Molarity Calculator

Type what you are dissolving, fill in what you know, and leave one box blank: that blank is what gets solved. The molar mass comes from your formula using IUPAC atomic weights, so a 250 mL flask of 0.100 M NaCl turns straight into a weighing instruction. Molality, normality and the three kinds of percent solution are all here too, with the differences between them spelled out.

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How this molarity calculator works

Tell it what you are dissolving, fill in what you know, and leave one box blank. That blank is the question. Ask for the mass and you get a weighing instruction; ask for the concentration and you get a concentration; ask for the volume and you get the flask size. The molar mass comes from the formula you type, using the IUPAC standard atomic weights, so you never have to look one up or trust a number you half remember.

The four buttons at the top are four genuinely different quantities, not four ways of saying the same thing, and knowing which one a problem wants is most of the skill. Molarity is moles per litre of finished solution. Molality is moles per kilogram of solvent, and it is the one that survives a temperature change. Normality is molarity multiplied by how many reacting units each formula unit brings, and it is meaningless until you say what reaction you mean. Percent comes in three incompatible flavours that people quote interchangeably and should not.

The formula

n = mass ÷ molar mass
M = n ÷ litres of solution
b = n ÷ kilograms of solvent
N = M × equivalents per mole
M from % w/v = 10 × percent ÷ molar mass
M from % w/w = 10 × percent × density ÷ molar mass

n is moles, M is molarity, b is molality and N is normality. The two words doing the real work are in bold: molarity divides by the volume of the solution you end up with, molality divides by the mass of the solvent you started with. The factor of 10 in the percent lines is just 1000 mL per litre divided by 100 mL per percent, and the density in the w/w line is there because a weight-per-weight percent knows nothing about volume until you tell it what a millilitre weighs.

Worked example

Make 250 mL of 0.100 M sodium chloride. NaCl is 58.44 g/mol. You need 0.100 mol/L × 0.250 L = 0.0250 mol, which is 0.0250 × 58.44 = 1.461 g.

Now the part that turns a right calculation into a wrong bottle. Weigh the 1.461 g, dissolve it in some water, and then add water until the total reaches the 250 mL mark. Do not weigh it out and add 250 mL of water: the salt takes up room too, so you would end up with more than 250 mL of solution and a concentration a little under 0.100 M. Make up to the mark, do not add the mark. That is what the word solution is doing in the definition of molarity.

And a check you can recognise. Physiological saline is labelled 0.9% w/v. Switch to percent mode and it comes out at 0.154 M, or 154 mM, which is exactly the figure on every bag of saline in every hospital. When a calculator reproduces a number the world already agreed on, you can trust the ones it gives you that you cannot check.

Molarity or molality: the one that survives a hot plate

These two get muddled constantly, partly because in dilute water they are nearly the same number and partly because the words are nearly the same word. The difference is one you can feel. Molarity divides by the volume of the solution, and volume changes with temperature. Warm a flask and the liquid expands, so the same moles now occupy more litres and the molarity drops, without a single molecule leaving. Molality divides by the mass of the solvent, and mass does not care how hot it is.

That is not a technicality; it decides which unit a problem has to use. Every colligative property is written in molality: freezing point depression, boiling point elevation, osmotic pressure by way of it. You cannot write freezing point depression in molarity, because the solution is being cooled, which is to say its volume is changing, which is to say the denominator of your concentration is moving while you measure. Any equation that spans a temperature range is written in molality for exactly this reason, and if your work involves a hot plate or a freezer, so should yours.

Enter a solution density above and this page converts between them exactly, which is a step most calculators skip. The logic is simple bookkeeping: one litre of a 1.000 M NaCl solution at 1.0400 g/mL weighs 1040.0 g, of which 58.44 g is salt, so the water is 981.6 g and the molality is 1.000 ÷ 0.9816 = 1.019 mol/kg. Nearly equal, and not equal. In concentrated solutions the two diverge sharply, which is when using the wrong one stops being a rounding error.

Normality, and why IUPAC would rather you did not

Normality is molarity multiplied by the number of reacting units per formula unit, and it exists because titration arithmetic is lovely in it: at the endpoint, normality times volume equals normality times volume, with no stoichiometric coefficients to chase. That convenience is real, which is why water treatment plants and analytical labs still use it.

The problem is that a normality is not a property of a bottle, it is a property of a reaction. Sulfuric acid is 2 N per mole when both protons are in play, and 1 N in a reaction that only takes one. Potassium permanganate is 5 N in acid solution, where manganese goes from +7 to +2, and 3 N in neutral or basic solution, where it stops at +4. Same bottle, same molarity, two different normalities, decided by what you pour it into. IUPAC has discouraged the unit for precisely this reason. This page will happily compute it, and it will keep saying out loud that the equivalents figure is your claim about the chemistry, not a fact about the compound.

Three percents that are not the same percent

A percent solution is ambiguous unless you say which percent. Weight per volume is grams of solute in 100 mL of solution, which is why 0.9% saline is 9 g/L. Weight per weight is grams in 100 g of solution, which needs a density before it can become a molarity. Volume per volume is millilitres in 100 mL, used for liquids like ethanol, and it needs the pure liquid's density for the same reason.

The gap between them is not small. Concentrated sulfuric acid is 98% w/w at a density of 1.84 g/mL. Run that through the conversion and it is 1803 g per litre, which is 18.4 M, and also about 180% w/v. A percent above 100 sounds like an error until you notice that w/v is comparing a mass to a volume and has no reason to stop at 100. Concentrated hydrochloric acid does the same trick more modestly: 37% w/w at 1.19 g/mL is 12.1 M. Both of those are numbers you can check against any reagent bottle, which is the point of showing them.

The practical lesson is that w/v is the one to write on your own labels. It needs no density, it converts to molarity in one step, and it cannot be misread. When you inherit a protocol that says "10% solution" without saying which, the honest move is to ask rather than to assume, because for anything denser or lighter than water the two answers differ by exactly the density.

Sources

Where the numbers on this page come from. We go to the body that publishes the figure, not to another calculator. See how we verify.

Frequently asked questions

How do I calculate molarity?

Divide moles of solute by litres of solution. Moles come from mass divided by molar mass, so the whole chain is molarity equals mass divided by molar mass divided by volume in litres. For 1.461 g of NaCl at 58.44 g/mol in 250 mL, that is 0.0250 mol in 0.250 L, which is 0.100 M. Enter any two of mass, volume and concentration above and the third comes back.

How much do I weigh out to make a solution of a given molarity?

Multiply the molarity by the volume in litres to get moles, then multiply by the molar mass. For 250 mL of 0.100 M NaCl: 0.100 times 0.250 is 0.0250 mol, times 58.44 is 1.461 g. Then dissolve that in less water than you need and top up to the mark, rather than adding the full volume to the solid. Molarity is per litre of finished solution, so adding 250 mL of water to a solid gives you more than 250 mL of solution and a concentration slightly too low.

What is the difference between molarity and molality?

Molarity is moles per litre of solution; molality is moles per kilogram of solvent. The practical difference is temperature: liquid volume expands when warmed, so a solution's molarity falls as it heats up even though nothing has left the flask, while molality cannot change because mass does not expand. That is why freezing point depression, boiling point elevation and every other colligative property is written in molality. In dilute water the two numbers are close, which is why the distinction is so easy to miss and so awkward when it bites.

How do I convert percent solution to molarity?

For a weight-per-volume percent, multiply by 10 to get grams per litre and divide by the molar mass: 0.9% w/v saline is 9 g/L, which at 58.44 g/mol is 0.154 M. For a weight-per-weight percent you also need the density, because w/w knows nothing about volume: 98% w/w sulfuric acid at 1.84 g/mL is 1803 g/L, which is 18.4 M. That is also why the same acid can be described as roughly 180% w/v without anything being wrong.

What is normality and is it the same as molarity?

Normality is molarity multiplied by the number of reacting units each formula unit supplies, so 0.1 M sulfuric acid acting as a diprotic acid is 0.2 N. They are the same number only when that factor is 1. The important caveat is that normality describes a reaction rather than a bottle: permanganate is 5 N in acid solution and 3 N in neutral solution at the same molarity, because the manganese ends up in a different oxidation state. IUPAC discourages the unit for that reason, though titration and water treatment work still uses it.

Why is 0.9% saline 154 mM?

Because 0.9% w/v means 9 grams of sodium chloride per litre, and sodium chloride is 58.44 g/mol, so 9 divided by 58.44 is 0.154 mol/L. It is worth knowing that the osmolarity is roughly double that, near 308 mOsm/L, because NaCl dissociates into two particles in water and osmotic effects count particles rather than formula units. That doubling is why saline is isotonic with blood at a concentration that looks surprisingly low.

Do I add solvent up to the volume or add the full volume?

Up to the volume, always, when you are making a molar solution. The solute takes up space of its own, so weighing out your solid and then adding a full 250 mL of water leaves you with more than 250 mL of solution and a concentration below what you wanted. Dissolve in a smaller amount first, then make up to the mark in a volumetric flask. This is the single most common way a correct calculation still produces a wrong bottle, and it is also why molality, which is defined against the solvent you started with, sidesteps the problem entirely.

How precise is a molarity calculation?

Usually less precise than the digits suggest, and the limit is rarely the arithmetic. Molar masses carry a published uncertainty, volumetric glassware carries a tolerance, and a balance carries its own. A class A 250 mL flask is specified to about plus or minus 0.12 mL, which is 0.05%, so quoting a concentration to five significant figures claims more than the glass can deliver. Match your reported precision to the least certain step, which for most bench work is the volume rather than the mass.

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