BYTETOOLS

Dilution Calculator

Solve C1V1 = C2V2 for any missing term and see how much solvent to add. Works in molarity, percent, ppm and mg/mL with metric and US volumes.

5
C₁ (M)
10
V₁ (mL)
0.5
C₂ (M)
100
V₂ (mL)

Volume of stock to use, V₁

C₁V₁ = C₂V₂ rearranged as V₁ = C₂ × V₂ ÷ C₁.

  • Measure 10 mL of the 5 M stock and add 90 mL of solvent to reach 100 mL.
  • Dilution factor: 1 : 10
  • Final volume in millilitres: 100 mL

“Solvent to add” assumes volumes are additive. For concentrated acids and other solutions with a large volume change on mixing, dilute to the final volume in a volumetric flask instead of adding a measured volume of solvent. Always add acid to water, never the reverse.

What is the Dilution Calculator?

The dilution equation C₁V₁ = C₂V₂ links a stock solution to a diluted one. To make 100 mL of 0.5 M from a 5 M stock you need 0.5 × 100 ÷ 5 = 10 mL of stock topped up with 90 mL of solvent.

  • Solves C₁V₁ = C₂V₂ for any of the four terms
  • Reports the solvent volume to add and the dilution factor
  • Molarity, normality, percent, ppm, mg/mL and g/L
  • Litres, millilitres, microlitres and US gallons
  • Warns when the requested final concentration exceeds the stock
  • 100% local — no data leaves your browser

How to use the Dilution Calculator

  1. 1

    Choose which of C₁, V₁, C₂ or V₂ you want to find.

  2. 2

    Pick the concentration unit and the volume unit.

  3. 3

    Enter the three values you already know.

  4. 4

    Read the missing term plus the solvent volume to add.

  5. 5

    Copy the recipe to keep with your experiment notes.

About the Dilution Calculator

The ByteTools Dilution Calculator rearranges C₁V₁ = C₂V₂ for whichever of the four terms you are missing. Tell it what to solve for, enter the other three values, and it returns the answer together with the volume of solvent to add and the dilution factor, so you can go straight from the screen to the bench.

Because the concentration units cancel on both sides of the equation, the tool works equally well in molarity, normality, percent, parts per million, mg/mL or g/L — you just have to use the same unit for the stock and the final solution. Volumes can be litres, millilitres, microlitres or US gallons.

Every calculation runs client-side in your browser. Nothing is transmitted anywhere, so recipes for your own solutions stay on your machine, and the calculator still opens when you are offline in the lab.

Frequently asked questions

How do you use the C1V1 = C2V2 formula?

C₁ and V₁ describe the concentrated stock, C₂ and V₂ the diluted solution you want. Rearrange for the unknown — to find the stock volume, V₁ = C₂V₂ ÷ C₁. The number of moles of solute stays the same on both sides.

How much water do I add to dilute a solution?

Subtract the stock volume from the final volume. Diluting 10 mL of stock up to 100 mL means adding roughly 90 mL of solvent. The calculator does this subtraction for you and shows it as the solvent to add.

What does a 1:10 dilution mean?

It normally means one part stock made up to ten parts total, so the concentration falls by a factor of ten. Some fields use 1:10 to mean one part stock plus ten parts solvent, an eleven-fold dilution, so check the convention in your protocol.

Can I use percent or ppm instead of molarity?

Yes. The units cancel across the equation, so any concentration unit works as long as you use the same one on both sides. Mixing molarity on one side with percent on the other would give a meaningless answer.

Why does my diluted acid not measure the volume I calculated?

Concentrated acids and some other solutions shrink when mixed with water, so volumes are not perfectly additive. Dilute to the final volume in a volumetric flask instead of adding a measured amount of water, and always add acid to water rather than the reverse.

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