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Pharmaceutical Chemistry

Dilution Calculator

Solves C₁V₁ = C₂V₂ for whichever of the four values you need — how much stock to take, the final volume, or the resulting concentration.

Final Volume (V₂)

Enter C₁, V₁ and C₂ to calculate the final volume.

Inputs

Concentration of the stock. Any unit — but the same unit as C₂.

Volume of stock taken. Any unit — but the same unit as V₂.

Concentration you want after diluting. Same unit as C₁.

Try an example

Worked example: a dilute antiseptic rinse from a concentrate

In a pharmaceutics practical you are asked to prepare 250 mL of a 0.05% w/v chlorhexidine gluconate rinse from a 20% w/v concentrate. How much concentrate do you measure, and how much water do you add? (Illustrative values for a bench exercise.)

Stock concentration, C₁
20 % w/v
Target concentration, C₂
0.05 % w/v
Final volume, V₂
250 mL
Calculator mode
Initial Volume (V₁)

  1. Write the equation

    C₁ × V₁ = C₂ × V₂ → V₁ = C₂ × V₂ ÷ C₁

  2. Substitute (same % unit on both sides, volumes in mL)

    V₁ = (0.05 × 250) ÷ 20

  3. Amount of solute that must end up in the flask

    C₂ × V₂ = 0.05 × 250 = 12.5 (%·mL, i.e. 0.125 g of chlorhexidine gluconate)

  4. Volume of concentrate

    V₁ = 12.5 ÷ 20 = 0.6250 mL

  5. Diluent and dilution factor

    Water = V₂ − V₁ = 250 − 0.625 = 249.3750 mL Dilution factor = C₁ ÷ C₂ = 20 ÷ 0.05 = 400 (a 1 in 400 dilution)

Measure 0.625 mL of the 20% concentrate and make up to 250 mL with water (about 249.4 mL of water).

The calculator prints V₁ = 0.6250 and solvent to add = 249.3750. In practice you would not measure the water separately: pipette 0.625 mL into a 250 mL volumetric flask and make up to the mark. A volume as small as 0.625 mL needs a graduated pipette or micropipette, not a measuring cylinder — or make an intermediate 1 in 20 dilution first.

Common mistakes

Mixing units between the two sides — entering C₁ in mg/mL and C₂ in % w/v, or V₁ in µL and V₂ in mL. The equation only balances when C₁ and C₂ share one unit and V₁ and V₂ share another.
Treating V₂ as the volume of water to add. V₂ is the final total volume; the diluent is V₂ − V₁.
Swapping C₁ and C₂. If the 'final' concentration comes out higher than the stock, the inputs are reversed — dilution can only lower a concentration.
Reading a ratio strength as a percentage: 1:1000 is 0.1% w/v, not 1%. Convert ratio strengths to the same unit as the other concentration first.
Using a measuring cylinder for a sub-millilitre V₁. The arithmetic is right but the measurement error can be larger than the volume itself.

Assumptions and limitations

C₁V₁ = C₂V₂ assumes the amount of solute is conserved and that the final volume is made up to the mark. Mixing liquids (for example ethanol and water) can change the total volume, so measure the final volume, not the sum of the parts.
It applies to dilution with a solvent that contains none of the solute. Mixing two solutions of different strengths needs alligation or a mass balance instead.
The result has no more precision than the volumes you can actually measure — round to what your pipette or flask can deliver.

Keep learning

Guide: Dilution and Concentration CalculationsThe concept in full, with practice questions.Serial Dilution CalculatorWhen one step would need a volume too small to pipette, split it into several smaller dilutions.Percentage Solution Calculator (w/v, w/w, v/v)Make the stock in the first place from a weighed solid.mg/mL ↔ Molarity CalculatorPut C₁ and C₂ into the same unit before diluting when one is molar and one is mass-based.

References

  1. Stockton SJ. Stoklosa and Ansel's Pharmaceutical Calculations. 16th ed. Philadelphia: Wolters Kluwer; 2021.
  2. Sinko PJ, editor. Martin's Physical Pharmacy and Pharmaceutical Sciences. 8th ed. Philadelphia: Wolters Kluwer; 2023.

Common questions

Prepared by the PharmaWallah student team. Verify results with your textbook or instructor. Report an error · Editorial policy