Molality Calculator (mol/kg of solvent)

Background.

Dissolve 22.52 g of glucose in 250 g of water and the solution should freeze at about −0.93 °C rather than 0 °C. The prediction comes from ΔT_f = K_f × b, with water's freezing-point constant of 1.86 K·kg/mol, and the b in it is molality: moles of solute per kilogram of solvent. Not per litre of solution, which is molarity, the 'M' on a reagent bottle. The two sound interchangeable and are not.

Molality divides by a mass, and mass does not change with temperature. A litre of solution made up at 20 °C takes up a little more room at 30 °C, so its molarity falls slightly although nothing has been added or taken away; near room temperature water expands by roughly 0.02 to 0.03% per degree. Molality has no volume in it, so the figure you make up at the bench still holds in an ice bath or at the boil. That is why freezing-point depression, boiling-point elevation and the other colligative equations are written in mol/kg, and why their constants are tabulated in K·kg/mol.

Molality also counts only the solvent. Mass percent divides by the whole solution, mole fraction by the total moles of everything present, molarity by the solution's volume. Four denominators give four different numbers for the same flask, and quietly swapping one for another is a classic source of wrong answers in solution chemistry.

Four questions are covered: the molality of a solution you have weighed out, how much solute to weigh for a target molality, how much solvent a fixed amount of solute needs, and what a molarity from a bottle label means in mol/kg. The first three need only masses and the solute's molar mass. The conversion needs one more fact that neither unit carries, the density of the solution. The default is pure water at 25 °C, 0.99705 g/mL, which is close for dilute aqueous solutions and can be several percent off for concentrated ones.

What is molality calculator?

Molality is the amount of a solute divided by the mass of the solvent it is dissolved in: b_B = n_B / m_A, in moles per kilogram (mol/kg). The IUPAC Green Book (section 2.10) and NIST Special Publication 811 (section 8.6.8) define it the same way. Both prefer the symbol b, because the older symbol m collides with m for mass, often in the same equation. NIST goes further and calls the word 'molal' and the unit-like '0.5 m' obsolete, recommending 'a molality of 0.5 mol/kg' instead; it treats 'molarity' and 'M' the same way, preferring 'amount-of-substance concentration' in mol/L. In practice you will still meet both shorthand forms on labels and in textbooks. The denominator is the solvent alone: 0.5 mol/kg of glucose means half a mole dissolved in each kilogram of water, so the finished solution weighs more than a kilogram per kilogram of water used.

How to use this calculator.

1. 01Choose what to work out. 'Molality' takes the grams of solute you weighed, its molar mass and the grams of solvent. 'Solute mass' takes a target molality and the grams of solvent and returns what to put on the balance. 'Solvent mass' takes a target molality and a fixed mass of solute and returns the solvent needed, in kilograms.
2. 02For 'Convert molarity', enter the mol/L figure, the solute's molar mass and the density of the solution itself, not of the pure solvent. Leave the density at the water default only for dilute aqueous solutions.
3. 03Check the molar mass against the exact formula you are weighing, water of crystallisation included. Copper(II) sulfate pentahydrate, CuSO₄·5H₂O, is 249.68 g/mol; the anhydrous salt is about 159.60 g/mol, and confusing the two puts the answer out by more than half.
4. 04Weigh the solvent rather than measuring its volume. At 25 °C, 250 mL of water weighs 249.26 g, so calling it 250 g adds a 0.3% error before any glassware tolerance, which defeats the purpose of a mass-based unit.
5. 05Fields that the chosen question does not use are ignored, so there is no need to clear them. The default molar mass is glucose, 180.156 g/mol; replace it for any other solute.
6. 06Read molality first, then the supporting figures: moles, grams of solute, kilograms of solvent, mass percent and the equivalent molarity at the density entered.

The formula.

Everything starts from b = n / m_A, with the amount of solute n = mass ÷ molar mass and the solvent mass m_A in kilograms. Solving for molality uses it directly. Solving for solute mass rearranges it to mass = b × m_A × M, and solving for solvent mass to m_A = (mass ÷ M) ÷ b.

Converting molarity c to molality needs a fixed amount of solution to reason about. Take exactly one litre. At density ρ in g/mL it weighs 1,000ρ grams. It holds c moles of solute weighing c × M grams, and everything else is solvent: 1,000ρ − cM grams. Dividing the c moles by that mass in kilograms gives b = 1,000c ÷ (1,000ρ − cM). Because the calculation is done per litre, in this mode the moles, grams of solute and kilograms of solvent shown are the amounts in one litre of the solution.

The other direction takes exactly one kilogram of solvent. It holds b moles weighing b × M grams, so the solution weighs 1,000 + bM grams and fills (1,000 + bM) ÷ 1,000ρ litres, which gives c = 1,000bρ ÷ (1,000 + bM). This is the equivalent molarity shown in every mode, and the mass percent comes from the same kilogram: 100bM ÷ (1,000 + bM). The two conversions are exact inverses; their only approximation is whatever density you supply. Since c ÷ b = 1,000ρ ÷ (1,000 + bM), molarity is always numerically below molality times the density, and the two figures approach a ratio of ρ, not equality, as the solution becomes dilute.

Some inputs are refused because the arithmetic stops describing a solution: a molar mass or density of zero or less, no solvent when solving for molality or solute mass, a target of zero when solving for solvent mass (it would need infinite solvent), and a molarity whose solute would outweigh the litre containing it. At the default density, for example, 6 mol/L of glucose would mean 1,080.94 g of glucose in a litre weighing 997.05 g.

A worked example.

Frequently asked questions.

References& sources.

1. [1]IUPAC, 'Quantities, Units and Symbols in Physical Chemistry' (the Green Book), 3rd edition, 2nd printing 2012 (ISBN 978-0-85404-433-7), section 2.10, composition-of-mixtures table, entry 'molality': symbol m or b, definition m_B = n_B/m_A, SI unit mol kg⁻¹, with note 14 explaining the m/b symbol collision and deprecating the '1 m solution' shorthand. Free full-text searchable PDF; retrieved 2026-07-29.
2. [2]NIST Special Publication 811, 2008 edition, 'Guide for the Use of the International System of Units (SI)', section 8.6.8 'Molality of solute B' — quantity symbol b_B (also m_B), SI unit mol/kg, defined as the amount of substance of solute B divided by the mass of the solvent, with the note that the term 'molal' and symbol 'm' are obsolete. Section 8.6.5 deprecates 'molarity' and 'M' in parallel. Independent of the IUPAC source above; retrieved 2026-07-29.
3. [3]NIST Chemistry WebBook, SRD 69 — Thermophysical Properties of Fluid Systems (IAPWS-95 formulation of Wagner & Pruß, 2002). Queried at T = 298.15 K and p = 101.325 kPa on 2026-07-29; returns a liquid-phase density of 997.04764 kg/m³ for water, which is the 0.99705 g/mL default this page uses for the molarity conversion.
4. [4]IUPAC Commission on Isotopic Abundances and Atomic Weights (CIAAW), Standard Atomic Weights 2021 — abridged values used to build the default molar mass: carbon 12.011, hydrogen 1.008, oxygen 15.999, giving M(C6H12O6) = 180.156 g/mol. Retrieved 2026-07-29.
5. [5]NIST Special Publication 811, 2008 edition, section 8.6.1 'Amount of substance', worked example: M(F2) = 37.9968 g/mol and n(F2) = 100 g / (37.9968 g/mol) = 2.63 mol. Used as this page's independent cross-check of the mass-to-moles path; this calculator returns 2.6318006 mol, inside NIST's stated rounding.
6. [6]IUPAC Compendium of Chemical Terminology (the Gold Book), entry 'molality' (M03970). Bibliographic reference only — the Gold Book web interface returns HTTP 403 to automated retrieval, so the identical table in the Green Book PDF above is the citation actually verified for this page. Recorded here for readers who have interactive access.