Molarity Calculator

Background.

This molarity calculator solves the central concentration equation of solution chemistry — M = n / V — for whichever of molarity, moles, volume, or solute mass you do not know, and also handles the dilution law C1V1 = C2V2 for preparing a working solution from a stock. Pick a 'solve for' mode, type the values you know, and the tool returns the missing quantity in SI units (mol/L for concentration, mol for amount, L for volume, g for mass).

Molarity — formally called amount-of-substance concentration in the IUPAC Gold Book and abbreviated 'M' on reagent bottles — is the workhorse concentration unit of wet-lab chemistry, biochemistry, pharmacy, water-quality engineering, and any field where you need to know how many particles of a species are present per unit volume of solution rather than per unit mass. The reason wet-lab protocols are written in molarity rather than percent-by-mass or grams-per-litre is reaction stoichiometry: chemistry happens between particles, not between grams, so a 0.1 M solution of HCl and a 0.1 M solution of NaOH neutralize one another in equal volumes regardless of the fact that HCl and NaOH have different molar masses.

There is, however, an important caveat baked into the definition that many introductory students miss: because molarity is moles per litre of solution and a litre of solution expands with temperature (water expands roughly 0.02 percent per kelvin near room temperature, more in organic solvents), the molarity of a given prepared solution drifts slightly with temperature even though the amount of solute has not changed. This is why analytical chemistry sometimes prefers molality (moles of solute per kilogram of solvent) for high-precision work and physical-chemistry equations: mass is invariant, volume is not.

Below the widget you will find the formal definition, the derivation of M = n/V from the SI definition of the mole, the dilution-law derivation from particle conservation (C1V1 = C2V2 because the same number of particles is now spread through a larger volume), worked examples for preparing a 0.1 M NaCl saline, a discussion of when to use molarity versus molality versus mass percent, the unit-conversion tricks every wet-bench chemist memorizes (mol/L = mmol/mL = µmol/µL), and the safety footnotes for diluting strong acids and bases. The solver beneath the calculator uses Decimal.js arbitrary-precision arithmetic and is registered at molarity.solve in the Quanta engine; the same code path is exercised by unit tests for every mode including the edge cases (zero volume, zero molarity, final concentration exceeding initial, mismatched solveFor selection).

What is molarity calculator?

Molarity, denoted M and formally called amount-of-substance concentration by IUPAC, is the number of moles of a solute dissolved in one litre of solution: M = n / V. A '1 M' solution — read as 'one molar' — contains one mole of the solute per litre of total solution volume, and a 0.1 M solution contains a tenth of that. The mole itself is the SI base unit for amount of substance and, since the 2019 SI redefinition, is defined as exactly 6.02214076 × 10²³ elementary entities (Avogadro's number is now an exact integer rather than an experimentally measured one). To convert between mass and moles you use the compound's molar mass M_m in g/mol: n = mass / M_m, so mass = M × V × M_m. The molar mass is read off the periodic table by summing atomic masses — for sodium chloride, NaCl, that is 22.99 (Na) + 35.45 (Cl) = 58.44 g/mol, which is the default the calculator uses if you leave the field blank. The key contrast students often confuse is molarity versus molality. Molality (lowercase m, mol/kg) is moles of solute per kilogram of solvent — not per kilogram of solution — and crucially it is temperature-independent because mass does not change when you heat or cool the bottle. Molarity is more convenient in practice (you measure volumes with a volumetric flask, not weigh the solvent on a balance) but it drifts by a fraction of a percent across normal temperature ranges and by several percent across the full liquid range. For most bench work the drift is negligible; for colligative-property calculations, boiling-point elevation, freezing-point depression, and high-precision physical chemistry, switch to molality.

How to use this calculator.

1. 01Pick a mode from the 'Solve for' menu — molarity, moles, volume, mass, or dilution volume. Each mode reads only the inputs it needs and ignores the rest.
2. 02For molarity mode (M = n / V): enter moles and volume in litres. The calculator returns M in mol/L and also reports the equivalent mass using the molar mass field.
3. 03For moles mode (n = M × V): enter molarity and volume. Useful when you have an existing stock and want to know how many moles a given aliquot contains.
4. 04For volume mode (V = n / M): enter moles and target molarity. The calculator returns the solution volume in litres — divide by 0.001 to get millilitres.
5. 05For mass mode (mass = M × V × molar mass): enter molarity, volume, and the molar mass of your compound. This is the everyday 'how much do I weigh out?' calculation. Default molar mass is 58.44 g/mol (NaCl); change it for any other solute.
6. 06For dilution mode (C1V1 = C2V2): enter the stock concentration C1, the volume of stock V1 you plan to take, and the final concentration C2 you want. The calculator returns V2, the total final volume. The water you add is V2 − V1.
7. 07Watch the units. All volumes in the calculator are litres, all masses are grams. Convert mL → L by dividing by 1000 and mg → g by dividing by 1000 before entering values.

The formula.

Three equations underlie every mode of this calculator. They follow directly from the definitions of amount, mass, and concentration.

M = n / V (definition of molarity) n = mass / M_m (mole–mass conversion via molar mass M_m) C1 × V1 = C2 × V2 (dilution law, from particle conservation)

From the first two you can express any one of {M, n, V, mass} in terms of the others — that is what the solveFor modes do under the hood. Setting solveFor = molarity gives M = n / V directly. Setting solveFor = moles gives n = M × V. Setting solveFor = volume gives V = n / M, which the calculator guards against M = 0 (division by zero). Setting solveFor = mass chains the two: mass = (M × V) × M_m, with M_m defaulting to 58.44 g/mol for NaCl when no molar mass is supplied.

The dilution law deserves its own derivation because students often memorize it without understanding it. When you take V1 litres of a stock solution at concentration C1, you have removed n = C1 × V1 moles of solute. If you then add solvent to bring the total volume to V2, you have not added or removed any solute — only diluted what was already there. So the new concentration is C2 = n / V2 = (C1 × V1) / V2, which rearranges to C1 × V1 = C2 × V2. The calculator rejects C2 > C1 (dilution cannot increase concentration) and C2 = 0 (division by zero), but it accepts the limiting case C1 = C2, which corresponds to zero dilution.

One last unit identity worth memorizing because it saves wet-bench time every day: 1 mol/L = 1 mmol/mL = 1 µmol/µL. The same number of significant figures applies whether you scale the volume by 1000× or by 1 000 000×, which is why benchtop pipetting in microlitres pairs naturally with millimolar concentrations.

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.