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M1V1 M2V2 Dilution Formula

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Use M1V1 = M2V2 when the amount of the same solute is conserved while a stock solution is diluted to a new final volume.

  • M1 is stock concentration.
  • V1 is volume of stock used.
  • M2 is final concentration.
  • V2 is final total solution volume.

The relationship follows from equal solute amounts before and after dilution: n = M × V.

Calculate required stock volume

Suppose you need 100.0 mL of 0.250 M solution from a 2.00 M stock.

V1 = (M2 × V2) / M1

V1 = (0.250 × 100.0 mL) / 2.00 = 12.5 mL

The calculation calls for 12.5 mL of stock brought to a final total volume of 100.0 mL under the applicable approved procedure. It does not mean “add 100.0 mL of solvent.”

Use the Dilution Calculator for this stock-to-final calculation. Use the Molarity Calculator when starting with dry solute mass rather than an existing stock.

Rearranged equations

  • final concentration: M2 = M1 × V1 / V2
  • final volume: V2 = M1 × V1 / M2
  • stock concentration: M1 = M2 × V2 / V1

Concentration units must match each other. Volume units must match each other. V1 and V2 can both be in mL because the shared conversion factor cancels.

When the formula does not apply directly

  • A chemical reaction changes the amount or identity of a species. Use balanced-equation stoichiometry.
  • Mixing two solutions containing the same solute is better handled by total moles divided by measured final volume.
  • Non-additive volumes require actual final volume rather than an assumed sum.
  • A stock concentration stated as mass percent must first be converted using its correct basis and required density.
  • Serial dilution requires applying the relation at each step and tracking the cumulative dilution factor.

Common mistakes

  • Using solvent volume in place of final volume.
  • Mixing M and mM without converting.
  • Swapping stock and final labels.
  • Treating dilution as a way to create a more concentrated solution.
  • Applying the relationship to titration without reaction stoichiometry.

Frequently asked questions

Is M1V1 = M2V2 a titration formula?

Not universally. It is a same-solute dilution relationship. Titration calculations generally require the stoichiometric ratio from the balanced reaction.

Is V2 the amount of solvent added?

No. V2 is final total solution volume.

Can I use mL without converting to L?

Yes, if V1 and V2 use the same volume unit and M1 and M2 use the same concentration unit.

Can dilution make a solution more concentrated?

Adding solvent reduces concentration. Producing a higher concentration requires another process and is not described by ordinary dilution.

Sources

Use this resource

1 available tool
Open the Molarity CalculatorRun the calculation with your own inputs, then return here to interpret it.

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