Solution density from mass percent
A 20 % solution of a solute at 1.84 g/mL in a solvent at 1 g/mL comes out at about 1.1 g/mL. Enter the mass percent and both pure densities to estimate the mixture density, its specific volume and the volume share of each part. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Solute mass percent
- 20
- Solute density
- 1.84
- Solvent density
- 1
- Mass fraction
- 0.2
- Solution density
- 1.1004784689
- Specific volume
- 0.9086956522
- Volume fraction solute
- 0.1196172249
Lab notebooks and process sheets often list a solute mass percent together with handbook densities of the pure solute and pure solvent, yet stop short of a single mixture density figure for dosing pumps, tank mass balances, or unit-conversion checks. Under the ideal volume-additivity assumption—no excess volume of mixing—the reciprocal of the solution density is the mass-weighted sum of the pure-component specific volumes, so one short calculation turns percent composition and two densities into an estimated ρ that is consistent across SI and customary mass-per-volume units. This capability runs that estimate deterministically: it accepts mass percent on a zero-to-one-hundred scale, requires strictly positive pure densities, returns solution density, specific volume, and ideal volume fractions, and fails with a clear invalid input error when a density is zero or negative.
Ideal density formula, mass percent, and when volume additivity applies
Mass percent of solute is one hundred times the mass of solute divided by the total solution mass. Convert it to mass fraction w by dividing by one hundred. For an ideal binary mixture that neither contracts nor expands on mixing, the specific volume of the solution equals w times the pure-solute specific volume plus one minus w times the pure-solvent specific volume.
Taking the reciprocal yields solution density: one over rho equals w over rho solute plus one minus w over rho solvent. Equivalently, on a one-hundred-unit mass basis the total volume is mass percent over solute density plus one hundred minus mass percent over solvent density, and rho is one hundred divided by that total volume. Pure-component densities must share a coherent unit such as grams per millilitre; the estimated mixture density is returned in the same unit system.
Real solutions can deviate because of hydrogen bonding, packing, or temperature effects, so treat the result as a first-principles textbook estimate, not a substitute for measured mixture density tables when precision matters for custody transfer or critical reactor fills. Still, the ideal model is the standard starting point in many chemistry courses, dilute aqueous estimates, and rough process sizing when only pure densities and a weight percent are known.
What you can do with it
Lab prep and solution make-up sheets
Technicians estimate mixture density from a target weight percent and pure-component densities when handbook mixture tables are missing, then size volumetric glassware and tank headspace.
Homework and teaching labs
Students verify the ideal volume-additivity derivation for binary solutions, compare estimated rho against measured values, and learn when excess volume makes the ideal model fail.
Process sizing and automation
Scripts and LIMS jobs convert mass-percent recipes into density estimates for pump curves, mass-balance checks, and unit conversion without embedding spreadsheet formulas.
FAQ
Is this the real measured density of the mixture?
No. It is the ideal estimate assuming zero excess volume of mixing. Real solutions may contract or expand; use measured tables when accuracy is critical.
Which units should I use for the densities?
Any coherent mass-per-volume unit pair (for example both g/mL or both kg/m³).
Is the solution density calculator free?
The browser tool runs free on your device.
How do I estimate solution density from a mass percent?
Work out the volume of 100 g of solution: the solute percent divided by the solute density, plus the rest divided by the solvent density. Dividing 100 by that total volume gives the estimated density.
Should I enter 20 % as 20 or as 0.2?
Enter 20. The mass percent goes on a scale from 0 to 100, and the calculator divides by 100 itself, so the result also shows the matching mass fraction of 0.2.
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/solution-density-from-percent \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"mass_percent":20,"solute_density":1.84,"solvent_density":1}'const res = await fetch("https://api.kit.forhosting.com/chem/solution-density-from-percent", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"mass_percent": 20,
"solute_density": 1.84,
"solvent_density": 1
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/solution-density-from-percent",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"mass_percent": 20,
"solute_density": 1.84,
"solvent_density": 1
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/solution-density-from-percent", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"mass_percent":20,"solute_density":1.84,"solvent_density":1}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"mass_percent":20,"solute_density":1.84,"solvent_density":1}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/solution-density-from-percent", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"mass_percent": 20,
"solute_density": 1.84,
"solvent_density": 1
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.solution_density_from_percent",
"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
The in-browser calculator is free on your device; the prepaid API charges $0.002 per successful item when the same contract is needed from servers, SDKs, or automated lab workflows.
Ideal density formula, mass percent, and when volume additivity applies
Identical inputs always produce identical JSON because the path is pure arithmetic with no network, no random seed, and no wall clock.
Required inputs, density validation, and reading the structured response
Numeric strings are accepted after trim. Send three required finite numbers: mass_percent between zero and one hundred inclusive, solute_density strictly greater than zero, and solvent_density strictly greater than zero. Aliases such as percent, w_percent, mass_pct, or wt_percent map to mass percent; density_solute, rho_solute, or d_solute map to solute density; and density_solvent, rho_solvent, or d_solvent map to solvent density. Zero or negative pure densities fail with invalid_input because volume equals mass over density is non-physical for non-positive density, and the product contract surfaces that message so UI forms can highlight the bad field. On success the response echoes mass_percent, mass_fraction, solute_density, and solvent_density with stable rounding, then reports solution_density as the estimated mixture rho, specific_volume as its reciprocal, and volume_fraction_solute and volume_fraction_solvent from the ideal partial volumes on the one-hundred-unit mass basis. The formula field always restates one over rho equals w over rho solute plus one minus w over rho solvent, and method is always volume_additivity so downstream code can branch without sniffing shapes. Missing fields, non-finite values, mass percent outside zero to one hundred, and non-positive densities are validation failures and are not charged after the engine rejects the request. Use solution_density alone for a single figure in a report; use volume fractions when you need a quick check that partial volumes sum to one under the ideal model.
API usage, pricing, lab workflows, and practical limits
Call the free in-browser solution density from mass percent calculator for homework checks, prep-sheet estimates, and quick sanity tests without spreadsheet macros. Keep pure densities positive and within ordinary handbook magnitudes; the engine bounds absolute values for isolate safety and rejects absurd magnitudes that would break floating-point trust. Pair this endpoint with mass fraction tools when you start from absolute solute and total masses rather than percent, or with molarity-to-mass-percent converters when the lab sheet lists molarity and you already know solution density by another route. Authors shipping SDKs can map solution_density and the volume fractions into tables that mirror the ideal mixing derivation students write by hand, while process engineers can use the same numbers as a transparent first estimate before consulting measured mixture density data for the final run book.
Technical questions
How do I estimate solution density from mass percent?
Send mass_percent (0–100), solute_density, and solvent_density as positive finite numbers. The response includes solution_density from ideal volume additivity: 1/ρ = w/ρ_solute + (1−w)/ρ_solvent.
What happens if a density is zero or negative?
The request fails with invalid_input. Non-positive pure-component densities are rejected because volume equals mass over density is non-physical, and the call is not charged after validation fails.