The molality calculator above converts a solute mass and a solvent mass into molality, the concentration unit measured in moles of solute per kilogram of solvent. It also runs the conversion most people actually arrive looking for: turning that molality into the equivalent molarity, which needs the solution density and the solute's molar mass, and cannot be done by dividing by 1,000 and hoping.
Arb Digital publishes free calculators for people who need a specific number without a login or an install. This one exists because molality is the concentration unit that gets skipped in teaching and then turns up unannounced in every colligative property calculation. It looks like molarity, it is spelled almost like molarity, and it has a completely different denominator.
What This Molality Calculator Does
Enter the solute either as a mass with its molar mass, or directly as an amount in moles, then enter the mass of solvent. The headline result is the molality in mol/kg. The grid shows the amount of solute in moles, the molarity that the same solution would have, the mass percent of solute, and the freezing point depression the solution would produce in water.
The density box exists only for the molarity conversion, and the calculator will tell you if you leave it blank. The i value, the van 't Hoff factor, exists only for the freezing point figure: it counts how many particles each formula unit releases in solution, which is 1 for a molecular solute like sugar and roughly 2 for sodium chloride.
The boundary against the adjacent tools is a real one, not a formality. The molarity calculator works in moles per litre of solution and is the right tool when you are making up to a mark in a volumetric flask. The mass percent calculator works in percentages and needs no molar mass at all. This page is the one to use when the denominator has to be solvent mass, which is any time temperature changes or colligative properties are involved.
Molality Is per Kilogram of Solvent, Not per Litre of Solution
This distinction is the whole reason the unit exists, so it deserves more than a footnote. Molarity is moles of solute divided by the volume of the finished solution in litres. Molality is moles of solute divided by the mass of solvent in kilograms. Three things differ: mass against volume, solvent against solution, and kilograms against litres.
The solvent-versus-solution part is the one that trips people. To make a 1 M solution you put the solute in a flask, dissolve it, and add solvent until the total volume reaches the mark — you never measure the solvent. To make a 1 m solution you weigh out exactly one kilogram of solvent and add the solute to it, so the final volume is whatever it turns out to be. The two procedures are different at the bench, not just on paper.
The mass-versus-volume part is what makes molality useful. Volume changes with temperature; mass does not. A 0.100 M solution prepared at 20°C is no longer exactly 0.100 M at 80°C, because the solution has expanded and the same moles now occupy more litres. A 0.100 m solution is still exactly 0.100 m at any temperature, because neither the moles nor the kilograms moved. That single property is why every freezing point and boiling point equation is written in molality, and why physical chemistry uses it in preference to molarity almost everywhere.
The two are close in dilute aqueous solution because a kilogram of water is close to a litre and the solute contributes little volume. As concentration rises they diverge, and always in the same direction for a solution denser than its solvent: the molarity comes out lower than the molality, because the solute mass has been added to the denominator's mass but the volume has grown less than proportionally.
How to Use It
- Enter the solute mass and its molar mass, or skip both and put the amount in moles into the third box.
- Weigh the solvent, not the solution. If you only know the solution mass, subtract the solute mass to get the solvent mass first.
- Choose grams or kilograms for the solvent. The conversion happens internally either way.
- Add the solution density if you want the molarity equivalent. Pure water is 1.00 g/mL; a 1 m salt solution is closer to 1.04.
- Set the i value to the number of particles each unit releases if you want a meaningful freezing point figure.
The Formula and How It Is Calculated
Molality is b = moles of solute ÷ kilograms of solvent. The default example is 5.844 g of sodium chloride, which at 58.44 g/mol is 0.1000 mol, dissolved in 100 g of water, which is 0.1000 kg. That gives b = 0.1000 ÷ 0.1000 = 1.000 mol/kg.
The conversion to molarity comes from taking exactly one kilogram of solvent as a basis. That kilogram holds b moles of solute, which weigh b × M grams, so the solution mass is 1,000 + bM grams and its volume is (1,000 + bM) ÷ ρ millilitres. Dividing the moles by that volume in litres gives c = 1000ρb ÷ (1000 + bM). For the example, c = (1000 × 1.04 × 1.000) ÷ (1000 + 58.44) = 1040 ÷ 1058.44 = 0.9826 mol/L. The mass percent is 5.844 ÷ 105.844 = 5.522%, and the freezing point depression is ΔT = Kf × b × i = 1.86 × 1.000 × 2 = 3.72°C.
The definitions used here follow the OpenStax treatment of other units for solution concentrations and, for the freezing point constant, the chapter on colligative properties, both on Chemistry LibreTexts.
Why Colligative Property Equations Insist on Molality
Freezing point depression, boiling point elevation and vapour pressure lowering all depend on the ratio of solute particles to solvent particles, and on nothing else about the solute. That is what colligative means. A ratio of particle counts is naturally expressed against a fixed amount of solvent, which is precisely what molality provides.
Using molarity would break the equations at the point where they are most needed. The whole exercise involves changing the temperature until something freezes or boils, and molarity drifts as the temperature moves. Writing ΔT = Kfb keeps the concentration fixed while the temperature is the variable, which is the only way the constant Kf can be a constant.
The van 't Hoff factor is where predictions and measurements part company. Sodium chloride should give i = 2 and calcium chloride i = 3, but measured values come in lower — around 1.9 and 2.7 in moderately dilute solution. Oppositely charged ions spend part of their time paired up, so the effective particle count is below the ideal. The gap widens as concentration rises, which is why colligative calculations are reliable in dilute solution and only indicative beyond about 0.1 mol/kg. For the full set of colligative relationships, the colligative properties calculator covers boiling point elevation and osmotic pressure alongside freezing point.
Getting the Solvent Mass Right When You Only Know the Solution
Most real problems hand you the wrong number. A label gives a mass percent, or a procedure gives a solution mass, and the molality formula wants the solvent alone. The fix is subtraction: solvent mass equals solution mass minus solute mass. A 5.522% solution weighing 105.844 g contains 5.844 g of solute and therefore 100.000 g of solvent.
Going from mass percent to molality directly, the relationship is b = (1000 × %) ÷ (M × (100 − %)), where % is the mass percent. The (100 − %) term is the solvent share, and forgetting it is the standard error. At 5% the difference between dividing by 100 and dividing by 95 is about five percent in the answer; at 40% it is two thirds.
Going from molarity to molality needs the density again, rearranged: b = 1000c ÷ (1000ρ − cM). Note the minus sign. Here you are removing the solute's mass from the solution's mass to recover the solvent's mass, which is the mirror image of the forward conversion. If your solution is dense and concentrated, that subtraction can take a large bite, and skipping it is what makes a hand-converted value come out badly wrong.
When the Solvent Is Not Water
Nothing in the definition of molality mentions water, but almost every worked example uses it, and that leaves two habits that break elsewhere. The first is assuming one litre of solvent weighs one kilogram. Benzene is 0.876 g/mL, so a litre of it is 876 g, and using it as a kilogram overstates the molality by 14 percent. The second is reusing water's freezing point constant. Kf is a property of the solvent, not a universal number: water is 1.86°C·kg/mol, benzene is 5.12, and camphor is around 40.
That last figure is why camphor is the classic solvent for determining molar mass by freezing point depression. A huge Kf turns a small amount of solute into a large, easily measured temperature drop. The freezing point figure in this calculator's grid uses water's constant and is labelled as such; for another solvent, substitute its own Kf into ΔT = Kfbi by hand.
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Browse All Free Tools Suggest a ToolCommon Mistakes to Avoid
- Dividing by the solution mass instead of the solvent mass — molality's denominator excludes the solute entirely, which is the single difference that defines the unit.
- Treating molality and molarity as interchangeable — they agree only in dilute water solutions. By 1 mol/kg the gap is already a few percent, and it grows steadily.
- Converting between them without a density — the conversion is impossible without one. Any method that does not use the solution density is not doing the conversion.
- Assuming a litre of solvent is a kilogram — true for water and nothing else. Ethanol is 0.789 g/mL and benzene 0.876.
- Using an ideal van 't Hoff factor at high concentration — ion pairing pushes the effective particle count below the formula value, so measured depressions come out smaller than predicted.
Related Free Tools From Arb Digital
Work in moles per litre with the molarity calculator, or in percentages with the mass percent calculator. Get a molar mass from a formula with the molar mass calculator, convert mass to amount with the moles to grams calculator, and prepare a working solution from a stock with the solution dilution calculator. For the wider set of freezing and boiling relationships, use the colligative properties calculator. The full free online tools hub lists everything else.
Frequently Asked Questions
Molality is the amount of solute in moles divided by the mass of solvent in kilograms, with the unit mol/kg and the symbol b or m. Its denominator is the solvent alone, which is what separates it from molarity.
Molarity divides moles of solute by the volume of the finished solution in litres. Molality divides moles of solute by the mass of the solvent in kilograms. The denominator differs in two ways at once: solution against solvent, and volume against mass.
Because both the moles of solute and the mass of solvent are unaffected by heating or cooling. Molarity does change, because the solution expands and the same moles then occupy a larger volume.
Use c = 1000 × density × b divided by (1000 + b × molar mass), with density in g/mL and molar mass in g/mol. The conversion cannot be done without the solution density, because it is the only link between the mass basis and the volume basis.
Because colligative properties depend on the ratio of solute particles to solvent, and because the calculation involves changing the temperature. A molarity would drift as the solution cooled, so the constant in the equation would not be constant.
It is the number of particles a formula unit releases in solution. Sugar gives 1, sodium chloride gives close to 2 and calcium chloride close to 3. Measured values fall short of the ideal because ions pair up, and the shortfall grows with concentration.
Only if you already know the amount of solute in moles, which the third input box accepts directly. Otherwise a molar mass is required, because molality is defined in moles and a balance measures grams.
This calculator is provided for education and general reference. It describes how molality is computed and is not laboratory or safety guidance; follow the procedures and risk assessments issued by your own institution.
