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Solution Dilution Calculator

Solve a dilution with C1V1=C2V2.

How it is calculated

Dilution only changes the amount of solvent, not the amount of dissolved substance, so the amount stays the same before and after: C1 × V1 = C2 × V2. The tool rearranges this to V2 = C1 × V1 ÷ C2, where C1 is the starting concentration, V1 the volume of stock solution you take, and C2 the concentration you want. C1 and C2 must use the same unit (M, %, mg/mL, whatever you have). V1 and the answers are in millilitres. It also gives the solvent to add: V2 − V1. C2 must be above zero. Pick a C2 lower than C1 for a real dilution, since a higher C2 gives a negative amount to add. Volumes are assumed to be additive.

Worked example

You have a 10 M stock and want a 2 M solution, using 25 mL of the stock. Final volume: V2 = 10 × 25 ÷ 2 = 250 ÷ 2 = 125.00 mL. Solvent to add: 125 − 25 = 100.00 mL. So you measure 25 mL of stock, then add solvent until the total is 125 mL. The concentration drops by a factor of 5 because the volume grows by a factor of 5.

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Common mistakes

  • Adding the full final volume of solvent. The answer to add is V2 − V1, because the stock already supplies V1.
  • Mixing units for C1 and C2, such as molar for the stock and millimolar for the target.
  • Entering V1 in litres. The tool labels the results in mL, so use mL throughout.
  • Entering a target stronger than the stock. C2 higher than C1 cannot be reached by dilution and gives a negative solvent amount.
  • Not topping up to the final volume. Add solvent to the mark in a volumetric flask rather than adding a measured amount on top, as some liquids do not mix volume-for-volume.

About this calculator

This calculator solves the dilution equation C1V1 = C2V2 (initial concentration × initial volume equals final concentration × final volume) for whichever variable is unknown — most often the final volume or the amount of solvent (water, buffer, etc.) that needs to be added to bring a stock solution down to a target working concentration.

Lab technicians preparing a reagent from a concentrated stock solution, students in a chemistry or biology lab diluting a sample before an experiment, and anyone mixing a concentrate-based cleaning or gardening solution to a specified strength use this same equation, since it holds regardless of the units used as long as concentration and volume units stay consistent on both sides.

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Comments (1)

  • Editorial team

    The solvent figure assumes volumes simply add. For careful lab work, especially with strong stocks such as 10 M solutions or ethanol and water mixes where the total shrinks a little, put the stock in a volumetric flask and top it up to the final-volume mark instead of measuring solvent separately. Which concentration units do you usually work in? Tell us if a molarity or percent helper would suit you.

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