Freezing Point Depression Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/9/2026
Freezing point depression is calculated with ΔTf = i × Kf × m, where i is the number of dissociated particles, Kf the solvent's cryoscopic constant, and m the molality. For a 1 mol/kg salt (NaCl) solution in water, the freezing point drops by about 3.72°C.
Explanation
Freezing point depression is a colligative property: its value depends only on the number of solute particles dissolved in the solvent, not on their precise chemical nature. Dissolving a substance in a solvent always lowers its freezing point compared with the pure solvent, an effect directly proportional to the solution's molality (moles of solute per kilogram of solvent, not to be confused with the molarity used by our molar concentration calculator, which relates the amount of solute to the volume of the solution rather than the mass of the solvent). The van't Hoff factor (i) accounts for the fact that some substances dissociate into several distinct particles once in solution: sodium chloride (NaCl) dissociates into one Na⁺ ion and one Cl⁻ ion, doubling the effective number of particles compared with its initial molar concentration (i=2), while a non-dissociating substance like glucose keeps i=1. This same principle explains why salt is spread on icy roads in winter: by dissolving into the thin film of water on the road surface, it lowers its freezing point enough to prevent ice from forming, even at slightly negative temperatures. The same effect, on a larger scale, also explains why salty seawater freezes at a lower temperature than fresh water. To prepare a solution at a precise molality from a solid solute and a solvent, our dilution calculator helps adjust the proportions ahead of this calculation.
Example: a 1 mol/kg NaCl solution in water
Inputs
Molality: 1 mol/kg. Van't Hoff factor: 2 (NaCl dissociates into 2 ions). Cryoscopic constant: 1.86 °C·kg/mol (water).
Calculation
ΔTf = 2 × 1.86 × 1 = 3.72°C.
Result
This solution's freezing point is lowered by about 3.72°C compared with pure water (freezing around −3.72°C).
Frequently asked questions
Why does salt melt ice on roads in winter?
Salt dissolved in the film of water on the road surface lowers its freezing point below the ambient temperature, which prevents the water from freezing or melts ice already formed, as long as the temperature doesn't drop below the new, lowered freezing point. Beyond a certain cold threshold (generally around −10°C to −20°C depending on concentration), salt loses its effectiveness because the solution itself eventually freezes.
Why use molality rather than molarity in this formula?
Molality (moles of solute per kilogram of solvent) doesn't depend on temperature, unlike molarity (moles per liter of solution), which varies slightly with temperature because a liquid's volume expands or contracts with heat. For a property like freezing point, which describes a change in temperature, molality is the physically consistent quantity to use.
Is the van't Hoff factor always an exact whole number?
In ideal theory, yes (2 for NaCl, 3 for CaCl₂), but in practice, dissociation is rarely fully complete, and interactions between ions in a concentrated solution mean the actually measured van't Hoff factor is often slightly below its theoretical whole-number value, especially at high concentration. This calculator uses the ideal theoretical value, an approximation good enough for most educational uses.