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How much stock do you need to make a dilution?

Dilution calculator (C1V1 = C2V2)

Tells you how many liters of concentrated stock to take, and how much water or other diluent to add, to reach a target concentration.

When to use itUse it when preparing working buffer from a 10× concentrate, or when setting the stock-to-water ratio for inline dilution (ILD).

Prefilled with an example: making 100 L of 1× buffer from a 10× stock. Change any value and the result updates.

× or mol/L, etc.

Enter 10 for a 10× concentrate. An actual concentration such as mol/L also works, as long as the field below uses the same unit.

× or mol/L, etc.

Same unit as the stock. If you think in ×, working strength is 1.

L

The total volume after dilution. Divide mL by 1,000 to get L.

Stock to take (V1)10 L
Diluent to add90 L
Dilution factor10 ×

Take 10 L of stock and add 90 L of water or other diluent to make 100 L at the target concentration (a 10× dilution).

How to read it

The row that matches your result is marked.

  • Stock no stronger than the targetDilution cannot reach itThe stock is not more concentrated than the target, so diluting it cannot reach the target. Check that C1 and C2 use the same unit (× or actual concentration).
  • Diluting 2 to 10 timesYour resultCommon range for inline dilutionOur related article gives a 10× concentrate as the typical example. The higher the factor, the smaller the storage tanks can be, but the values are what individual companies have published, and there is no fixed standard.
  • Diluting more than 10 timesWatch solubility and viscosityFor high-salt or concentrated buffers, you may not be able to make a stock strong enough for the factor you want, and the tank savings level off. The practical limit is set by solubility and viscosity.
  • In-process measurementsConfirm quality by measured pH and conductivityWith inline dilution, quality is held by measuring pH and conductivity during the run, not by testing a batch afterward. Acceptance values come from each buffer's specification and are not set by this equation.

How it is calculated

The calculation comes from C1 × V1 = C2 × V2 (the amount of solute is the same before and after dilution). The diluent to add is V2 − V1, and the dilution factor is C1 ÷ C2. Use the same unit for C1 and C2 (both in ×, or both as actual concentrations).

C1 × V1 = C2 × V2 → stock volume V1 = C2 × V2 ÷ C1 dilution factor = C1 ÷ C2

Source: The basic dilution equation C1V1 = C2V2, which follows from the amount of solute being the same before and after dilution.

With your numbers

  1. V1 = C2 × V2 ÷ C1 = 1 × 100 ÷ 10 = 10 L
  2. diluent to add = V2 − V1 = 100 − 10 = 90 L
  3. dilution factor DF = C1 ÷ C2 = 10 ÷ 1 = 10×

Limits of this calculation

  • Always enter C1 and C2 in the same unit (both in ×, or both in mol/L). If the units are mixed, the result means nothing.
  • C1V1 = C2V2 assumes ideal mixing, in which volumes simply add. With concentrated or viscous solutions the volume can shift, and so can pH and conductivity, so correct by measurement.
  • The equation gives only the volumes of stock and diluent. It does not guarantee that pH or conductivity will be in specification. Quality is assured by in-process measurement (calibration and response of the pH and conductivity meters, and mixing).
  • Impurities and endotoxin in the water used for dilution (water for injection, for example) or in the stock go straight into the product. Water quality control is assumed.
  • At start-up and right after a changeover, it takes time to reach the target composition, so that liquid has to be diverted to waste. The equation covers only the steady-state composition.
  • C1V1 = C2V2 is a standard equation; the related Japanese article gives neither the equation nor any acceptance factors. Only the typical example of a 10× concentrate comes from that article.

Primary sources

Every calculator gives an estimate for learning, built on published information and primary sources. Real decisions follow the applicable guidance and expert judgment.