Freezing Point Depression Calculator
Calculate freezing point depression, molality, the van't Hoff factor, the cryoscopic constant, or an unknown solute's molar mass using ΔTf = i × Kf × m, with full step-by-step working.
Choose what to solve for, pick a solvent, then enter the known values.
Freezing point depression (ΔTf)
Formula used: ΔTf = i × Kf × m
0.93 °C
Freezing point drop
-0.93 °C
New freezing point
0.5 mol/kg
Molality
1.86 °C·kg/mol
Cryoscopic constant
Interactive Ice Bath & Thermometer
A live view of dissolved solute particles and the resulting drop in freezing point.
Step-by-Step Freezing Point Depression Calculation
Here's exactly how this answer was calculated, one step at a time.
Given: m = 0.5 mol/kg, i = 1, solvent = Water (H₂O)
Step 1: Start with the colligative property equation
Freezing point depression depends only on how many dissolved particles are present per kilogram of solvent, not on what the solute is.
ΔTf = i × Kf × mStep 2: Identify the known values
i = 1, Kf = 1.86 °C·kg/mol, m = 0.5 mol/kgStep 3: Substitute into ΔTf = i × Kf × m
ΔTf = 1 × 1.86 × 0.5Step 4: Report the result
ΔTf = 0.93 °C, so the new freezing point is -0.93 °C
Calculated result:
0.93 °C
Freezing Point Depression Calculator: Find ΔTf Online
This free freezing point depression calculator works out how much a dissolved solute lowers the freezing point of a liquid, using the equation ΔTf = i × Kf × m. It also works in reverse: give it a measured freezing point drop and it can find the molality, the van't Hoff factor, the cryoscopic constant, or even the molar mass of an unknown solute. It is built for chemistry students, lab technicians, and anyone checking a colligative properties question or a homework answer.
Just pick what you want to solve for, choose a solvent from the list or enter your own Kf and freezing point, type in the values you already know, and the calculator shows the answer along with the full step-by-step working. No sign-up, no downloads, and no ads blocking the tool itself.
What Is Freezing Point Depression?
Freezing point depression is the drop in a liquid's freezing point that happens when you dissolve something in it. Pure water freezes at 0 °C, but salt water freezes at a lower temperature, because the dissolved salt particles get in the way of water molecules lining up into an orderly ice crystal. This is a colligative property, meaning it depends on how many particles are dissolved, not on what those particles actually are.
This is not a chemical reaction. The solute does not react with the solvent; it simply interferes with the solvent's ability to form a solid lattice. Because forming a stable solid requires molecules to settle into a regular pattern, and dissolved particles disrupt that pattern, the liquid needs to be cooled further before it can freeze.
Freezing Point Depression Formula: ΔTf = i × Kf × m
The core formula is ΔTf = i × Kf × m. ΔTf is the drop in freezing point in °C, i is the van't Hoff factor, Kf is the cryoscopic constant of the solvent in °C·kg/mol, and m is the molality of the solution in mol/kg. Molality is used instead of molarity because molality is based on the mass of the solvent, which does not change as the solution cools.
For example, dissolving 1 mole of sugar in 1 kg of water gives a 1 molal solution. Sugar does not split into ions in water, so i = 1. Using water's Kf of 1.86 °C·kg/mol, the freezing point drops by 1.86 °C, from 0 °C down to about -1.86 °C. Ionic solutes like salt produce a bigger drop for the same molality, because they split into more particles once dissolved.
What Is the Cryoscopic Constant (Kf)?
The cryoscopic constant, Kf, is a fixed property of each solvent. It tells you how much the freezing point falls for every 1 molal increase in concentration, assuming the solute does not split into ions. Water has a Kf of 1.86 °C·kg/mol, while solvents like cyclohexane (20.0) or camphor (37.7) have much larger constants, so the same molality produces a far bigger freezing point drop in those solvents.
Kf values are usually looked up in a reference table rather than derived from scratch, since they depend on the solvent's molar mass, its normal freezing point, and its enthalpy of fusion. This calculator includes preset Kf values for common lab solvents, and it also lets you calculate an unknown solvent's Kf from experimental data if you already have a measured ΔTf, molality, and van't Hoff factor.
What Is the Van't Hoff Factor?
The van't Hoff factor, i, tells you how many particles one unit of solute produces once it dissolves. A molecular solute that stays whole, such as sugar or ethylene glycol, has i = 1. An ionic compound that fully separates into ions has a higher i: sodium chloride splits into Na+ and Cl-, giving i = 2, while calcium chloride splits into three ions total (one Ca2+ and two Cl-), giving i = 3.
This matters a lot for freezing point depression, because a salt solution at the same molality as a sugar solution will lower the freezing point roughly two or three times as much, simply because it produces more particles per formula unit dissolved. This is exactly why salt works so much better than sugar for melting ice on a road. Real solutions sometimes show a slightly lower effective i than the ideal value because of ion pairing, especially at higher concentrations, but for classroom problems the ideal value is what's normally expected.
How to Calculate Freezing Point Depression Step by Step
Start by identifying the molality of the solution — moles of solute divided by kilograms of solvent. Next, identify the van't Hoff factor based on whether the solute is molecular or ionic. Then look up or measure the solvent's cryoscopic constant. Multiply all three together: ΔTf = i × Kf × m. Subtract that result from the solvent's normal freezing point to get the new freezing point of the solution.
As a worked example: dissolve 0.30 mol of NaCl in 0.50 kg of water. Molality is 0.30 ÷ 0.50 = 0.60 mol/kg. Since NaCl splits into 2 ions, i = 2. With Kf = 1.86 °C·kg/mol for water, ΔTf = 2 × 1.86 × 0.60 = 2.232 °C. The solution should start freezing at about -2.232 °C instead of 0 °C. Switch this calculator to the depression mode and enter these same numbers to see the identical result with full working shown.
Finding an Unknown Molar Mass From Freezing Point Depression
One of the most useful lab applications of this formula is finding the molar mass of an unknown compound. This technique is called cryoscopy, and it is often preferred over the boiling point method because Kf values tend to be larger than Kb values, giving a bigger and more measurable temperature change for the same concentration. Dissolve a known mass of the unknown solute in a known mass of solvent, measure the freezing point drop, and then rearrange the formula to solve for molar mass: M = (i × Kf × mass of solute) / (ΔTf × kg of solvent).
For instance, dissolving 2.00 g of an unknown non-ionic compound in 50.0 g (0.0500 kg) of benzene produces a ΔTf of 1.024 °C. With i = 1 and Kf = 5.12 for benzene, the molar mass works out to (1 × 5.12 × 2.00) / (1.024 × 0.0500) = 200 g/mol. This calculator has a dedicated molar mass mode built for exactly this kind of lab problem — just enter the solute mass, solvent mass, and measured ΔTf, and it does the rearranged algebra for you with every step shown.
Freezing Point Depression vs Boiling Point Elevation
Freezing point depression and boiling point elevation are two sides of the same colligative-properties coin. Dissolving a solute lowers the freezing point (ΔTf = iKfm) and raises the boiling point (ΔTb = iKbm) at the same time, for the same underlying reason: the solute lowers the vapor pressure and disrupts how easily the solvent can form an organized solid or escape as a gas.
The two effects usually have very different sizes for the same solvent, because Kf and Kb are not equal. Water's Kf is 1.86 °C·kg/mol, over three times larger than its Kb of 0.512 °C·kg/mol. That's why salting an icy road has a much bigger effect on the freezing point than the same amount of salt would have on the boiling point of water on a stove. If you're comparing the two properties, our boiling point elevation calculator uses the matching ΔTb = i × Kb × m equation.
Common Solvents and Their Freezing Point Constants
This calculator includes preset Kf values and normal freezing points for water (Kf 1.86, fp 0.0 °C), benzene (Kf 5.12, fp 5.5 °C), cyclohexane (Kf 20.0, fp 6.5 °C), glacial acetic acid (Kf 3.90, fp 16.6 °C), tert-butanol (Kf 9.1, fp 25.5 °C), nitrobenzene (Kf 8.1, fp 5.7 °C), naphthalene (Kf 6.9, fp 80.2 °C), and camphor (Kf 37.7, fp 178.8 °C), which is one of the largest cryoscopic constants known and is why it is a classroom favorite for molar mass determination.
If your solvent is not on the list, or your instructor has given you a different experimental value, switch to the custom solvent option and enter your own Kf and pure freezing point. The rest of the calculation works exactly the same way regardless of which solvent you choose.
Real-World Examples of Freezing Point Depression
Salting icy roads and sidewalks is the most familiar example: rock salt dissolves into the thin layer of water on ice, lowering its freezing point so the ice melts even below 0 °C. Car radiators use ethylene glycol antifreeze for the same reason, mixed into the coolant so the engine's cooling system does not freeze solid in cold winter weather.
Homemade ice cream making uses this principle too — packing ice with salt around a mixture bowl lowers the temperature of the ice-water bath well below 0 °C, which pulls heat out of the cream mixture fast enough for it to freeze smoothly. Even antifreeze proteins in some cold-water fish work on a related idea, though biological systems add extra complexity beyond the simple ΔTf = iKfm relationship covered here.
Common Mistakes When Calculating Freezing Point Depression
The most common error is forgetting the van't Hoff factor for ionic solutes. Leaving i at 1 for a salt like NaCl or MgCl2 will give an answer that is far too small, since these compounds produce two or three particles per formula unit when they dissolve. Always check whether the solute is molecular or ionic before choosing i.
Another frequent mistake is mixing up molarity and molality, or using the mass of the whole solution instead of just the solvent. The Kf equation specifically needs molality, based on solvent mass alone. A third common slip is unit mismatch — mixing grams and kilograms, or forgetting to convert milligrams — which is why this calculator includes unit selectors on every mass field to help avoid that kind of error. It's also easy to forget that ΔTf gets subtracted from the pure freezing point, not added, since the effect lowers the temperature rather than raising it.
Why Use an Online Freezing Point Depression Calculator
Doing this math by hand is not hard once you know the formula, but it is easy to slip up on a unit conversion, forget the van't Hoff factor, or make a small arithmetic error, especially during an exam or a busy lab session. A calculator built specifically for this formula removes that risk and lets you check your own working in seconds.
This tool covers all six directions the formula can be solved in: the freezing point drop itself, molality, the van't Hoff factor, the cryoscopic constant, an unknown solute's molar mass, and the mass of solute needed to hit a target freezing point. That range makes it useful for coursework, lab report calculations, and quick sanity checks on experimental cryoscopy data alike.
Freezing Point Depression Calculator FAQ and Quick Reference
Use ΔTf = i × Kf × m to find the freezing point drop directly. Rearrange to m = ΔTf / (iKf) to find molality, i = ΔTf / (Kf·m) to find the van't Hoff factor, or Kf = ΔTf / (i·m) to find an unknown solvent's cryoscopic constant. To find an unknown solute's molar mass from lab data, use M = (i × Kf × mass of solute) / (ΔTf × kg of solvent).
This calculator is meant for study, homework checking, and general lab planning. Always confirm the van't Hoff factor for ionic solutes, double-check your solvent's Kf value against your course material, and verify your final numbers against your lab manual before submitting graded work.
Frequently Asked Questions
What is the formula for freezing point depression?
ΔTf = i × Kf × m, where i is the van't Hoff factor, Kf is the solvent's cryoscopic constant, and m is the molality of the solution.
What is Kf for water?
Water's cryoscopic constant (Kf) is 1.86 °C·kg/mol, and its normal freezing point is 0 °C at standard atmospheric pressure.
How do you find molar mass from freezing point depression?
Use M = (i × Kf × mass of solute) / (ΔTf × kg of solvent), after measuring the freezing point drop produced by a known mass of solute in a known mass of solvent.
Why does salt water freeze at a lower temperature than pure water?
Dissolved salt ions disrupt the water molecules' ability to form an ordered ice crystal, so the liquid must be cooled further below 0 °C before it freezes.
Is freezing point depression the same as boiling point elevation?
They are related colligative properties from the same dissolved solute, but they use different constants (Kf vs Kb) and are usually different in size for the same solvent.
What van't Hoff factor should I use for NaCl?
Sodium chloride fully dissociates into Na+ and Cl- ions in water, so the ideal van't Hoff factor is i = 2.