Dilution Calculator: C1 V1 = C2 V2

The dilution equation for solutions.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose which quantity you want to find.

Enter the other values in the units shown.

The calculator gives the answer with the formula, the substituted numbers, and the answer in other units.

Formulas used

  • C_1V_1 = C_2V_2
  • C_2 = \frac{C_1V_1}{V_2}
  • V_1 = \frac{C_2V_2}{C_1}

Worked example

With the default numbers in the calculator above:

  1. The formula, arranged to find the final concentration: final concentration = (starting concentration x volume of the stock solution) / (final volume)
  2. Put the values in (every value in its SI unit): final concentration = (2 x 25) / (250)
  3. The answer: final concentration: 0.2 mol/L
  4. The same answer in other units: 200 mmol/L

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

What is the dilution formula?

C1 times V1 equals C2 times V2: the moles of solute before and after are the same.

How do I dilute a stock solution?

Take the volume V1 of stock, then add water until the total volume is V2.

Do the units matter?

Use the same unit for both volumes, and the same unit for both concentrations.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any chemistry text (dilutions).

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