Ideal gas temperature calculator
One mole of gas at 101325 Pa filling 0.022414 m³ sits at about 273 K. Enter pressure in pascals, volume in cubic metres and the amount in moles; the gas constant defaults to 8.314462618 J/(mol·K). 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
- Volume
- 0.022414
- Moles
- 1
- Gas constant
- 8.314462618 K
- Creativity
- 273.1503711477
This ideal gas temperature calculator returns the absolute temperature of an ideal gas in kelvin from pressure, volume, mole count, and the gas constant using the rearrangement T equals P times V divided by n times R of the ideal gas law PV equals nRT. Physics students, laboratory technicians, and process engineers use that identity whenever they already know how hard a sample presses, how much space it occupies, and how many moles are present, and they need kelvin rather than a Celsius reading or a guess from room conditions. The engine accepts pressure in pascals, volume in cubic metres, moles in mol, and an optional gas constant in joules per mole-kelvin that defaults to the CODATA molar gas constant, then returns a deterministic temperature with the formula echoed for worksheets and tests.
What ideal-gas temperature means and how T = PV/nR is obtained
Absolute temperature of an ideal gas is the kelvin value that makes the state equation PV equals nRT hold for a given pressure, volume, and amount of substance. Starting from that law, divide both sides by nR to obtain T equals P V over n R.
With P in pascals, V in cubic metres, n in moles, and R in joules per mole-kelvin, the product PV has units of joules and nR has units of joules per kelvin, so T is returned in kelvin, the absolute scale required by every ideal-gas formula and by SI laboratory reporting. The advertised failure is a mole count of zero or a negative mole count, because those values make temperature undefined or non-physical in this rearrangement.
Typical textbook checks include one hundred one thousand three hundred twenty-five pascals, about zero point zero two two four one four cubic metres, and one mole, which recovers roughly two hundred seventy-three kelvin with the default gas constant. Doubling the pressure at fixed V and n doubles T; doubling n at fixed P and V halves T.
Where an ideal-gas temperature calculator earns its keep
Students meet absolute temperature from the ideal gas law when a physics textbook gives pressure, volume, and moles in SI units and asks for T in kelvin, when a lab fills a vessel of known volume with a measured amount of gas at a stated pressure, or when a contest problem requires converting those three quantities into an absolute temperature under ideal assumptions.
Teachers can pre-generate answer keys for modest P, V, and n without trusting opaque calculator apps that silently switch between pascals and atmospheres or between Celsius and kelvin. Developers call the same contract from scripts to seed deterministic test vectors for physics education products, to normalize user-entered gas inputs before reporting temperature, or to satisfy programming-challenge statements that demand T rather than a hand-waved estimate.
Process and quality workflows sometimes need a fast offline source of ideal-temperature checks so online pressure and volume readings can be converted without reopening a full thermodynamics package. Pair it with molar-volume, density, and combined gas-law helpers when you are building a small lab of free, deterministic ideal-gas tools that share the same validation style and a stable numeric contract.
What you can do with it
Homework ideal-gas temperature checks
Convert textbook pressure, volume, and mole counts in SI units into absolute temperature T in kelvin for PV=nRT drills and answer-key prep.
Lab and tutoring software
Normalize user-entered P, V, and n into kelvin for vessel labs, interactive lessons, and offline teaching demos.
FAQ
What does the ideal gas temperature calculator cost?
It is free in your browser on this page.
How is temperature defined here?
Pressure is in pascals, volume in cubic metres, moles in mol. The result is absolute temperature in kelvin.
What happens if the mole count is zero or negative?
Zero or negative moles make T undefined (division by zero) or non-physical for this ideal-gas rearrangement.
Can I use a different gas constant R?
Zero R is rejected. Keep P in pascals and V in cubic metres for consistent SI units.
Does this tool convert Celsius or use real-gas equations?
No. It returns kelvin from ideal-gas T = PV/(nR) only. Supply SI pressure and volume yourself, and use a van der Waals or combined-gas-law tool for other models.
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/phys/ideal-gas-temperature \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"pressure":101325,"volume":0.022414,"moles":1}'const res = await fetch("https://api.kit.forhosting.com/phys/ideal-gas-temperature", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"pressure": 101325,
"volume": 0.022414,
"moles": 1
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/ideal-gas-temperature",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"pressure": 101325,
"volume": 0.022414,
"moles": 1
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/ideal-gas-temperature", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"pressure":101325,"volume":0.022414,"moles":1}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"pressure":101325,"volume":0.022414,"moles":1}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/ideal-gas-temperature", 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,
"volume": 0.022414,
"moles": 1
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.ideal_gas_temperature",
"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
Zero or negative mole counts are rejected with invalid_input because division by n would be undefined or non-physical.
What ideal-gas temperature means and how T = PV/nR is obtained
This calculator returns the normalized pressure, volume, moles, and gas constant, the computed temperature, the unit string K, a short formula reminder T equals PV over nR, and the method tag ideal_gas_temperature. There is no approximate equation-of-state path and no random sampling: the engine either multiplies two finite scalars and divides by the product of moles and R or rejects the input with invalid_input.
Input contract, SI units, and error behaviour
Moles must be greater than zero: a zero or negative mole count is rejected because T equals PV over nR is undefined when n is zero and non-physical when n is negative, and those failures are not billed. Keep units consistent: pascals with cubic metres and joules per mole-kelvin. Mixing atmospheres with cubic metres, or litres with pascals, produces a number that is not kelvin even if the algebra looks the same. POST a JSON body with three required finite numbers: pressure for P in pascals, volume for V in cubic metres, and moles for n in moles. Each field may arrive as a JSON number or as a numeric string; aliases P and p for pressure, V and vol for volume, and n and amount for moles are accepted so spreadsheets, query strings, and typed forms can reuse the same contract. Missing fields, empty strings, and non-finite values fail with invalid_input naming the field. An optional gas_constant field, with aliases R, r, and R_gas, overrides the default molar gas constant of eight point three one four four six two six one eight joules per mole-kelvin when your problem statement uses a rounded textbook R such as eight point three one four; a zero gas constant is rejected because it would divide by zero. Computation forms T equals pressure times volume over moles times gas_constant in ordinary floating-point arithmetic, rounds to twelve decimal places for stable goldens across runtimes, and collapses negative zero to plain zero for clean comparisons. Pair the free browser run on this page with the priced API when you need the identical mathematical result inside an automated pipeline without re-implementing T equals PV over nR yourself.
Where an ideal-gas temperature calculator earns its keep
Product and tutoring tools use the endpoint when a learner types pressure, volume, and moles and the interface must show a clean kelvin result with a formula echo. On this page the work runs entirely in your browser; through the API each successful lookup costs $0.002, failed validation is not charged, and nothing is stored after the response returns. That split — free interactive exploration and a priced, identical API — matches the rest of the KIT tier-A catalog and lets you move from a classroom demo to an automated pipeline without changing the mathematical result.
Integration use cases
Deterministic test fixtures
Generate reproducible kelvin values for unit tests, property checks, and CI assertions on the ideal-gas T = PV/(nR) formula.