Molar volume calculator
At 101325 Pa and 273.15 K one mole of ideal gas fills about 0.0224 m³, the classic 22.4 litres. Enter absolute pressure and kelvin temperature to get the molar volume and the R·T product for checking your working. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Pressure
- 101,325
- Creativity
- 273.15
- Gas constant
- 8.314462618
- Molar volume
- 0.0224139695
- Product rt
- 2,271.09546411
Ideal-gas molar volume is the volume occupied by one mole of gas when the equation of state holds. From PV equals nRT with n set to one mole, the volume V becomes R times T divided by P: that quotient is the molar volume Vm. This calculator takes absolute pressure and absolute temperature—plus an optional gas constant that defaults to the SI value 8.314462618 joules per mole per kelvin—and returns Vm together with the intermediate product R·T so you can check intermediate algebra on homework sheets and lab notebooks. Classic STP checks recover roughly 0.0224 cubic metres per mole (about 22.4 litres per mole) near one atmosphere and zero Celsius when you use consistent units. Non-positive temperature is rejected because absolute zero and below are outside the model.
How ideal-gas molar volume follows from PV = nRT
Start from the ideal-gas law PV equals nRT, where P is absolute pressure, V is volume, n is amount of substance in moles, R is the universal gas constant, and T is absolute temperature in kelvin. For a single mole, n equals one, so V equals RT over P. That volume of one mole is the molar volume Vm, often written with a subscript m.
In SI units you typically send P in pascals, T in kelvin, and leave R at the default 8.314462618 joules per mole per kelvin, which yields molar volume in cubic metres per mole. At standard pressure 101325 pascals and 273.15 kelvin with SI R you recover about 0.022414 cubic metres per mole, matching the classic 22.4 litres per mole after scaling by one thousand.
The tool does not convert Celsius or Fahrenheit to kelvin, does not apply compressibility factors for real gases, does not compute mass density from molar mass, and does not solve multi-point Boyle or Charles problems that omit the gas constant. Absolute temperature must be strictly positive: T less than or equal to zero is rejected with invalid input instead of returning zero volume or a non-physical result.
Where molar volume calculations show up in real work
Secondary-school chemistry courses constantly assign STP and SATP molar-volume problems that give P and T and ask for the volume of one mole, often before introducing mass density or partial pressures. University general-chemistry and introductory thermo labs use the same two-number reduction as a sanity check for tank fill estimates and balloon sizing when amount of substance is known in moles. Process technicians convert measured absolute pressure and temperature into approximate molar volume before estimating tank inventory in moles from a measured geometric volume.
Keep gas density (rho equals P M over R T) on its own landing when the search intent is mass per volume rather than volume per mole: the formulas share R and T but answer different homework questions and different SEO queries. If you need hydrostatic liquid pressure, thermal expansion, or unit conversion between atmospheres and pascals, use the matching specialized calculators instead of stretching this ideal-gas molar volume tool beyond PV equals nRT for one mole.
What you can do with it
STP and SATP homework keys
Compute Vm = RT/P for textbook standard states so teachers and auto-graders share one ground truth, including the non-positive temperature rejection.
Tank and balloon mole estimates
Convert measured absolute pressure and temperature into ideal-gas molar volume before dividing a geometric volume by Vm to estimate moles.
FAQ
What happens if temperature is zero or negative?
Non-positive absolute temperature is not allowed under the ideal-gas molar volume model Vm = RT/P.
Is the gas constant required?
Provide your own positive R when working in a non-SI consistent unit set (for example L·atm/(mol·K)).
What does it cost?
The browser tool is free and runs locally.
How do I get the molar volume in litres per mole?
Enter the pressure in atmospheres together with a gas constant of 0.08205746 L·atm/(mol·K), and the result comes out in litres per mole, close to 22.4 L/mol at standard conditions.
Does it correct for real gases?
No. It applies the ideal-gas law only, without compressibility factors. For gases far from ideal behaviour, such as at very high pressure, treat the result as an ideal-gas estimate.
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/thermo/gas-molar-volume \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"pressure":101325,"temperature":273.15}'const res = await fetch("https://api.kit.forhosting.com/thermo/gas-molar-volume", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"pressure": 101325,
"temperature": 273.15
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/thermo/gas-molar-volume",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"pressure": 101325,
"temperature": 273.15
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/thermo/gas-molar-volume", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"pressure":101325,"temperature":273.15}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"pressure":101325,"temperature":273.15}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/thermo/gas-molar-volume", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"pressure": 101325,
"temperature": 273.15
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "thermo.gas_molar_volume",
"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 ideal-gas molar volume follows from PV = nRT
Chemistry worksheets often prefer litres and atmospheres with R equals 0.08205746 litre atmospheres per mole per kelvin, producing Vm in litres per mole near the familiar 22.4 L/mol at STP; this calculator accepts an explicit gas_constant so those consistent systems work without hidden unit conversion.
What you send and what you get back
Classic textbook checks include STP near one atmosphere and zero Celsius recovering roughly 0.0224 cubic metres per mole, SATP near 298.15 kelvin with a slightly larger Vm, and explicit R when working in litre-atmosphere units for 22.4 L/mol style answers. If you later need mass density from molar mass, Boyle rearrangements without R, Kelvin conversion from Celsius, or real-gas Z-factor corrections, treat those as separate search intents and landings rather than overloading this molar volume calculator page. Send finite numbers under the fields pressure and temperature. pressure is absolute pressure in any unit consistent with your choice of R; it must be positive. temperature is absolute temperature in kelvin and must be greater than zero; zero or negative values fail with a message that names the non-positive temperature rule. gas_constant is optional: when omitted the engine uses 8.314462618 and sets gas_constant_defaulted to true; when provided it must be a finite positive number and gas_constant_defaulted is false. Missing fields, non-numeric strings, NaN, and Infinity fail with invalid_input and are not charged. On success the response echoes cleaned pressure, temperature, and gas_constant, reports molar_volume as R·T/P, includes product_rt for intermediate checks, states the unit convention for SI, and includes the formula string and method ideal_gas_molar_volume. Pricing for successful API calls is the published base of $0.002 per item; validation failures do not consume prepaid balance.
Where molar volume calculations 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.
Integration use cases
Curriculum widgets and API fixtures
Drive browser demos and CI golden tests from the same isomorphic solver so classroom tools never disagree with backend grading.
Technical questions
What formula does this molar volume calculator use?
Vm = R · T / P. Given absolute pressure, absolute temperature, and optional gas constant R (default 8.314462618 J/(mol·K)), the response returns the molar volume of one mole of ideal gas and the intermediate product R·T.
What units should I use?
SI defaults are Pa for pressure, K for temperature, and R = 8.314462618 J/(mol·K), giving molar volume in m³/mol. For other systems pass a matching gas_constant and keep units consistent; the tool does not convert units for you.