Free Molarity Calculator with Worked Steps

The molarity formula, and how to rearrange it

Molarity is the amount of solute, in moles, divided by the volume of the solution, in litres: M = n ÷ V. The units are mol/L, which chemists abbreviate to a capital M — a 0.5 M solution contains 0.5 moles of solute in every litre of solution.

Because it is one equation with three quantities, you can solve for any of them as long as you know the other two. The calculator above does the rearranging for you, but you should be able to do it yourself:

• Molarity: M = n ÷ V
• Moles of solute: n = M × V
• Volume of solution: V = n ÷ M
• Mass of solute: find n = M × V first, then multiply by the molar mass (m = n × Mm)

A worked example: 5.85 g of NaCl in 500 mL

This is the example the calculator loads with, so you can follow along. Suppose you dissolve 5.85 g of table salt in enough water to make 500 mL of solution.

First, grams have to become moles, because molarity counts particles, not weight. The molar mass of NaCl is 22.99 (Na) + 35.45 (Cl) = 58.44 g/mol, so n = 5.85 g ÷ 58.44 g/mol = 0.1001 mol.

Second, the volume has to be in litres: 500 mL ÷ 1000 = 0.500 L.

Finally, substitute into the formula: M = 0.1001 mol ÷ 0.500 L = 0.200 mol/L. The answer is a 0.200 M sodium chloride solution. Notice that every step is either a unit conversion or a substitution — there is no hidden magic, and this is exactly what the steps panel in the calculator prints.

Molarity vs molality: the mistake that changes your answer

Molarity (mol/L) and molality (mol/kg) look and sound almost identical, but they divide by different things. Molarity divides by litres of the finished solution. Molality divides by kilograms of the solvent alone — the water you dissolved the solute into, not the mixture you ended up with.

For dilute solutions in water the two numbers come out close, because a litre of dilute aqueous solution weighs about a kilogram. They are still not the same quantity, and for concentrated solutions or solvents other than water they diverge badly. Exam questions exploit this: if a problem gives you the mass of the solvent, it is a molality problem; if it gives you the volume of the solution, it is a molarity problem.

That is why this calculator puts molality on its own tab with its own inputs. The molality tab asks for the mass of the solvent only, in grams or kilograms, and never asks for a volume — so you cannot accidentally compute mol per litre and label it mol per kilogram.

Other mistakes that cost marks

• Forgetting to convert millilitres to litres. Plugging 500 mL straight into M = n ÷ V makes your answer 1000 times too small. The calculator shows this conversion as its own step so you never skip it on paper.
• Using grams where moles belong. The n in the formula is always moles. If you are given a mass, divide by the molar mass first — that is a separate, visible step, not part of the molarity formula itself.
• Using the volume of water added instead of the volume of solution. Molarity is defined per litre of the whole solution. In practice you dissolve the solute and then fill to the mark; the solution volume is what the flask reads, not what you poured in.
• Getting the molar mass wrong. Diatomic elements (Cl₂ is 70.90 g/mol, not 35.45) and hydrated salts (CuSO₄·5H₂O includes the five waters) are the classic traps. This calculator takes the molar mass as an input, so check it against the periodic table before trusting the result.
• Reporting more precision than your data has. If your mass was weighed to three significant figures, an answer quoted to seven figures is wrong even if the arithmetic is right.

How to check your answer

Three quick checks catch almost every error. First, cancel the units: mol ÷ L gives mol/L, so if your written-out fraction does not cancel to the unit you want, a conversion is missing. This is the single fastest way to find a mL/L slip.

Second, do an order-of-magnitude sanity check. Everyday lab solutions run from about 0.001 M to a few molar; concentrated hydrochloric acid is about 12 M and that is near the practical ceiling for aqueous solutions. If your answer says 400 M, a conversion went the wrong way.

Third, substitute back. If you solved for volume and got 0.25 L, multiply it by the molarity you were given and confirm it returns the moles you started with. The steps panel in the calculator is built for exactly this — compare its substitution line against your own working line by line and the first disagreement is where your error lives.