Molarity calculator with working

A molarity calculator finds the concentration of a solution in moles of solute per litre of solution. Molarity is moles divided by litres, written M or mol/L, and mol/dm³ in the UK. Type the moles or the mass of solute and the volume, and the calculator gives the molarity, or works backwards to the mass you need to weigh out.

The calculator has seven modes, so the same tool finds the molarity, the moles in a solution, the volume, or the mass to weigh out, and converts between mol/L and g/L. Each answer comes with the formula, the numbers put in, and the answer in other units.

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Molarity Calculator

Find concentration from mass, moles and volume

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How to use the molarity calculator

1. Pick a group: Concentration for the main jobs, or Units to convert between mol/dm³ and g/dm³.
2. Pick the mode for what you want to find. The table below shows what each one needs.
3. Choose your units. Volume can be in mL, L, cm³, dm³ or m³, concentration in mol/L or mol/dm³ (and smaller units), and mass in mg, g or kg. The working converts them for you.
4. Type the values you know. The answer appears with the formula, the substitution and the same answer in other units.

From mass also shows the moles and the mass concentration in g/dm³. Most modes draw a graph of concentration against volume for the same amount of solute, which shows why adding water lowers the molarity. You need the molar mass of your solute for the mass modes: the Molar Mass Calculator works it out from a formula. For practice, Practice and help sets random questions with hints and worked solutions.

The molarity formula

Molarity, also called molar concentration or amount concentration, is the number of moles of solute in each litre of solution:

Here c is the molarity in mol/L, n is the amount of solute in moles, and V is the volume of the whole solution in litres. A 1 M solution has 1 mole of solute in every litre. Since 1 L is the same as 1 dm³, 1 mol/L = 1 mol/dm³ = 1 M, so UK and US answers are the same number.

If you start from a mass in grams, turn it into moles first by dividing by the molar mass M. Putting n = m/M into the formula gives:

Volumes in mL or cm³ must be divided by 1,000 to get litres or dm³. Leaving them in mL makes the answer 1,000 times too small, which is the most common mistake with molarity.

Worked examples you can check in the calculator

Example 1: molarity from grams

2.922 g of sodium chloride, NaCl (molar mass 58.44 g/mol), is dissolved and made up to 100 mL of solution. Find the molarity.

The solution is 0.500 M. In From mass, type 2.922 g, 58.44 g/mol and 100 mL. The calculator also shows the moles, 0.05 mol, and the mass concentration, 29.22 g/dm³.

Example 2: the mass to weigh out

How much glucose, C₆H₁₂O₆ (molar mass 180.16 g/mol), do you need for 250 mL of a 0.150 M solution?

Weigh out 6.76 g to 3 significant figures. This is the Mass needed mode, the one lab staff use most when making up solutions.

Example 3: moles in a sample

How many moles of sodium hydroxide are in 25.0 cm³ of 0.200 mol/dm³ NaOH?

There are 0.00500 mol. Calculations like this are the first step of a titration. In Moles, set the volume unit to cm³ and type 25 directly.

Example 4: the volume that holds a given amount

What volume of 2.0 M hydrochloric acid contains 0.50 mol of HCl?

You need 0.25 L, which is 250 mL. The Volume mode gives the answer with conversions to other volume units, so you can read it in mL as well.

Example 5: mg/mL to molarity

A glucose solution is 10 mg/mL. What is its molarity? A milligram per millilitre is the same as a gram per litre, so this is 10 g/L:

That is 0.0555 M, or 55.5 mM. Use To mol/dm³ with a mass concentration of 10 g/dm³.

Now check you can do one without the calculator:

Molarity units: M, mol/L, mol/dm³ and mM

For volumes, 1 L = 1 dm³ = 1,000 mL = 1,000 cm³. For mass concentration, 1 mg/mL = 1 g/L, so the number stays the same when you switch between them.

Molarity, molality and other ways to give concentration

Molarity is not the only measure of concentration. These are easy to mix up:

Molality uses the mass of the solvent, not the volume of the solution, so it does not change with temperature. It is used for colligative properties such as freezing point depression. For dilute solutions in water, the molarity and molality are close, but they are not the same thing.

Diluting a solution: c₁V₁ = c₂V₂

Adding water does not change the moles of solute, only the volume. So the concentration and volume before and after are linked by c₁V₁ = c₂V₂. To dilute 50 mL of 2.0 M acid down to 0.50 M, the final volume is 2.0 × 50 ÷ 0.50 = 200 mL, so you add 150 mL of water. The Dilution Calculator does this, and plans serial dilutions too.

Common mistakes

• Leaving the volume in mL. Divide by 1,000 first, or pick mL as the unit in the calculator and let it convert.
• Using the volume of water added. Molarity uses the volume of the final solution. Dissolve the solute in less water, then make it up to the final volume.
• Using the wrong molar mass. A hydrate weighs more per mole. Copper sulfate, CuSO₄, is 159.60 g/mol, but the blue crystals, CuSO₄·5H₂O, are 249.68 g/mol.
• Confusing M and M. M on its own after a number means molarity (mol/L). M as a letter in a formula means molar mass (g/mol).
• Mixing up mg and g. 5 mg is 0.005 g. Check the mass unit before you divide by the molar mass.
• Rounding too early. Keep the full number of moles, then round the final molarity.

Practise concentration in a short timed paper

Molarity and moles come up in High School Chemistry and AP Chemistry practice, and in GCSE Chemistry Higher in the UK. Each daily paper is a short timed paper of 8 questions worth 25 to 35 marks, and the papers mix topics, so concentration will not come up in every one.

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Chemistry · Moles and quantitiesConcentration calculator: molarity, mass and volumeFind the concentration of a solution in mol/dm³ (mol/L) or g/dm³, the moles or mass in it, or the mass to weigh out, with worked examples.