The molarity calculator above links the four quantities that describe a solution made by weighing a solid: the mass of solute, its molar mass, the volume of the finished solution and the resulting concentration in moles per litre. Choose which one you want back, fill in the rest, and the calculation runs as you type. Volumes can be entered in microlitres, millilitres or litres, because bench work rarely arrives in the unit the formula wants.
Arb Digital publishes free calculators aimed at the step people actually get stuck on. With molarity that step is almost never the division; it is remembering that the volume in the formula is the volume of solution, not the volume of solvent, and that a mass means nothing until it has been divided by a molar mass. This page keeps both of those visible rather than burying them.
What This Molarity Calculator Does
In its default mode it takes a mass, a molar mass and a volume and returns the molarity. Switch the selector and it rearranges: give it a target molarity and a volume and it tells you the mass to weigh, or give it a mass and a molarity and it tells you the volume to make up to. A fourth mode solves for molar mass, which is useful when you know the concentration of a prepared standard and want to check what the solute must have been.
Whatever mode you pick, the grid always shows all four supporting numbers: moles of solute, mass in grams, volume in litres and the mass concentration in grams per litre. That last one is included deliberately, because a great many product labels and biological recipes are written in g/L or mg/mL rather than in molarity, and converting between the two is the most common reason people arrive at a page like this.
One boundary worth stating: the live concentration converter changes the units of a concentration you already have, such as moving between mol/L and mg/mL. This page derives the concentration in the first place, from a mass on a balance. They are different jobs and it is worth using the right one.
How to Use It
- Pick what you want to solve for. The inputs adjust so you are never asked for the value you are trying to find.
- Get the molar mass right. Use the formula of the exact solid you have, including any water of crystallisation, and take it from the molar mass calculator if you are unsure.
- Enter the final solution volume and choose its unit. Microlitres are there for small-scale work where converting by hand invites a factor-of-a-thousand slip.
- Read the mass to weigh out from the grid, which is the number you will take to the balance.
- Check the mass concentration if your protocol is written in g/L or mg/mL, so you can confirm the two descriptions agree.
The Formula and How It Is Calculated
Molarity is moles of solute per litre of solution: M = n / V. Because moles come from mass and molar mass as n = m / Mr, the combined form is M = m / (Mr × V) with m in grams, Mr in grams per mole and V in litres. Rearranged for the mass you need to weigh, that is m = M × Mr × V.
Working the default example: 5.844 g of sodium chloride divided by 58.44 g/mol is 0.1 mol, and 0.1 mol in 100 mL, which is 0.1 L, gives 1.0 mol/L. Change the volume to 1 L and the same mass gives 0.1 mol/L. Going the other way, 250 mL of 0.5 mol/L sodium chloride needs 0.5 × 58.44 × 0.25 = 7.31 g. The molar masses behind these figures are built from the standard atomic weights published by the IUPAC Commission on Isotopic Abundances and Atomic Weights, the same conventional values mirrored in the NIST atomic weights and isotopic compositions database.
Volume of Solution, Not Volume of Solvent
This is the single most common conceptual error in preparing a solution, and it hides well because it usually produces a small mistake rather than an obvious one. Molarity is defined per litre of finished solution. Dissolved solute occupies space, so adding a solid to one litre of water gives a solution of more than one litre, and the concentration ends up below the intended value.
For a dilute solution the effect is negligible. For a concentrated one it is not. A saturated sodium chloride solution is roughly 26 percent by mass, and the volume change on dissolving is large enough that ignoring it shifts the concentration by several percent. This is why volumetric flasks exist: you dissolve the solid in a part-full flask, then make up to the calibrated mark, so the final volume is fixed regardless of what the solute did to it.
The related trap is that a solution prepared by volume changes concentration with temperature, because the liquid expands while the amount of solute stays put. A solution made up at 20 degrees and used at 40 is measurably weaker. Where that matters, molality — moles per kilogram of solvent — is used instead, precisely because mass does not change with temperature.
Molarity, Molality, Normality and Percent
Four concentration units appear in ordinary work and they are not interchangeable. Molarity is moles per litre of solution and is the default in most of chemistry. Molality is moles per kilogram of solvent, used for colligative properties and for anything measured across a temperature range. Percent by mass is grams of solute per hundred grams of solution, common on reagent bottles and in industry.
Normality is the one that causes real trouble. It is the number of equivalents per litre, where an equivalent depends on the reaction rather than on the substance. Sulfuric acid at 1 mol/L is 2 normal in an acid-base reaction because each molecule can donate two protons, but the same bottle would be described differently in a reaction where only one proton transfers. A concentration that changes depending on what you are doing with it is a concentration that should be written down carefully. If a protocol says normality, convert it to molarity and record the conversion factor you used.
The other frequent conversion is between molarity and mass concentration. The grid on this page prints grams per litre alongside molarity for exactly that reason. Milligrams per millilitre is numerically identical to grams per litre, which surprises people often enough to be worth saying outright.
Hydrates, Purity and Why the Label Matters
The molar mass you enter has to be the molar mass of the solid in the bottle, not of the idealised compound. Copper sulfate is a standard example: the anhydrous salt is 159.6 g/mol, while the pentahydrate sold in most stockrooms is 249.7 g/mol. Weighing out the pentahydrate but calculating with the anhydrous figure gives a solution about 36 percent weaker than intended, with nothing on screen to reveal the error.
Stated purity is the second adjustment. A reagent quoted as 98 percent pure needs its weighed mass divided by 0.98 to deliver the intended amount of the actual compound. Some hygroscopic solids also pick up water from the air between the bottle and the balance, which is why standards are dried before use and why a solution intended as a primary standard is made from a compound chosen for being stable rather than convenient.
None of this changes the arithmetic on this page. It changes the two numbers you feed it, which is where accuracy is usually won or lost. When you are checking a prepared solution against its nominal value, the percent error calculator is the natural next step.
Where Molarity Sits in a Longer Calculation
Molarity is rarely the end of a problem. It is the input to a dilution, where the solution dilution calculator takes a stock concentration and gives the volumes for a working solution. It is the input to a titration, where the titration calculator uses it with a delivered volume to find an unknown. It is what the pH calculator needs before it can say anything about acidity, and it is half of what the Henderson-Hasselbalch calculator needs for a buffer.
Going backwards, it depends on a molar mass, which depends on a correct formula. If you are deriving a formula from measured composition, an empirical formula calculator is where that chain begins. And for straightforward mass-to-amount conversions with no solution involved, the moles to grams calculator is the shorter route.
Arb Digital publishes hundreds of free calculators across chemistry, maths, finance and marketing — no sign-up, no limits. If something you need is missing, tell us and we will look at building it.
Browse All Free Tools Suggest a ToolCommon Mistakes to Avoid
- Adding solvent to a fixed volume instead of making up to a mark — molarity is per litre of solution, and dissolved solute takes up space.
- Using the anhydrous molar mass for a hydrated salt — the pentahydrate of copper sulfate is 90 g/mol heavier than the anhydrous form.
- Leaving the volume in millilitres — the formula needs litres, so 100 mL entered as 100 gives an answer a thousand times too small.
- Treating normality as molarity — a 1 mol/L sulfuric acid solution is 2 normal for acid-base purposes, and the factor is not always two.
- Ignoring stated purity — a solid quoted at 98 percent delivers 98 percent of the moles your weighing implies.
Related Free Tools From Arb Digital
Start with the molar mass calculator to turn a formula into g/mol, then use the moles to grams calculator for straight mass-to-amount work. The solution dilution calculator makes a working solution from a stock, the titration calculator finds an unknown concentration, and the concentration converter changes the units of a value you already have. The full free online tools hub lists everything else.
Frequently Asked Questions
Molarity is the amount of solute in moles divided by the volume of the finished solution in litres, written mol/L or M. It is the most common way to express concentration in chemistry because it links directly to reaction stoichiometry.
Multiply the target molarity by the molar mass and by the volume in litres. For 250 mL of 0.5 mol/L sodium chloride at 58.44 g/mol, that is 0.5 times 58.44 times 0.25, which is 7.31 g.
The solution. You dissolve the solid in part of the solvent, then make up to the final volume. Adding solute to a full litre of water produces slightly more than a litre of solution and therefore a slightly weaker concentration than intended.
Molarity is moles per litre of solution and changes with temperature because liquids expand. Molality is moles per kilogram of solvent and does not, which is why it is preferred for colligative property work and for measurements across a temperature range.
Multiply the molarity by the molar mass. A 0.1 mol/L sodium chloride solution at 58.44 g/mol is 5.844 g/L. Milligrams per millilitre is numerically the same as grams per litre.
Yes. Use the molar mass of the solid you actually have. Copper sulfate pentahydrate is 249.7 g/mol against 159.6 g/mol for the anhydrous form, so using the wrong one makes the solution far weaker than planned.
Normality counts equivalents per litre rather than moles per litre, and an equivalent depends on the reaction. Sulfuric acid at 1 mol/L is 2 normal when both protons are transferred. Convert to molarity and note the factor used.
This calculator is provided for education and general reference. It describes how concentration is computed and is not laboratory, safety or handling guidance; follow the procedures and risk assessments issued by your own institution.
