Molality to molarity calculator
A 1 mol/kg salt solution with a density of 1.04 g/mL and a molar mass of 58.44 g/mol is about 0.983 mol/L. Add density and molar mass to move from molality to the molarity that rate laws and titrations use. Free in your browser.
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- Your data stays on your device
Run — free
Worked example
- Molality
- 1
- Density
- 1.04
- Molar mass
- 58.44
- Molarity
- 0.9825781339 mol/L
- Mass solute g
- 58.44
- Mass solution g
- 1,058.44
- Volume L
- 1.0177307692
A molality to molarity calculator turns three laboratory numbers into the volume-based concentration used in kinetics, equilibria, and most titration problems. Enter molality in moles of solute per kilogram of solvent, the density of the solution in grams per milliliter, and the molar mass of the solute in grams per mole; the tool returns molarity in moles per liter, intermediate mass and volume on a one-kilogram solvent basis, a readable formula, and step-by-step substitution so you can check the arithmetic by hand.
What molality and molarity mean and how they convert
Molality, often written lowercase m or with a small m, is moles of solute per kilogram of solvent. It does not depend on the volume of the solution, so it stays constant when temperature changes expand or contract the liquid. Molarity, often written capital M, is moles of solute per liter of solution and is the concentration that appears in rate laws, equilibrium constants, and most analytical methods.
Because molarity needs volume while molality needs only solvent mass, you cannot convert between them without knowing how much space the whole solution occupies. The standard closed-form route assumes a known solution density ρ in grams per milliliter and a known solute molar mass M_w in grams per mole.
Taking one kilogram of solvent as the basis, moles of solute equal the molality m, mass of solute equals m times M_w grams, total solution mass equals one thousand plus m times M_w grams, and solution volume in liters equals that total mass divided by ρ times one thousand. Dividing moles by that volume yields the textbook formula M equals m times ρ divided by one plus m times M_w over one thousand.
Density and molar mass must both be strictly positive; a zero density would imply infinite volume, and a zero or negative molar mass is not physical for a real pure solute. This calculator implements that conversion only: it does not invert molarity to molality without density, look up densities from tables, or model multi-solute mixtures.
Practical tips, limits, and related searches
Use the density of the solution, not the pure solvent, whenever the problem gives it; for dilute aqueous solutions the density is near one gram per milliliter, but concentrated salts and organics can differ enough to change molarity in the second decimal place. Keep molar mass in grams per mole and density in grams per milliliter so the factor of one thousand in the formula stays consistent; do not mix kilograms per mole with grams per milliliter without converting first.
Prefer sending numbers rather than pre-formatted strings when you control the client; string numbers are accepted only when they match a strict finite numeric pattern. Prefer this capability when you already have m, ρ, and M_w and only need M; if your source is a word problem with grams and liters, convert to molality and density first.
Round-trip checks are easy: recompute m times ρ over one plus m times M_w over one thousand by hand and confirm it equals the published molarity within the same twelve-decimal rounding, and confirm that moles divided by the published volume_L reproduces molarity on the one-kilogram basis.
What you can do with it
Homework checks for concentration conversion
Students enter molality, density, and molar mass from textbook problems and compare hand-written molarity and intermediate volume against a deterministic result before submitting.
Lab batch unit reconciliation
Technicians convert a molal specification on a batch ticket into the molar working concentration used at the bench without opening a spreadsheet for each check.
FAQ
How do you convert molality to molarity?
Use M = (m · ρ) / (1 + m · M_w / 1000), where m is molality in mol/kg, ρ is solution density in g/mL, and M_w is solute molar mass in g/mol. The result M is molarity in mol/L.
What density unit should I use?
Grams per milliliter (g/mL), which is numerically the same as kg/L or g/cm³. Pair it with molar mass in g/mol so the formula’s factor of 1000 is correct.
Is molality the same as molarity?
No. Molality is moles per kilogram of solvent; molarity is moles per liter of solution. They match only in special dilute cases when density and solute mass make volume and solvent mass line up.
Is the molality to molarity calculator free?
The browser tool is free and runs locally.
Should I use the density of the solution or of the pure solvent?
Use the density of the solution whenever the problem gives it. Dilute water solutions are close to one gram per millilitre, but concentrated salts and organics can differ enough to change the molarity.
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/molality-to-molarity \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"molality":1,"density":1.04,"molar_mass":58.44}'const res = await fetch("https://api.kit.forhosting.com/chem/molality-to-molarity", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"molality": 1,
"density": 1.04,
"molar_mass": 58.44
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/molality-to-molarity",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"molality": 1,
"density": 1.04,
"molar_mass": 58.44
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/molality-to-molarity", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"molality":1,"density":1.04,"molar_mass":58.44}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"molality":1,"density":1.04,"molar_mass":58.44}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/molality-to-molarity", 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,
"density": 1.04,
"molar_mass": 58.44
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.molality_to_molarity",
"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.
Limits
max_abs | 1000000000000 |
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
When density or molar mass is zero or negative the conversion is undefined or non-physical, so the API returns a clear invalid_input error instead of Infinity or a silent NaN.
How to call the API and what comes back
Molality must be non-negative; density and molar mass must be strictly positive—values at or below one times ten to the minus fifteen, or any non-positive density or molar mass, are rejected. Send a JSON body with three required finite numbers: molality (aliases m, molal, b) in mol per kilogram of solvent, density (aliases rho, the Greek letter rho, solution_density, d) in grams per milliliter—which is numerically equal to kilograms per liter—and molar_mass (aliases M_w, Mw, molecular_weight, solute_molar_mass, mm) in grams per mole. Absolute values must stay within the published limit of one trillion so intermediate products remain finite in IEEE double precision on the Worker and in the browser. On success the response echoes rounded molality, density, and molar_mass, sets molarity to the rounded mol-per-liter value, unit to the string mol/L, mass_solute_g and mass_solution_g and volume_L to the one-kilogram-solvent intermediates, formula to M equals m times rho over one plus m times M_w over one thousand, message to a short English summary, and steps to an ordered array of substitution lines. Failed validation—missing fields, non-finite numbers, values outside absolute limits, negative molality, or zero or negative density or molar mass—returns invalid_input and is never charged. Pricing is a flat $0.002 per successful request with unit item and zero marginal unit price.
Practical tips, limits, and related searches
For teaching, pair examples: one molal sodium chloride with density one point zero four grams per milliliter and molar mass fifty-eight point four four grams per mole yields roughly zero point nine eight three molar; half molal with density one point one and molar mass one hundred yields about zero point five two four molar; and density zero demonstrates the hard invalid_input path that protects division by a non-physical volume. This landing targets people searching for a molality to molarity calculator, convert molality with density, or molal to molar online; it is not a mass-percent tool, not a pure molarity-from-moles calculator, and not a temperature-dependent density model. Failed tasks that return invalid_input do not consume prepaid balance, which keeps exploratory scripts cheap when learners deliberately set density to zero.
Integration use cases
Unit tests for solution-chemistry software
Generate known-good molality-to-molarity cases plus deliberate zero-density or zero-molar-mass rejections for coding kata and API contract tests.
Technical questions
What happens when density or molar mass is zero?
The conversion is undefined or non-physical. This tool returns invalid_input instead of Infinity or NaN.