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How to Calculate Dilutions (C1V1 = C2V2, Step by Step)

A clear, worked guide to the dilution formula C1V1 = C2V2 — how to dilute a stock solution, find the volume to add, and avoid the most common mistakes.

Jun 24, 2026DilutionCalcDilutionCalc

Diluting a solution is one of the most common tasks at the bench, in the classroom, and in the workshop — yet the arithmetic trips people up constantly. This guide walks through the single equation you need and shows exactly how to apply it.

The dilution formula

When you dilute a solution you add solvent but keep the amount of solute the same. Because the moles of solute don't change, this product is conserved:

C₁ × V₁ = C₂ × V₂

  • C₁ — concentration of your starting (stock) solution
  • V₁ — volume of stock you take
  • C₂ — concentration you want after dilution
  • V₂ — final total volume

Know any three of these and you can solve for the fourth. The fastest way is to let the dilution calculator do the rearranging — leave one field blank and it solves it instantly.

Step by step: diluting a stock

Say you have a 10 M stock and you need 50 mL of a 1 M working solution.

  1. Identify what you know: C₁ = 10 M, C₂ = 1 M, V₂ = 50 mL.
  2. Solve for the stock volume V₁ = (C₂ × V₂) ÷ C₁ = (1 × 50) ÷ 10 = 5 mL.
  3. Add solvent to reach the final volume: 50 − 5 = 45 mL of solvent.

So you measure 5 mL of stock into a vessel and top up to 50 mL. The solution dilution calculator is built exactly for this "dilute my stock" case.

Keeping units consistent

The equation is a ratio, so the only rule is: C₁ and C₂ must share a unit, and V₁ and V₂ must share a unit. You can mix molar (M) with millimolar (mM) only if you convert first. If you work in mg/mL but think in molarity, the mg/mL to molarity converter bridges the two using molecular weight.

Common mistakes

  • Forgetting the solvent step. V₁ is the stock to take, not the solvent to add. The solvent is V₂ − V₁.
  • Trying to "dilute" upward. You can't reach a higher concentration by adding solvent — C₂ must be less than C₁.
  • Mismatched units. Convert before you calculate, not after.

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