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Dilution, Molarity and Normality Calculator

Solve C₁V₁ = C₂V₂, calculate molarity or normality, and convert common liquid concentration units.

Dilution, molarity, normality and concentration

Dilution equation

Use the same concentration unit for C₁ and C₂, and the same volume unit for V₁ and V₂.

Molarity from mass

Normality from molarity

Choose the factor for the stated reaction or equivalence definition; the calculator does not assume one.

Concentration unit conversion

In short: Solve one unknown in a dilution equation, calculate molarity from mass and final volume, calculate reaction-specific normality, or convert among % w/v, mg/mL and liquid ppm.

Formulas

Dilution

C₁ × V₁ = C₂ × V₂

Enter consistent units for the two concentrations and consistent units for the two volumes. The calculator solves for exactly one selected unknown. The WHO Maintenance Manual for Laboratory Equipment, 2nd edition (2008), chapter 9, gives the corresponding rearrangement for stock volume: V₁ = V₂ × C₂ / C₁.

Molarity and normality

M = mass (g) ÷ [molar mass (g/mol) × final solution volume (L)]
N = M × n-factor

Molarity is moles of solute per litre of final solution. Normality depends on equivalents per litre for a specified reaction; enter the applicable reaction-specific n-factor. The WHO Maintenance Manual for Laboratory Equipment, 2nd edition (2008), chapter 9, describes molarity, normality and equivalent weight. USP General Chapter <1160>, Pharmaceutical Calculations in Pharmacy Practice (2022), covers calculation principles used in pharmacy practice.

The molarity calculation assumes the entered mass is the amount of the stated solute. It does not adjust for assay, purity, water content or a hydrate unless those are accounted for before entering the mass or molar mass.

Concentration conversions

% w/v = grams of solute per 100 mL of final solution
mg/mL = (% w/v) × 10
liquid ppm = mg/L
ppm = (mg/mL) × 1000

For the ppm option, this tool uses the WHO INTOX Poisons Centre Training Manual, WHO/FWC/PHE/EPE/13.01 (2013), chapter 2.4, which expresses liquid ppm as mg/L. Mass-fraction ppm (mg/kg) is a different basis and is not calculated by this converter.

Assumptions and defaults

  • No numeric value is prefilled. Select the one unknown in the dilution form and enter the other three values.
  • C₁ and C₂ must use the same concentration unit; V₁ and V₂ must use the same volume unit.
  • Enter a molar mass for the particular chemical form being used. The calculator does not infer a chemical formula or reaction stoichiometry.
  • Enter the n-factor for the particular reaction when calculating normality; no universal factor is assumed.
  • Concentration input values must be non-negative. The converter uses % w/v, mg/mL and the liquid ppm convention mg/L described above.

Worked examples

  • Diluting a 10 mg/mL stock to 1 mg/mL at a final volume of 100 mL gives V₁ = 10 mL.
  • Using molar mass 40.00 g/mol for NaOH, 4 g in a final volume of 1 L gives 0.100 mol/L. USP-NF’s Sodium Hydroxide monograph (2017) identifies NaOH and its formula mass as 40.00; this arithmetic example assumes the weighed amount is pure NaOH and is not assay-corrected.
  • 1% w/v = 10 mg/mL = 10,000 mg/L = 10,000 ppm on the liquid basis used here.

Limitations

The results are arithmetic conversions. They do not prescribe a method of preparation, account for volume change on mixing, establish solution stability, or replace analytical verification. For normality, a result is meaningful only with the reaction and n-factor that define the equivalent amount.

Results support, not replace, your validated procedure.

References

  • United States Pharmacopeia, USP-NF General Chapter <1160>, Pharmaceutical Calculations in Pharmacy Practice (2022). Official chapter preview and citation.
  • World Health Organization, Maintenance Manual for Laboratory Equipment, 2nd edition (2008), chapter 9 “Dilutor.” Official WHO publication.
  • World Health Organization, INTOX Poisons Centre Training Manual, WHO/FWC/PHE/EPE/13.01 (2013), chapter 2.4 “Units, calculations and conversions.” Official WHO training manual.
  • United States Pharmacopeia, USP-NF monograph Sodium Hydroxide (2017), formula mass NaOH 40.00. Official monograph preview.