Molality Calculator (mol/kg of solvent)

Background.

Molality is the concentration unit that divides by the mass of the solvent instead of the volume of the solution. Written b (or the older m), its definition is b = n_B / m_A, where n_B is the amount of solute in moles and m_A is the mass of solvent in kilograms. That one substitution — solvent mass for solution volume — is the entire reason two similar-sounding units exist, and it is the reason molality turns up in every equation for freezing-point depression, boiling-point elevation and osmotic pressure while molarity turns up on every reagent bottle.

This calculator answers four different questions rather than converting between units. You can hand it the mass you weighed out and the mass of solvent you used and get the molality back. You can give it a target molality and a quantity of solvent and get the grams to put on the balance. You can give it a fixed quantity of solute and a target molality and get the mass of solvent to add. And you can hand it a molarity printed on a bottle and convert it to molality, which requires the density of the solution — a fact the calculator makes you confront rather than hiding behind an assumption.

The practical distinction is worth being blunt about. A litre of solution expands when you warm it. A kilogram of solvent does not. Water near room temperature expands by roughly 0.025 percent per kelvin, so a solution made up carefully at 20 °C and used at 30 °C has drifted in molarity by about a quarter of a percent without a single molecule changing. Over the full liquid range of water the drift is several percent. Molality has no volume term anywhere in its definition, so it cannot drift: the number you calculate at the bench is the number that holds in the freezer and in the autoclave. That invariance is not a nicety. It is what makes molality the correct variable for colligative properties, whose derivations assume the amount of solvent is fixed while the temperature is deliberately being changed.

There is a second, subtler distinction. Molality divides by solvent, not by solution. Mass percent divides by solution. Mole fraction divides by total amount of substance. Parts per million divides by the mass of solution too. Four different denominators, four different numbers for the same bottle — and the single most common error in solution chemistry is silently swapping one denominator for another. The calculator reports mass percent alongside molality precisely so you can see the two diverge as concentration rises.

Converting between molality and molarity is exact algebra, not an approximation, but it needs one piece of information neither unit carries: the density of the solution. Take a basis of one litre. That litre weighs 1000ρ grams and holds c moles of solute weighing c·M grams, so the solvent left over weighs 1000ρ − c·M grams. Divide and you have the molality. The calculator ships with the density of pure water at 25 °C as a default, because that is the only density it can honestly know in advance — and it labels the resulting molarity as a lower bound, because every real solute makes the solution denser than the water it was dissolved in. Enter your own measured density and the conversion becomes exact.

Below the widget you will find the formal IUPAC and NIST definitions, the full derivation of both conversion directions, the hand-computed glucose example that the unit tests are built from, a discussion of why both standards bodies now discourage the words "molal" and "molar" entirely, and the domain edges where the arithmetic stops meaning anything — including the point at which a stated molarity would imply that a litre of solution contains no solvent at all.

What is molality calculator?

Molality, symbol b (also written m in older literature), is defined by IUPAC as the amount of substance of a solute divided by the mass of the solvent: b_B = n_B / m_A, with the SI unit mole per kilogram (mol/kg). The IUPAC Green Book, 3rd edition, gives exactly this definition in its section 2.10 table, and NIST Special Publication 811 gives it independently in section 8.6.8 — the two agree on the equation, the symbol and the unit.

Both documents also warn against the notation you will actually meet in the wild. The Green Book's note 14 points out that the symbol m is used for two different things in the same expression — m_B for the molality of solute B and m_A for the mass of solvent A — and recommends b to avoid the collision. It adds that a solution of molality 1 mol/kg is 'occasionally called a 1 molal solution, denoted 1 m solution; however, the symbol m must not be treated as a symbol for the unit mol kg⁻¹'. NIST SP 811 section 8.6.8 is blunter: 'The term molal and the symbol m should no longer be used because they are obsolete.' The same publication's front-matter checklist deprecates 'molarity' and 'M' in the same breath, in favour of amount-of-substance concentration and mol/L.

So the correct modern way to describe a solution is 'a molality of 0.5 mol/kg', not 'a 0.5 molal solution' and certainly not '0.5 m'. This page uses mol/kg throughout and mentions the older forms only because you will find them on labels and in textbooks.

What makes molality worth the extra weighing step is that it contains no volume. Volume is a function of temperature and pressure; mass is not. Every quantity derived from molality inherits that invariance, which is why the colligative equations — freezing-point depression ΔT_f = i·K_f·b, boiling-point elevation ΔT_b = i·K_b·b — are written in molality and would be wrong if written in molarity, since those equations change the temperature as part of the experiment.

How to use this calculator.

1. 01Choose what you are solving for. The four options ask genuinely different questions, not the same question in different units — read the labels before assuming.
2. 02For 'Molality': enter the grams of solute you weighed, its molar mass in g/mol, and the grams of SOLVENT. The solvent figure is the mass of the water (or ethanol, or whatever) on its own — not the mass of the finished solution and not a volume.
3. 03For 'Solute mass': enter the molality you want, the molar mass, and the grams of solvent you are starting with. The answer is what to put on the balance.
4. 04For 'Solvent mass': enter the molality you want, the grams of solute you have, and the molar mass. Useful when a vial contains a fixed amount and you need to know how much solvent to add.
5. 05For 'Convert molarity to molality': enter the mol/L figure from the bottle, the molar mass, and — this is the important one — the density of that solution. The default density is pure water and will under-report the molality of anything but a very dilute solution.
6. 06Check the molar mass. It is the single most common source of a wrong answer here. Sum the atomic masses of the actual formula, hydrate water included: copper(II) sulfate pentahydrate is 249.68 g/mol, not the 159.61 g/mol of the anhydrous salt.
7. 07Weigh the solvent if you can. Measuring 250 mL of water in a cylinder and calling it 250 g introduces a 0.3 percent error at room temperature and more if the lab is warm — which defeats the entire point of choosing a mass-based unit.
8. 08Read the equivalent-molarity output as a lower bound unless you replaced the density. It is reported so you can compare with a bottle label, not so you can skip measuring.

The formula.

Three equations do all the work, and every mode is one of them rearranged.

b = n_B / m_A definition of molality, m_A in kg n_B = mass_B / M mole–mass conversion b = 1000c / (1000ρ − cM) molarity → molality, exact given ρ c = 1000bρ / (1000 + bM) molality → molarity, exact given ρ

The first two need no comment. The conversions do, because students often memorise them without the derivation and then cannot tell whether they have the fraction the right way up.

Going from molarity to molality, take a basis of exactly one litre of solution. Its mass is 1000ρ grams, since ρ is in g/mL and there are 1000 mL in a litre. That litre holds c moles of solute, whose mass is c·M grams. Everything left is solvent, so the solvent mass is (1000ρ − c·M) grams, which is (1000ρ − c·M)/1000 kilograms. Divide the c moles by that and you get b = 1000c/(1000ρ − c·M).

Going the other way, take a basis of exactly one kilogram of solvent. It holds b moles of solute weighing b·M grams, so the solution weighs (1000 + b·M) grams and occupies (1000 + b·M)/(1000ρ) litres. Divide b by that and you get c = 1000bρ/(1000 + b·M).

The two are exact algebraic inverses of one another — substituting the first into the second returns c identically — and the module asserts that round trip as a test rather than trusting the algebra alone.

One consequence is worth stating because the direction surprises people. The ratio c/b equals 1000ρ/(1000 + bM), which is always less than ρ, and ρ for water at 25 °C is 0.99705 kg/L. So for a dilute aqueous solution molarity is always numerically a little smaller than molality, and as the solution gets more dilute the two converge — not to equality, but to a ratio equal to the solvent density in kg/L. In the worked example below, 0.500 mol/kg corresponds to 0.4573 mol/L, and 0.4573 is indeed below 0.500.

Rounding: every intermediate value is carried at full arbitrary precision using Decimal.js. Nothing is rounded part-way through. Rounding happens once, to ten decimal places, at the moment each output is returned. There are no thresholds or piecewise branches in this formula, so there is no rounding boundary to straddle; the guarded edges are domain edges instead.

Invalid domain: a molar mass of zero or less is rejected, as is a solvent mass of zero when the formula would divide by it, a target molality of zero when solving for solvent mass (which would demand infinite solvent), and a non-positive density. The subtlest rejection is in the conversion mode: if 1000ρ − cM ≤ 0, the stated molarity implies that a litre of solution weighs less than the solute it supposedly contains. That is not a large number — it is a physically impossible one — so the calculator refuses rather than returning a negative or infinite molality.

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; the module 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.