Ideal gas pressure calculator
One mole of gas at 298.15 K in 0.024465 m³ exerts about 101325 Pa, roughly one standard atmosphere. Enter moles, kelvin and cubic metres; the gas constant is fixed at 8.314462618 J/(mol·K), so the answer is always in pascals. Free in your browser.
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Worked example
- Moles
- 1
- Creativity
- 298.15
- Volume
- 0.024465
- Resistance (Ω)
- 8.314462618
- Pressure
- 101,326.6719622604
- Pressure unit
- Pa
The pressure of an ideal gas follows from the equation of state PV equals nRT once the amount of gas, the absolute temperature, and the occupied volume are known. This physics calculator rearranges that identity for pressure and returns P equals n R T over V in pascals, using the CODATA molar gas constant so that moles, kelvin, and cubic metres stay in SI. Volume and temperature must be strictly positive: a zero or negative volume would divide by a non-physical container size, and a non-positive kelvin reading is not a thermodynamic temperature.
What the ideal-gas law computes and which quantities to enter
Start from the ideal-gas law written as P V equals n R T. Pressure is the unknown on this landing, so the working formula is P equals n times R times T divided by V. Amount n is the number of moles of gas in the sample.
Temperature T is the thermodynamic temperature in kelvin: convert Celsius with T(K) equals t(°C) plus 273.15 before you call, because twenty degrees Celsius is 293.15 kelvin and feeding twenty would understate the pressure by more than an order of magnitude. Volume V is the container volume in cubic metres; a flask of 24.465 litres is 0.024465 cubic metres, not 24.465. The gas constant is fixed at 8.314462618 joules per mole kelvin, the CODATA recommended value, so the returned pressure is always in pascals when those SI units are respected.
This page does not convert litres to cubic metres, does not accept a custom R, and does not apply a compressibility factor. It answers one physics question: given moles, kelvin temperature, and cubic-metre volume, what is the ideal-gas pressure in pascals. Both volume and temperature must be strictly greater than zero.
Zero volume would make the division undefined; negative volume is not a physical container. Zero kelvin is not a reachable macroscopic state, and a negative temperature has left the absolute scale.
Where an ideal gas pressure calculator earns its keep
Secondary-school physics and first-year university courses constantly assign ideal-gas problems that give n, T, and V and ask for pressure in pascals, often for a sealed flask, a piston held at fixed volume, or a lecture demonstration of room-temperature air. Exam-prep generators need a deterministic oracle that marks wrong the case of a zero or negative volume or temperature instead of silently returning infinity that a buggy grader might treat as success.
Laboratory notebooks and light process estimates use the same SI rearrangement as a baseline before anyone reaches for a real-gas equation of state. Failed validation does not consume balance. Keep temperature in kelvin end to end, convert litres to cubic metres before calling, and pin the pascal value in tests so homework checks, LMS plugins, and edge workers stay reproducible without standing up a thermodynamics solver of your own.
Variable-volume Boyle work, isochoric Gay-Lussac ratios, combined-gas rearrangements, and van der Waals corrections remain outside this landing, so treat the number as the classic PV equals nRT pressure in pascals. Round-trip checks are easy: multiply the returned pressure by volume and confirm it equals n R T within the same twelve-decimal rounding used for goldens.
What you can do with it
Sealed-flask and lecture demos
Estimate ideal-gas pressure in pascals for classroom flasks, rigid cylinders, and SI lecture notes without embedding a full thermodynamics package.
FAQ
How is ideal-gas pressure computed from moles, temperature, and volume?
Send finite numbers moles (n), temperature (T in kelvin), and volume (V in m³), all strictly positive for T and V.
Why is the result in pascals?
The gas constant is fixed at the SI CODATA value 8.314462618 J/(mol·K). With n in moles, T in kelvin, and V in cubic metres, nRT/V has units of pascals. Convert litres to m³ before calling; this landing does not accept a custom R.
Do I enter Celsius or kelvin?
Kelvin only. Convert first: T(K) = t(°C) + 273.15. Feeding a Celsius reading as temperature will understate the pressure because zero Celsius is not absolute zero.
How do I enter a volume in litres?
Convert it to cubic metres first by dividing by 1000, because the calculator does not convert litres. A flask of 24.465 litres is entered as 0.024465 cubic metres, not as 24.465.
What happens if the volume or temperature is zero or negative?
The calculation is refused. A zero volume would divide by nothing, a negative one is not a real container, and zero or negative kelvin is not a temperature a gas sample can have.
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-pressure \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"moles":1,"temperature":298.15,"volume":0.024465}'const res = await fetch("https://api.kit.forhosting.com/phys/ideal-gas-pressure", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"moles": 1,
"temperature": 298.15,
"volume": 0.024465
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/ideal-gas-pressure",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"moles": 1,
"temperature": 298.15,
"volume": 0.024465
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/ideal-gas-pressure", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"moles":1,"temperature":298.15,"volume":0.024465}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"moles":1,"temperature":298.15,"volume":0.024465}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/ideal-gas-pressure", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"moles": 1,
"temperature": 298.15,
"volume": 0.024465
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.ideal_gas_pressure",
"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 path is pure arithmetic with no network, no clock, and no randomness, so homework checks, lab notebooks, and API clients always receive the same JSON.
What the ideal-gas law computes and which quantities to enter
The arithmetic is a single multiply-divide on finite numbers, fully deterministic, with no network, no random seed, and no wall clock, so identical inputs always serialize to the same JSON.
Input contract, response shape, and error behaviour
Volume must be strictly positive: a zero or negative volume fails with a message that volume must be positive, matching the product promise that the one-over-V singularity never masquerades as a finite answer. A non-positive mole amount is also rejected because this landing computes the pressure of a gas sample, not a signed accounting remainder. Classic textbook checks include one mole of gas at 298.15 kelvin occupying 0.024465 cubic metres, which lands near one standard atmosphere, about 101325 pascals. POST a JSON body with three required finite numbers: moles, the amount of substance n; temperature, the absolute temperature T in kelvin; and volume, the container volume V in cubic metres. Each field may arrive as a JSON number or as a numeric string; aliases n and amount for moles, T and temp for temperature, and V, v and vol for volume are accepted so notebooks and lab exports map without renaming columns. Missing fields, empty strings, and non-finite values fail with invalid_input naming the field. Temperature must likewise be strictly positive: a zero kelvin input and a negative temperature fail as invalid_input and are not billed. On success the body echoes cleaned moles, temperature, and volume, reports the CODATA r actually used, reports pressure in pascals from n R T over V, and documents formula P equals nRT over V with method ideal_gas_pressure. Pricing for successful API calls is the published base of $0.002 per item; validation failures do not consume prepaid balance.
Integration use cases
Homework and exam checks
Enter moles, kelvin temperature, and cubic-metre volume, compare P in pascals with hand work, and get a clear invalid_input when volume or temperature is zero or negative.
Curriculum fixtures and auto-graders
Produce deterministic PV=nRT pressure checks for lessons, LMS plugins, and CI goldens at $0.002 per successful API item.
Technical questions
What happens if volume or temperature is not positive?
The task fails with invalid_input. Volume must be a positive cubic-metre container size and temperature must be positive kelvin; zero or negative values make P = nRT/V undefined or unphysical, so the engine rejects the request and does not bill the call.
What does the ideal gas pressure calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.