Concentration calculator: molarity from moles, mass and volume

Concentration is how much solute is in a given volume of solution. Molar concentration (molarity) is moles divided by volume: c = n ÷ V, in mol/dm³ in the UK or mol/L (M) in the US, which are the same unit. 0.50 mol dissolved to make 250 mL of solution is 0.50 ÷ 0.250 = 2.0 mol/L. This concentration calculator is our Molarity Calculator: it finds the concentration from moles or from a mass, works backwards to the moles, volume or mass to weigh out, and converts between mol/dm³ and g/dm³.

Try it

Molarity Calculator

Find concentration from mass, moles and volume

Open the calculatorGo to its page

How to use the concentration calculator

1. Open the Molarity Calculator. Under Calculate, choose Concentration or Units.
2. In Concentration, choose what to find: From moles or From mass (the concentration), Moles, Mass needed or Volume. In Units, choose To g/dm³ or To mol/dm³.
3. Type the values you know. Volumes can be in mL, cm³, L, dm³ or m³ and masses in mg, g or kg: pick the unit from each box and the working converts it.
4. Read the answer and the steps. From mass also gives the moles and the mass concentration.
5. The graph shows how the concentration would change if the same amount of solute were in more or less solution.
6. To practise, press Random problem in the Practice section.

You need the molar mass for anything involving a mass, for example 58.44 g/mol for sodium chloride. The molar mass calculator works it out from a formula. Percentage concentrations and ppm aren't included.

Concentration formulas

V must be in dm³ (litres) for an answer in mol/dm³. Convert cm³ or mL by dividing by 1000, or let the calculator convert it. V is the volume of the whole solution, not the volume of water added.

Worked examples you can check in the calculator

Example 1: concentration from moles

0.50 mol of solute is made up to 250 mL of solution. Convert the volume: 250 mL = 0.250 L. Then c = 0.50 ÷ 0.250 = 2.0 mol/L, also written 2.0 M or 2.0 mol/dm³. These are the From moles mode's starting values.

Example 2: concentration from a mass

5.844 g of sodium chloride (M = 58.44 g/mol) is dissolved to make 250 mL of solution. Choose From mass:

The concentration is 0.400 mol/L. The calculator also shows the 0.100 mol of salt and a mass concentration of 5.844 ÷ 0.250 = 23.4 g/dm³.

Example 3: the mass to weigh out

How much sodium chloride do you weigh out to make 250 mL of 0.10 M solution? Choose Mass needed: m = c × V × M = 0.10 × 0.250 × 58.44 = 1.46 g. Dissolve it in less water than you need, then make it up to exactly 250 mL in a volumetric flask.

Example 4: moles from a concentration

A titration uses 25.0 cm³ of 0.200 mol/dm³ sodium hydroxide. How many moles is that? n = c × V = 0.200 × 0.0250 = 0.00500 mol. Choose Moles in the calculator, and enter 25.0 with cm³ as the unit.

Example 5: glucose solution

9.0 g of glucose, C₆H₁₂O₆ (M = 180.16 g/mol), is dissolved to make 500 mL. c = 9.0 ÷ (180.16 × 0.500) = 0.0999 mol/L, which is about 0.10 M. Its mass concentration is 9.0 ÷ 0.500 = 18 g/L.

Example 6: converting mol/dm³ to g/dm³

Multiply by the molar mass to go from mol/dm³ to g/dm³, and divide to go back. 0.50 mol/dm³ sodium chloride is 0.50 × 58.44 = 29.22 g/dm³. Choose Units, then To g/dm³.

Try one

Molarity and dilution

Adding water lowers the concentration but leaves the moles of solute the same. Double the volume and the concentration halves, which is the curve on the calculator's graph. To work out a dilution directly, use C₁V₁ = C₂V₂: the dilution calculator guide covers it.

Common mistakes

• Using cm³ or mL in c = n ÷ V. Convert to dm³ (litres) first, or the answer is 1000 times too small.
• Using the mass instead of moles. Divide the mass by the molar mass first, or use From mass.
• Using the volume of water added. V is the final volume of the solution.
• Mixing up mol/dm³ and g/dm³. Multiply by the molar mass to change mol/dm³ into g/dm³.
• Wrong molar mass. Add up the atoms from the formula carefully, counting everything in brackets.

Read next

Chemistry · Moles and quantitiesMolarity calculator: concentration, moles, mass and volumeFree molarity calculator: find molarity from moles or grams, the mass to weigh out, moles or volume, in mol/L or mol/dm³, with worked examples.