Dilution Calculator (C₁V₁ = C₂V₂)
Work out how much stock solution and solvent you need to reach a target concentration using C₁V₁ = C₂V₂.
How it works
C₁ · V₁ = C₂ · V₂ · V₁ = (C₂ · V₂) ÷ C₁ · solvent to add = V₂ − V₁
Diluting a solution keeps the amount of solute fixed while the volume grows, so the product of concentration and volume is conserved: C₁V₁ = C₂V₂. Rearranging gives the volume of concentrated stock to pipette out; the remainder of the final volume is pure solvent. Because only a ratio is used, C₁ and C₂ can be in any concentration unit as long as both match.
Worked example
To make 250 mL of 1.5 M from a 6 M stock: V₁ = (1.5 × 250) ÷ 6 = 62.5 mL of stock, topped up with 187.5 mL of solvent.
Sources: Dilution (equation) — Wikipedia
Frequently asked questions
Do C₁ and C₂ need the same units?
Yes. The equation depends on their ratio, so both concentrations must be expressed the same way — both molarity, both mg/mL, or both percent. The unit then cancels out.
Why can I not target a higher concentration?
Dilution only adds solvent, which lowers concentration. To go stronger you would have to add more solute or evaporate solvent, so the tool blocks a target above the stock strength.
How do I read the dilution factor?
It is C₁ ÷ C₂ — how many times more dilute the product is. A 6 M stock taken to 1.5 M is a 4× dilution, roughly one part stock to three parts solvent by volume.
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