Science & Engineering
Molarity Calculator - Solution Concentration & Dilution
Calculate solution molarity (moles per liter), dilute solutions using C₁V₁=C₂V₂, and convert between grams, moles, and liters. All offline.
Leave one field blank - it will be calculated from the other two.
Molarity formula
M = n / V where M is molarity (mol/L), n is the number of moles, and V is the volume in litres.
Dilution formula
C₁V₁ = C₂V₂ - the amount of solute is conserved during dilution. C₁ and V₁ are the initial concentration and volume; C₂ and V₂ are the final concentration and volume.
Tips
- Convert mL to L by dividing by 1000 before entering volume.
- To convert grams to moles, divide the mass in grams by the molar mass (g/mol) of the substance. Use the Molar Mass Calculator to find molar mass from a formula.
Concentration units comparison
| Unit | Symbol | Definition | Use case |
|---|---|---|---|
| Molarity | M or mol/L | moles of solute per liter of solution | Most common in chemistry labs |
| Molality | m or mol/kg | moles of solute per kilogram of solvent | Colligative properties (boiling point elevation, freezing point depression) |
| Normality | N | equivalents of solute per liter (acid/base or redox) | Titrations; being phased out for modern chemistry |
| Mass percent | % w/w | mass of solute / mass of solution × 100 | Industrial formulations, concentrated acids |
| Parts per million | ppm | mg of solute per liter (for dilute aq. solutions) | Environmental monitoring, trace analysis |
Making a standard solution (step-by-step)
- Calculate the required mass: mass (g) = molarity × volume (L) × molar mass (g/mol).
- Weigh the solute precisely using an analytical balance.
- Dissolve in ~80% of the final volume of solvent (usually distilled water) in a beaker.
- Transfer to a volumetric flask: rinse the beaker 3 times with small amounts of solvent and add to the flask.
- Add solvent to the calibration line: approach slowly with a wash bottle in the last few drops to hit the mark precisely.
Serial dilution
To prepare very dilute solutions, serial dilution is more accurate than a single large dilution. A 1:10 dilution (transfer 1 mL into 9 mL) repeated three times gives a final concentration of 1:1,000 of the original. The formula is:
final concentration = C₁ × (dilution factor)^nWhere n is the number of serial dilution steps. For 1 M -> 1 µM: three 1:100 dilutions (10 µL into 990 µL) gives 10⁻⁶ M.