Molarity Calculator

Background.

How many grams of salt go into 500 mL of a 0.1 M solution? Most molarity questions are a version of that one, and they all rest on one definition: molarity is moles of solute per litre of finished solution. Multiply a molarity by a volume and you have moles; multiply the moles by the compound's molar mass and you have the mass to weigh out. For sodium chloride that is 0.1 × 0.5 = 0.05 mol, then 0.05 × 58.44 = 2.922 g.

You can work in five directions. Choose what you want — molarity, moles, volume, the mass of solute, or the final volume of a dilution — and fill in the fields that choice needs; the others are ignored. Concentrations go in as mol/L, amounts as moles, volumes as litres, so 250 mL is entered as 0.25.

There is no box for a mass you have already weighed. If you dissolved 5.00 g of NaCl and want to know the molarity, convert the mass to moles first (5.00 ÷ 58.44 = 0.0856 mol) and solve for molarity from that and the volume.

Chemists count in moles rather than grams because reactions happen between particles. Equal volumes of 0.1 M hydrochloric acid and 0.1 M sodium hydroxide neutralise each other exactly, even though a mole of HCl weighs 36.46 g and a mole of NaOH about 40.00 g. Express both as grams per litre and that one-to-one match disappears from view.

Measuring per litre has a cost: a litre of liquid is not a fixed amount of anything. Water expands by a little over 0.02% for each degree of warming near room temperature, so a solution made up at 20 °C is very slightly weaker at 30 °C with not a single particle lost. For routine bench work that drift is too small to matter. Where it does, chemists use molality, moles per kilogram of solvent, which does not change with temperature.

What is molarity calculator?

Molarity is the amount of a dissolved substance in moles divided by the volume of the whole solution in litres. Its unit is mol/L, written M on labels and in methods, so 0.1 M is read as 'a tenth molar'; IUPAC's formal name for the quantity is amount-of-substance concentration, symbol c. A mole is exactly 6.02214076 × 10²³ particles, fixed by the 2019 redefinition of the SI. The volume is that of the finished solution, not of the water you started with: a 1 M sodium chloride solution is 58.44 g of salt made up to one litre in total, which takes slightly less than a litre of water. For a sense of scale, concentrated hydrochloric acid as sold is about 12 M, sodium in blood plasma sits around 0.14 M, and many biological buffers are used at tens of millimolar. Older titration methods sometimes state normality instead, which counts reacting equivalents rather than molecules: 1 M sulfuric acid is 2 N as an acid, because each molecule can give up two hydrogen ions.

How to use this calculator.

1. 01Choose what to solve for. Molarity uses Moles and Volume; Moles uses Molarity and Volume; Volume uses Moles and Molarity; Mass uses Molarity, Volume and Molar mass; Dilution volume uses the three dilution fields (C1, V1 and C2). Fields a mode does not use can be left as they are.
2. 02Convert to base units before typing: millilitres to litres by dividing by 1,000 (500 mL is 0.5), millimoles to moles the same way, and millimolar to mol/L likewise (25 mM is 0.025).
3. 03For Molar mass, use the figure for exactly what is in the jar, including any water of crystallisation — the label or a periodic-table sum will give it. The default, 58.44 g/mol, is sodium chloride; change it for anything else, because the mass shown in every mode except dilution is calculated from this field.
4. 04For a dilution, enter the stock concentration as C1, the volume of stock you will measure out as V1, and the concentration you want as C2. C2 cannot be higher than C1. The answer is the total volume to make the solution up to, not the amount of water to add.
5. 05If you start from a weighed mass, divide it by the molar mass to get moles, then solve for molarity with that number and the final volume.

The formula.

Everything follows from the definition M = n ÷ V, where M is the molarity in mol/L, n the amount of solute in moles and V the volume of solution in litres. Solving for moles rearranges it to n = M × V; solving for volume gives V = n ÷ M. The mass of solute links moles to grams through the molar mass: mass = n × molar mass, so in mass mode the full chain is mass = M × V × molar mass. In the molarity, moles and volume modes the mass shown alongside uses the same step with whatever molar mass is in the field.

The dilution law comes from one observation: adding solvent changes the volume but not the number of solute particles. Measure out V₁ litres of stock at concentration C₁ and you have C₁ × V₁ moles. Make that up to a total volume V₂ and the moles are unchanged, now spread through more liquid, so C₂ × V₂ = C₁ × V₁, which rearranges to V₂ = C₁ × V₁ ÷ C₂. The water to add is roughly V₂ − V₁.

That 'roughly' is the main physical caveat. The equations treat volumes as exact, but liquid volumes do not always add: mixing concentrated acids, or ethanol, with water gives a little less than the sum of the parts. That is why the reliable method is to bring the solution up to a mark on a volumetric flask rather than measuring the water separately.

A few inputs have no physical answer and are refused: a volume of zero when solving for molarity, a molarity of zero when solving for volume, a molar mass of zero or less in mass mode, and in a dilution a stock volume or target concentration of zero, or a target stronger than the stock. A target equal to the stock is accepted and returns V₂ = V₁, no dilution at all.

A worked example.

Frequently asked questions.

References& sources.

1. [1]IUPAC Gold Book, 'amount-of-substance concentration, c' — the formal IUPAC definition of molarity, c = n / V, including the modern recommendation to use 'c' rather than 'M' as the quantity symbol and the explicit note that 'molar concentration' and 'molarity' are accepted synonyms. International Union of Pure and Applied Chemistry.
2. [2]Atkins, P. W. & de Paula, J. (2014). Atkins' Physical Chemistry, 10th ed. Oxford University Press. Chapter 1A 'The properties of gases' and Foundations section on amount of substance, molar quantities, and the distinction between molarity and molality including the temperature-dependence argument.
3. [3]NIST 'Definition of the Mole' (2019 SI redefinition) — the mole is defined as exactly 6.02214076 × 10²³ elementary entities; Avogadro's number is now an exact, fixed integer rather than an experimentally measured constant. National Institute of Standards and Technology, Physical Measurement Laboratory.
4. [4]Skoog, D. A., West, D. M., Holler, F. J. & Crouch, S. R. (2014). Fundamentals of Analytical Chemistry, 9th ed., Cengage. Chapter 4 on concentration units, the molarity-versus-molality discussion, and the standard protocols for preparing solutions by mass and by dilution from stock.
5. [5]NIST Chemistry WebBook — searchable database of molar masses, thermochemistry, and spectroscopy for over 100,000 compounds; the canonical primary source for molar-mass values entered into molarity calculations. National Institute of Standards and Technology.
6. [6]Lide, D. R. (ed.) (2005). CRC Handbook of Chemistry and Physics, 86th ed., CRC Press. Section 8 'Analytical Chemistry' on solubility tables, density of aqueous solutions versus concentration, and conversion factors between molarity, molality, mass percent, and ppm.