a volumetric flask. This approach is used daily in biology labs for preparing buffer solutions, reagents, and standards.
Can I use the dilution calculator for percent concentration solutions, not just molarity?
Yes — the formula C₁V₁ = C₂V₂ works for any concentration unit, including % w/v, % v/v, mg/mL, or ppm, as long as both concentrations are expressed in the same unit. For instance, diluting a 70% ethanol solution to 30% uses exactly the same math. Just enter 70 as C₁ and 30 as C₂ along with your volumes. The calculator will return the final concentration in whatever unit you input.