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Molarity Dilution Calculator

Solve C1V1 = C2V2 for the stock volume you need

How it is calculated

Moles of solute do not change on dilution, so C1V1 = C2V2. You enter the stock concentration C1, the target concentration C2 and the final volume V2. The tool returns the stock volume V1 = C2V2 / C1 and the solvent to add, V2 − V1, both with two decimals.

Concentrations just need the same unit, and the volumes come out in whatever unit you gave for V2 (mL stays mL). No result is given if C1 or V2 is zero or negative, if C2 is negative, or if the target is more concentrated than the stock. A target C2 of zero is accepted: V1 is then 0 and the whole volume is solvent. The solvent figure assumes volumes add up exactly.

Worked example

You have a 12 M stock and want 500 mL of a 1 M solution. V1 = 1 × 500 / 12 = 41.67 mL of stock. The solvent is 500 − 41.67 = 458.33 mL. In practice you measure 41.67 mL of stock and then add solvent until the total reaches 500 mL.

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Common mistakes

  • Adding the full 458.33 mL of solvent to a flask without watching the total: the aim is a final volume of 500 mL, and real mixtures can contract or expand slightly, so top up to the mark instead.
  • Mixing units, such as C1 in mol/L and C2 in mmol/L: both concentrations must use the same unit or the ratio is wrong by a factor of 1000.
  • Entering the initial volume as V2: the volume field is the final volume after dilution, not the stock you start with.
  • Swapping stock and target, which gives no result since the target cannot exceed the stock.

About this calculator

The dilution equation C₁V₁ = C₂V₂ holds because the total moles of solute stay constant when a solution is diluted with solvent — only the volume changes, so concentration falls in exact proportion to how much the volume grows. Solving for the stock volume needed, V₁ = C₂V₂/C₁, tells you exactly how much of a concentrated stock solution to measure out before topping it up to the target volume with solvent.

This is one of the first calculations taught in general chemistry lab courses, and it's used constantly in real lab work: preparing buffers and reagents at a working concentration from a concentrated stock, pharmacists and pharmacologists diluting drug stocks to a dosing concentration, and molecular biologists diluting DNA, enzyme, or antibody stocks for PCR, assays, and cell culture. Getting it right matters because both under- and over-diluting a reagent can invalidate an experiment or a compounded preparation.

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Comments (1)

  • Editorial team

    Look at the stock volume V1 before you start. Diluting a 12 M stock to 1 M in 500 mL needs 41.67 mL, easy to measure. But if V1 comes out below about 1 mL, pipetting error becomes a large share of it, and a two-step dilution through an intermediate solution is usually more accurate. What stock concentration and final volume are you working with?

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