Freezing Point Depression Calculator (ΔTf = i · Kf · b)

Background.

Seawater freezes at about −1.9 °C instead of 0 °C, a glass of sweet tea in the freezer turns slushy before it turns solid, and a road sprinkled with salt stays wet on a morning that would otherwise glaze it with ice. All three are the same effect. Dissolve almost anything in a liquid and the liquid has to be cooled further before it freezes.

In dilute solutions the size of that drop depends on how many dissolved particles there are, not on what they are. The working equation is ΔTf = i · Kf · b. Here b is the molality, moles of solute per kilogram of solvent; Kf is the solvent's cryoscopic constant, 1.86 K·kg/mol for water; and i, the van 't Hoff factor, is the number of particles each dissolved formula unit releases. One mole of ethylene glycol in a kilogram of water therefore lowers the freezing point by 1.86 K, to −1.86 °C.

There are three ways to use the relation. Run it forwards to find the freezing point of a solution you have made. Run it backwards — cryoscopy — to find the molar mass of an unknown substance from how far it lowers a solvent's freezing point. Or work out Kf itself from the solvent's freezing point, molar mass and enthalpy of fusion, which matters for solvents other than water, where tabulated constants do not always agree.

The equation is a dilute-solution approximation. It holds well up to roughly 0.1 mol/kg, degrades above that, and degrades sooner for salts, whose ions do not behave as fully independent particles. Engine coolant, road brine and clinical samples are all handled with measured data in practice, and the limits further down explain why.

What is freezing point depression calculator?

Freezing-point depression is one of the four colligative properties of solutions, alongside vapour-pressure lowering, boiling-point elevation and osmotic pressure. Colligative means the effect depends on the number of dissolved particles rather than their chemical identity: a mole of glucose and a mole of urea in the same kilogram of water lower its freezing point by the same amount. The reason lies in the liquid. Dissolved solute lowers the chemical potential of the liquid solvent, while the ice that forms is essentially pure solvent and is unaffected. Freezing happens where liquid and solid have equal chemical potential, so with the liquid's lowered, the two meet at a lower temperature. The concentration measure is molality, moles of solute per kilogram of solvent, because it contains no volume and so does not change as the solution is cooled. Clinical laboratories use the same principle in freezing-point osmometers, which measure how far a blood or urine sample's freezing point falls to report its osmolality.

How to use this calculator.

1. 01Choose what to work out: the freezing point of a solution, the molar mass of a solute from a measured depression, or the cryoscopic constant of a solvent from its thermodynamic data.
2. 02Enter the mass of solvent alone, in grams, not the mass or volume of the finished solution. Weigh water rather than measuring it by volume, since a litre of water is not exactly a kilogram at room temperature.
3. 03Set the van 't Hoff factor: 1 for substances that dissolve as whole molecules, such as glucose, urea or ethylene glycol. For a salt the ion count — 2 for NaCl, 3 for CaCl₂ — is an upper limit; real solutions behave as if the factor were smaller.
4. 04Keep Kf at 1.86 for water. For another solvent, use the derivation mode with its normal freezing point, molar mass and enthalpy of fusion, which the NIST Chemistry WebBook lists for many compounds.
5. 05In cryoscopy mode, enter the measured depression as a positive number: a solvent that freezes at 0 °C and a solution that freezes at −0.62 °C give a depression of 0.62 K.
6. 06Read the depression in kelvin and the solution's freezing point in °C, and check the molality output: above about 0.1 mol/kg, treat the result as an approximation.

The formula.

Four relations do all the work. Molality is b = (solute mass ÷ molar mass) ÷ kilograms of solvent. The depression is ΔTf = i · Kf · b, and the solution's freezing point is the pure solvent's freezing point minus ΔTf. Run backwards, b = ΔTf ÷ (i · Kf), and the solute's molar mass is M = solute mass ÷ (b × kilograms of solvent). The cryoscopic constant is Kf = R · Tf² · M_A ÷ ΔfusH, with R = 8.314462618 J/(mol·K), Tf the solvent's freezing point in kelvin, M_A its molar mass in kg/mol and ΔfusH its molar enthalpy of fusion in J/mol.

The linear equation is a simplification of an exact condition: at the freezing point the solvent's chemical potential is the same in the liquid and in the solid. Written out for an ideal solution, that condition contains ln(1 − x), where x is the solute's mole fraction. Replacing ln(1 − x) with −x, treating the enthalpy of fusion as constant over the small temperature range, and converting mole fraction to molality give ΔTf = Kf · b. The approximations are good when x is small, which is why the equation is reliable for dilute solutions and drifts as concentration rises. It also assumes the solute does not evaporate and does not enter the solid.

The constant can be checked from first principles. Feistel and Wagner's 2006 equation of state for ice, adopted by IAPWS, gives a melting enthalpy of 333.427 kJ/kg; multiplied by water's 0.018015 kg/mol that is 6.0067 kJ/mol. Then Kf = 8.314462618 × 273.15² × 0.018015 ÷ 6,006.7 = 1.8605 K·kg/mol, within 0.03 % of the handbook 1.86. For benzene, NIST data — freezing point 278.64 K, enthalpy of fusion 9.8663 kJ/mol, molar mass 78.114 g/mol — give 5.111 K·kg/mol against the usual tabulated 5.12. A Kf derived this way is applied to the depression at full precision.

The formula shows what makes a solvent sensitive: a high freezing point, which is squared, heavy molecules and a small enthalpy of fusion.

Some entries cannot give an answer and are refused: a van 't Hoff factor, cryoscopic constant, solvent mass or solute molar mass of zero or less; in cryoscopy, a zero depression or zero solute mass, which would imply an infinite or undefined molar mass; and in the derivation, a freezing point at or below absolute zero, or a zero enthalpy of fusion.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Feistel, R. & Wagner, W. (2006). 'A New Equation of State for H2O Ice Ih', Journal of Physical and Chemical Reference Data 35(2), 1021–1047 — the equation of state adopted by IAPWS in 2006. Melting-curve table at the normal-pressure melting point (T = 273.152519 K, p = 0.1013 MPa) gives Δh_melt = 333.427 kJ/kg; §3.5 compares this with the experimental determinations of Giauque & Stout (1936: 333.49 and 333.42), Osborne (1939: 333.54) and Haida et al. (1974: 333.41). This is the value from which this page derives Kf(water) = 1.8605 K·kg/mol. Peer-reviewed, free PDF; retrieved 2026-07-29.
2. [2]NIST Chemistry WebBook, SRD 69 — phase-change data. For benzene: T_fus = 278.64 ± 0.08 K (average of 57 values) and Δ_fus H = 9.8663 kJ/mol at 278.69 K from Oliver, Eaton & Huffman (1948), compilation DH. Used for the worked non-water derivation on this page, which returns Kf = 5.111 K·kg/mol against the commonly tabulated 5.12. Retrieved 2026-07-29.
3. [3]NIST Special Publication 811, 2008 edition, section 8.6.8 'Molality of solute B' — b_B = n_B/m_A, SI unit mol/kg, defined per mass of SOLVENT. Section 8.5 'Temperature interval and temperature difference' establishes that {Δt}°C = {ΔT}K, which is why the depression on this page needs no unit conversion. Retrieved 2026-07-29.
4. [4]IUPAC, 'Quantities, Units and Symbols in Physical Chemistry' (Green Book), 3rd edition, 2nd printing 2012, section 2.10 composition table: molality m_B, b_B = n_B/m_A with SI unit mol kg⁻¹, and note 14 on the m/b symbol collision. Confirms independently of NIST that the concentration variable in the colligative equations is per kilogram of solvent. Retrieved 2026-07-29.
5. [5]Hamer, W. J. & Wu, Y.-C. (1972). 'Osmotic Coefficients and Mean Activity Coefficients of Uni-univalent Electrolytes in Water at 25 °C', Journal of Physical and Chemical Reference Data 1(4), 1047–1100. Tabulates practical osmotic coefficients φ for 79 uni-univalent electrolytes; the effective van 't Hoff factor is i = ν·φ, and φ is below 1 throughout the dilute range, which is why a real salt depresses less than its ion count predicts. Cited for the direction and origin of the deviation; specific tabulated coefficients were not extracted from the scanned tables and no numeric φ is asserted on this page. Free NIST reprint; retrieved 2026-07-29.
6. [6]IUPAC Commission on Isotopic Abundances and Atomic Weights (CIAAW), Standard Atomic Weights 2021, abridged values — the source of every molar mass on this page: H 1.008, C 12.011, O 15.999, giving M(H2O) = 18.015, M(C2H6O2) = 62.068, M(C6H6) = 78.114 g/mol. Retrieved 2026-07-29.