Molarity Calculator

The calculator above holds four quantities: mass, molecular weight, volume and concentration. Fill in any three and it works out the fourth, then shows the molarity, the mass concentration and the number of moles together, with the arithmetic underneath.

What molarity is

Molarity, also called molar concentration, is the amount of a substance dissolved per unit volume of solution. It is measured in moles per litre, written mol/L and almost always shortened to M, so a 2 M solution holds two moles of solute in every litre.

M = n ÷ V

where M is the molarity in mol/L, n is the moles of solute, and V is the volume of the solution in litres.

Working from a mass instead of moles

In practice you rarely know the moles. You have a balance and a bottle of powder, so what you actually know is a mass. Divide that mass by the molecular weight to get moles, and the formula becomes:

M = m ÷ (MW × V)

with m the mass in grams, MW the molecular weight in g/mol, and V the volume in litres. That is the equation printed above the calculator, and it is why the tool asks for a molecular weight at all.

The second of those is the one people need most often. You almost never want to know the molarity of something already made; you want to know how much to weigh out to make what you need.

Volume of solution, not volume of solvent

The V in the formula is the final volume of the finished solution, which is not the same as the volume of solvent you started with. Dissolving a solid adds to the volume, and for concentrated solutions the increase is large enough to matter.

That is what a volumetric flask is for. Add the weighed solid, add some solvent, swirl until it has dissolved completely, then top up to the graduation mark and mix. Measuring out a litre of water and tipping the solid into it gives you slightly more than a litre of solution, and therefore slightly less than the molarity you wanted.

Diluting a stock solution

Most lab work starts from a concentrated stock rather than from powder. The relationship for diluting is:

C₁V₁ = C₂V₂

The moles do not change when you add solvent, so concentration times volume before equals concentration times volume after. To make 250 mL of 0.1 M from a 2 M stock: V₁ = (0.1 × 250) ÷ 2 = 12.5 mL of stock, made up to 250 mL.

One safety point that is not about arithmetic. When diluting concentrated acid, add the acid to the water, never water to the acid. The heat released can boil the small amount of water on contact and spit acid back at you.

Molarity against molality, and why it matters

Molarity is per litre of solution. Molality is moles per kilogram of solvent, and the difference is not pedantry.

Volume changes with temperature; mass does not. A solution made up to exactly 1.000 L at 20 degrees occupies slightly more at 40 degrees, so the same flask now holds a slightly lower molarity even though nothing was added or removed. Molality is unaffected, which is why it is preferred for work involving temperature changes, such as freezing point depression and boiling point elevation.

For everyday bench work at room temperature the difference is small and molarity wins on convenience, because measuring a volume is faster than weighing a solvent.

Mass concentration, ppm and ppb

The calculator reports mass concentration alongside molarity, and that is simply mass divided by volume, in grams per litre. Notice what is missing from it: the molecular weight. Mass concentration does not care what the substance is, which is why the calculator cannot work backwards from a mass concentration to a molecular weight, and says so rather than returning a wrong answer.

Parts per million and parts per billion are treated here as mg/L and µg/L. That equivalence relies on the solution having the density of water, one kilogram per litre, which is close enough for dilute aqueous solutions and is where those units are normally used. For a solvent of a different density, or a concentrated solution, convert deliberately rather than assuming.

Getting the molecular weight right

The molecular weight is the one input the calculator cannot check for you, and it is where most wrong answers begin. Add up the standard atomic weights of every atom in the formula: NaCl is 22.99 plus 35.45, which is 58.44 g/mol.

Two traps. Hydrates carry water in the formula, and it counts: copper sulfate pentahydrate, CuSO₄·5H₂O, is about 249.7 g/mol against 159.6 for the anhydrous salt, so using the wrong one puts you out by more than a third. And a reagent that is not 100% pure needs the stated assay applied, since 95% purity means 5% of what you weighed was never the compound at all.

Disambiguation of terminology

Several of these words are used loosely and interchangeably, and mostly that is fine. Here is what each one strictly means.

Molarity	Moles of solute per litre of solution
Molar concentration	The same thing as molarity
Mole	The SI unit for amount of substance. One mole is 6.02214076 × 1023 particles, the Avogadro number
Solvent	The component present in the largest quantity, usually water
Solute	Whatever is dissolved into the solvent, solid, liquid or gas
Solution	The mixture the two make together
Molar mass	The mass of one mole of a substance, in g/mol
Molecular weight	Strictly the unitless ratio of a molecule's mass to the atomic mass constant. Used interchangeably with molar mass in practice
Molecular mass	The mass of one molecule, usually in daltons, counting the actual nuclides rather than standard atomic weights
Molality	Moles of solute per kilogram of SOLVENT, not the same as molarity

The distinction worth holding on to is molar mass against molecular weight. Molar mass is a mass per mole with units of g/mol. Molecular weight is properly a ratio and therefore unitless, and since the 2019 redefinition of the SI base units the two differ very slightly in numerical value where they used to be identical. In the context of a molarity calculation they can be treated as the same number, which is why this page asks for a molecular weight in g/mol and does the sensible thing with it.

Reading your result

Check which quantity was solved for before anything else, since it tells you which three inputs the answer rests on. A molarity that looks wrong is nearly always a molecular weight problem or a volume entered in the wrong unit rather than an arithmetic one.

The long decimals are there so you can chain a result into another calculation without losing precision. They are not a claim about your solution: a balance reading to two decimal places and a flask accurate to half a percent do not support fourteen significant figures, so round to what your glassware justifies when you write it down.

To work out the molecular weight from a chemical formula, use the Molecular Weight Calculator, and for converting a volume between litres, millilitres and US units, the Volume Calculator covers the shapes and the Conversion Calculator the plain unit change.