Solution Dilution Calculator
Diluting a concentrated stock solution down to a target concentration is one of the most common lab tasks — this uses the standard C₁V₁ = C₂V₂ relationship to find exactly what final volume achieves the desired result.
Inputs
Result
V₂ = 200 mL
Add solvent up to this final volume
How it works
C₁V₁ = C₂V₂
How the solution dilution calculator works
C₁V₁ = C₂V₂, rearranged to solve for the final volume: V₂ = (C₁ × V₁) ÷ C₂.
This works because the total amount of solute (moles) stays constant during dilution — only the volume of solvent around it increases.
Worked example: diluting 50 mL of a 2 M stock solution to 0.5 M
- V₂ = (2 × 50) ÷ 0.5 = 100 ÷ 0.5 = 200 mL.
- This means adding solvent to the original 50 mL until the total volume reaches 200 mL — not adding 200 mL of solvent on top of the original 50 mL.
Common mistakes to avoid
Adding the calculated V₂ as extra solvent rather than diluting up to that total volume
The result represents the total final volume the solution should occupy, not the additional amount of solvent to add — practically, this usually means adding solvent gradually until the total volume in a graduated container reaches V₂, not simply adding V₂ worth of solvent on top of V₁.
Mismatching concentration and volume units between C₁/V₁ and C₂
The formula is unit-agnostic as long as both concentrations use the same unit and volumes stay consistent within the equation — mixing molarity with a different concentration unit, or millilitres with litres without converting, breaks the proportional relationship the formula depends on.
Frequently asked questions
Why does the total amount of solute stay the same during dilution?
Diluting only adds more solvent around the existing solute — no solute is added or removed, so the total moles of solute present is identical before and after, which is exactly the principle the C₁V₁ = C₂V₂ formula is built on.
How do I know how much solvent to actually add in practice?
Subtract the original volume (V₁) from the calculated final volume (V₂) — that difference is the amount of solvent to add to reach the target concentration.
Can this formula be used for a concentration in the opposite direction (making a solution stronger)?
The same relationship applies mathematically, but making a solution more concentrated (by removing solvent, or adding more solute) is a fundamentally different practical process than simple dilution — the formula's core relationship still holds if solute amount is conserved.
Does this account for volume changes from mixing different solutions (non-ideal mixing)?
No — this assumes ideal dilution where combined volumes add straightforwardly, which is a very good approximation for most dilute aqueous solutions but can be slightly inaccurate for solutions where mixing causes a genuine, measurable volume change.
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