Solution Dilution Calculator — C₁V₁ = C₂V₂
Use the dilution equation C₁V₁ = C₂V₂ to find any unknown: the stock volume needed, the final concentration after adding solvent, or the volume to add. Works with any consistent units (mol/L, mg/mL, %, ppm, etc.).
Solve for
Computed from C₁V₁ = C₂V₂
- 1
Amount of solute (C₁ × V₁)
1 × 100 = 100 - 2
Final volume V₂
100 ÷ 0.1 = 1,000
How does this calculator work?
The dilution equation C₁V₁ = C₂V₂ conserves the total amount of solute as you add solvent. Knowing any three of the four variables gives the fourth by rearrangement. The dilution factor is C₁/C₂ and the solvent to add equals V₂ − V₁.
Formula
How this is calculated
When a solution is diluted by adding solvent, the total amount of solute is conserved while the volume increases. This gives the equation C₁V₁ = C₂V₂, where C₁ and V₁ are the concentration and volume of the stock (original) solution, and C₂ and V₂ are those of the final diluted solution. Because the equation links four variables, knowing any three lets you solve for the fourth by simple rearrangement.
The dilution factor (DF = C₁/C₂ = V₂/V₁) quantifies how much more dilute the final solution is. A DF of 10 means the concentration dropped by 10×. The volume of solvent to add is simply V₂ − V₁. Always use consistent units: if concentration is in mol/L, both volumes must be in litres; if concentration is in mg/mL, volumes must be in mL.
This formula assumes ideal mixing (no volume change on mixing) and no chemical reaction between solute and solvent. For strongly exothermic dilutions (such as concentrated sulfuric acid), add the concentrated solution slowly to water — never the reverse — as a safety precaution not captured by this equation.
Frequently asked questions
The dilution factor (DF) is how many times more dilute the final solution is: DF = C₁/C₂ = V₂/V₁. A 10× dilution of a 1 mol/L stock gives 0.1 mol/L; a 100× dilution gives 0.01 mol/L.
Yes — mol/L, mg/mL, %, ppm and any other unit all work as long as both concentrations use the same unit. V₁ and V₂ must also share the same volume unit (mL, L, µL, etc.).
In a serial dilution each step dilutes the previous result: apply C₁V₁ = C₂V₂ step by step, using the C₂ of one step as the C₁ of the next. Three sequential 1:10 dilutions give a net 1:1000 (1000×) dilution.
Also known as
TG we-Calculate Editorial Team. (2026). Solution Dilution Calculator — C₁V₁ = C₂V₂ [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/solution-dilution-calculator
TG we-Calculate Editorial Team. "Solution Dilution Calculator — C₁V₁ = C₂V₂." TG we-Calculate. 2026. https://we-calculate.com/calculator/solution-dilution-calculator.
TG we-Calculate Editorial Team, "Solution Dilution Calculator — C₁V₁ = C₂V₂," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/solution-dilution-calculator
@misc{wecalculate_solution_dilution_calculator, title = {Solution Dilution Calculator — C₁V₁ = C₂V₂}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/solution-dilution-calculator}}, year = {2026}, note = {TG we-Calculate} }
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