Freezing point depression calculator
Work out the freezing-point drop for any solution: one mole of sodium chloride per kilogram of water, counted as two particles with a constant of 1.86, lowers the freezing point by 3.72 °C. A non-electrolyte at half that molality drops 0.93 °C. Free in your browser.
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Worked example
- Molality
- 1
- Cryoscopic
- 1.86
- Van t hoff factor
- 2
- Delta tf
- 3.72
Freezing-point depression is a colligative property: adding a non-volatile solute lowers the temperature at which the solvent freezes, and the size of that drop depends on how many particles the solute contributes per kilogram of solvent, not on the chemical identity of the solute beyond its van 't Hoff factor. The standard dilute-solution formula is delta Tf equals i times Kf times m, where m is molality in moles of solute per kilogram of solvent, Kf is the cryoscopic constant of the pure solvent, and i accounts for dissociation or association in solution. Students use the relation for homework on aqueous salt solutions and antifreeze mixtures; lab instructors grade freeze-point experiments against the same closed form; process engineers size brine and glycol recipes before running a crystallizer or cold-weather product. This calculator accepts molality, cryoscopic constant, and van 't Hoff factor, returns the depression magnitude delta Tf with unit labels and the formula string for audit, and rejects negative molality so a non-physical concentration never becomes a silent negative drop.
How freezing-point depression is defined and computed
Start from the colligative relation taught in general and physical chemistry: the freezing point of a dilute solution is lower than that of the pure solvent by an amount delta Tf that is proportional to the molal concentration of solute particles. Write delta Tf equals i times Kf times m.
Here m is molality, the amount of solute in moles divided by the mass of solvent in kilograms; Kf is the cryoscopic constant of the solvent, a tabulated material property with units of degrees Celsius times kilogram per mole (or kelvin times kilogram per mole—the temperature-interval size is the same); and i is the van 't Hoff factor, a dimensionless multiplier equal to one for ideal non-electrolytes, roughly two for fully dissociated sodium chloride, and larger for salts that release more ions.
The product i times m is effectively the molality of dissolved particles.
Where freezing-point depression calculators show up in real work
Secondary-school and introductory university chemistry courses assign colligative-property drills that multiply molality by a tabulated Kf and a stated van 't Hoff factor; a single trusted oracle speeds grading and demo setup without hand-waving floating-point noise. Laboratory courses measure freeze points of aqueous salt or sugar solutions and compare experimental depression to the ideal i Kf m prediction, so students need the same closed form their report cites.
Food scientists and cold-chain engineers estimate how much sugar, salt, or glycol shifts the freeze point of brines and syrups when designing storage or freeze-concentration steps. Automotive and industrial formulation work sizes antifreeze and de-icing mixtures against a target depression before running a full thermo package. If you later need molality from moles and solvent mass, boiling-point elevation with Kb, osmotic pressure, or automatic Kf lookup tables for common solvents, treat those as separate search intents and landings rather than overloading this freezing-point depression calculator page.
What you can do with it
Homework and exam answer keys
Compute ΔTf = i × Kf × m for textbook aqueous and organic solvent sets so students and auto-graders share one closed-form ground truth.
Lab freeze-point experiment checks
Predict ideal depression for measured molality and stated i before comparing to experimental freeze-point data in teaching labs.
Brine and antifreeze formulation
Estimate how much solute loading shifts freeze point for cold-chain, de-icing, or glycol recipes at a target molality.
FAQ
What formula does this freezing point depression calculator use?
The standard colligative relation ΔTf = i × Kf × m, where m is molality (mol/kg), Kf is the cryoscopic constant of the solvent, and i is the van 't Hoff factor.
What happens if molality is negative?
Negative molality is non-physical; the product rule requires m ≥ 0.
What van 't Hoff factor should I use?
For strong electrolytes, ideal i is the number of ions per formula unit (e.g. 2 for NaCl, 3 for CaCl2). Real solutions may use an effective i from experiment.
What does it cost?
The browser tool is free and runs locally.
Does it give the freezing temperature of the solution?
No, it gives the size of the drop. To get the temperature at which the solution freezes, subtract that depression from the freezing point of the pure solvent. A separate tool covers the final temperature of an ice-salt mixture.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/chem/freezing-point-depression \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"molality":1,"cryoscopic_constant":1.86,"van_t_hoff_factor":2}'const res = await fetch("https://api.kit.forhosting.com/chem/freezing-point-depression", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"molality": 1,
"cryoscopic_constant": 1.86,
"van_t_hoff_factor": 2
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/freezing-point-depression",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"molality": 1,
"cryoscopic_constant": 1.86,
"van_t_hoff_factor": 2
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/freezing-point-depression", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"molality":1,"cryoscopic_constant":1.86,"van_t_hoff_factor":2}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"molality":1,"cryoscopic_constant":1.86,"van_t_hoff_factor":2}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/freezing-point-depression", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"molality": 1,
"cryoscopic_constant": 1.86,
"van_t_hoff_factor": 2
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.freezing_point_depression",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
How freezing-point depression is defined and computed
Molality must be finite and non-negative: zero molality is the pure-solvent limit and yields a depression of zero, while a negative molality is non-physical and fails validation with a clear invalid_input message rather than a silent nonsense result. The capability evaluates the closed form in deterministic floating-point arithmetic: no random seeds, no wall-clock timestamps, no network calls, and no model drift, so identical inputs always produce identical JSON. It does not convert grams of solute into moles, look up solvent Kf tables for you, compute boiling-point elevation, or return the absolute freezing temperature of the mixture; those are separate search intents with their own landings when product coverage grows.
What you send and what you get back
Classic textbook checks include one molal aqueous sodium chloride with i equals two and Kf equals one point eight six giving a depression of three point seven two degrees, half-molal non-electrolyte in water with i equals one giving zero point nine three degrees, and zero molality giving a depression of zero. Send three required finite numbers under the fields molality, cryoscopic_constant, and van_t_hoff_factor. molality is the solution molality in moles per kilogram of solvent and must be greater than or equal to zero; negative values fail because colligative formulas assume a non-negative concentration. cryoscopic_constant is Kf for your solvent—about one point eight six degrees Celsius kilogram per mole for water, different for benzene, acetic acid, and other laboratory solvents. van_t_hoff_factor is i for your solute under the idealization you are using; non-electrolytes use one, and ideal strong electrolytes use the stoichiometric ion count. Missing fields, non-numeric strings, NaN, Infinity, and negative molality fail with invalid_input and are not charged. On success the response echoes cleaned molality, cryoscopic_constant, and van_t_hoff_factor, provides delta_tf as the primary depression in degrees Celsius or kelvin, includes a units hint object, sets method to freezing_point_depression_colligative, and formula to delta Tf equals i times Kf times m so homework write-ups can cite the same expression. Pricing for successful API calls is the published base of $0.002 per item; validation failures do not consume prepaid balance.
Where freezing-point depression calculators show up in real work
Because this capability is a pure parse engine, API pricing is the published base of $0.002 per successful item and failed validation does not consume balance.
Technical questions
Is delta_tf the absolute freezing temperature?
No. delta_tf is the depression magnitude (°C or K). The solution freezes near Tf°(pure solvent) − ΔTf. Absolute Tf needs the pure-solvent freezing point as a separate input or table.