Molarity Calculator

What molarity actually measures

Molarity is a count of how many particles of a dissolved substance sit inside a fixed volume of the finished solution. Chemists count particles in moles, a unit that stands in for a fixed, enormous number of molecules (roughly 6.022×10²³ of them, Avogadro's number) rather than a mass or a volume, because a reaction between two substances depends on how many molecules of each are present, not how many grams. Divide the moles of dissolved substance, the solute, by the volume of the whole solution it ends up sitting in, and the result is molarity, written mol/L or abbreviated to a capital M. A "0.1 M" solution reads as "0.1 molar," meaning 0.1 mole of solute per litre of solution.

The volume that goes on the bottom of that division is the volume of the finished solution, not the volume of solvent poured in to start with. Dissolving a spoonful of solid into water changes the total volume slightly, so a chemist making up "1 litre of 1 M salt solution" adds solid to somewhat less than a litre of water, then tops the whole thing up to exactly 1 litre once the salt has dissolved, usually in a volumetric flask marked with a single calibration line. Measuring the solvent alone and assuming the total comes out the same is a common beginner's mistake, and it is exactly why the definition insists on solution volume throughout.

The formula, and the mass bridge behind it

Molarity itself is one short equation:

Most real questions do not start with moles already counted out; they start with a mass on a set of scales. Getting from a mass to a mole count needs the substance's molar mass, the number of grams that one mole of it weighs, found by adding up the atomic masses of every atom in its formula from the periodic table:

Chaining the two equations together is what this tool's "Molarity" tab does behind the seg above: mass converts to moles via the molar mass, then moles convert to molarity via the volume. Whichever quantity is being solved for, mass, molarity or volume, the other two plus the molar mass are enough to work backwards through the same two steps, which is why the molar mass field never disappears; it is needed in every direction.

This tool works throughout in mol/L, the unit named molar and abbreviated M. The identical idea scales down for small concentrations: a millimolar solution (mM) holds a thousandth of a mole per litre, and a micromolar one (µM) a millionth, both common once concentrations get very dilute, such as in biology and pharmacology.

Molarity versus molality: solution or solvent

Molarity and molality sound alike and get mixed up constantly, but they divide moles by two genuinely different things. Molarity divides by the volume of the whole solution, in litres; molality divides by the mass of the solvent alone, in kilograms, ignoring the solute entirely and ignoring the finished volume altogether. A solution can be, say, 1 molal (1 mol of solute per kilogram of solvent) and a slightly different figure in molar, because the solute itself adds some volume and some mass to the mix that the two definitions handle differently.

The practical difference that matters most is temperature. Volume expands and contracts a little as a liquid warms or cools, so a solution's molarity drifts very slightly with temperature even though nothing has been added or removed. Mass does not change with temperature, so molality stays fixed regardless of how warm the room is. That is why molality, not molarity, is the concentration unit behind precise physical-chemistry work such as freezing-point depression and boiling-point elevation, while molarity remains the everyday unit for making up solutions on the bench, since volumetric glassware measures volume directly.

A worked example: physiological saline

Normal saline, the salt solution used throughout medicine and biology, is quoted as 0.9% w/v sodium chloride, meaning 0.9 grams of salt dissolved in every 100 mL of finished solution, or 9 grams per litre. Sodium chloride's molar mass is 58.44 g/mol, so:

That 0.154 M figure is the default this calculator opens with, and it is worth keeping in mind as a reference point: solutions well below it read as dilute, solutions well above it as concentrated, at least in the everyday sense the results panel uses for its comparison.

Diluting a stock solution: M₁V₁ = M₂V₂

Labs rarely make every working solution from solid powder; it is faster and more accurate to keep one strong stock solution on the shelf and dilute a small measured amount of it down whenever a weaker, working concentration is needed. Diluting adds solvent but never adds or removes any solute, so the number of moles of solute stays exactly the same before and after; only the volume it is spread through changes. Writing "moles before equals moles after" as M×V on each side gives the dilution equation:

Rearranged for whichever term is unknown, the same equation gives four short formulas, one per quantity, which is exactly what the "Dilution" tab's seg switches between. Try the classic lab question: how much of a 10 M stock is needed to make 250 mL of a 0.5 M working solution? V₁ = (M₂×V₂)÷M₁ = (0.5×250)÷10 = 12.5 mL. The instruction that follows reads as a lab step rather than a bare number: take 12.5 mL of the 10 M stock and dilute it to 250 mL in total.

That last phrase, dilute to a total rather than dilute with a fixed amount of solvent, is a deliberate distinction, not a stylistic quirk. "Add 237.5 mL of water" only lands on the right concentration if the 12.5 mL of stock was measured with equal precision and nothing was lost along the way; "dilute to 250 mL total," filled to a calibration mark in a volumetric flask, fixes the final concentration correctly regardless of exactly how much solvent that turned out to need. Working to a target total volume is the more forgiving and more accurate habit, which is why this tool's instruction line is always phrased that way.

Because dilution only ever adds solvent, it can only ever lower a concentration or leave it unchanged, never raise it. Asking this tool for a target concentration higher than the stock, or a final volume smaller than the stock volume being measured out, describes something that cannot physically happen by adding solvent alone; the results panel flags both cases plainly rather than printing a misleading number.

Reading the working, the chart and the table

Every answer on the Molarity tab shows its two-step working in full: mass converted to moles by the molar mass, then moles converted to (or from) molarity by the volume, so a wrong-looking answer can be traced back to whichever line disagrees with expectation. The bar chart sets the resulting molarity against physiological saline's 0.154 M as a familiar landmark, and the table beneath places the same result among a short list of concentrations chemists actually encounter day to day, from a dilute working solution up to concentrated laboratory acids, sorted from weakest to strongest with your own figure spliced into its rightful place.

The Dilution tab's chart instead compares the stock volume actually measured out against the solvent added to reach the final total, a quick visual check that the smaller portion really is the stock and the larger one really is the top-up. Its table lists all four terms of M₁V₁ = M₂V₂ alongside the solvent added and the dilution factor, V₂÷V₁, which doubles as how many times more concentrated the stock is than the working solution.

Stock solutions and working concentrations

Keeping one concentrated stock solution and diluting it as needed, rather than weighing out solid every time, saves time, cuts down on weighing errors for very small target masses, and keeps a single bottle's concentration to check rather than dozens. The trade-off is that a stock has to be strong enough to dilute usefully across the whole range of working concentrations a lab actually needs, and concentrated stocks of hazardous substances, strong acids especially, demand careful handling exactly because they are concentrated. Choosing a stock concentration a few multiples above the highest working concentration ever needed is the usual practical rule of thumb, leaving room to dilute down comfortably rather than needing several different stock strengths on the shelf.

Questions people ask

Reference concentrations in the table above are typical, widely quoted figures for common laboratory solutions; exact values vary with the specific preparation, purity and temperature, so treat them as a guide rather than a certified specification.