Gay-Lussac final pressure calculator
A sealed sample at 1 atm heated from 300 K to 600 K reaches 2 atm, because pressure rises in step with absolute temperature. Enter the starting pressure and both temperatures to get the new pressure in the same unit. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- P1
- 1
- T1
- 300
- T2
- 600
- P2
- 2
- Ratio
- 0.0033333333
When a fixed amount of ideal gas is held at constant volume, Gay-Lussac's law says pressure and absolute temperature stay directly proportional: the ratio P1 over T1 equals P2 over T2. This calculator is built for the common homework and lab case where you already know the initial pressure, the initial absolute temperature, and the new temperature after an isochoric heating or cooling, and you need the final pressure. It rearranges the law to P2 equals (P1 times T2) divided by T1, returns the conserved pressure-to-temperature ratio, and rejects a zero initial temperature so division by zero never becomes a silent Infinity.
How Gay-Lussac's law gives the final pressure
Joseph Louis Gay-Lussac and earlier work by Amontons established that for a fixed amount of gas held at constant volume, pressure rises in direct proportion to absolute temperature. Written for two states of the same sample, the relation is P1 over T1 equals P2 over T2. Solving for the unknown final pressure produces the working formula P2 equals (P1 times T2) divided by T1.
Temperature must be on an absolute scale such as kelvin or rankine so that the zero point is true absolute zero; mixing Celsius values without conversion will give wrong answers because zero Celsius is not zero on the absolute scale. Pressure may be given in atmospheres, kilopascals, bars, or torr as long as P1 and the returned P2 use the same unit.
This tool does not convert between unit systems, does not bring volume into the ideal-gas law, does not apply Boyle's or Charles's relations, and does not correct for real-gas compressibility factors. It answers only the isochoric direct-temperature question: given the starting pressure and temperature and the new temperature, what pressure results. Zero initial temperature is the critical validation edge because the rearrangement divides by T1; a zero or near-zero T1 fails with invalid input instead of inventing an infinite pressure.
Zero initial pressure is likewise rejected because those states fall outside the simple Gay-Lussac model for a meaningful starting sample.
Where final-pressure Gay-Lussac calculations show up in real work
Secondary-school chemistry and physics courses constantly assign problems that give two absolute temperatures and one pressure and ask for the missing isochoric final pressure, often for sealed flask demos, autoclave sketches, or tire-pressure stories under a constant-volume idealization. University general-chemistry labs use the same three-number reduction before they introduce variable volume and the full ideal-gas equation. Process technicians and safety trainees sanity-check closed rigid vessels when only an isochoric temperature swing is known and the target is a new pressure.
If you later need to solve for final temperature given final pressure, Boyle's law with volume, Charles's law with volume and temperature, the combined gas law, mole-based ideal-gas calculations, unit conversion between atmospheres and pascals, or real-gas equations of state, treat those as separate search intents and landings rather than overloading this Gay-Lussac final pressure calculator page.
What you can do with it
Homework and lab answer keys
Compute P2 from P1, T1, and T2 so teachers and auto-graders share one Gay-Lussac final-pressure ground truth, including the zero initial-temperature rejection.
Sealed-vessel and autoclave checks
Estimate final pressure after a measured temperature change under a constant-volume assumption for demos, lab notebooks, and safety briefings.
FAQ
What formula does this calculator use?
Gay-Lussac's law at constant volume: P2 = (P1 · T2) / T1. The response also returns the conserved ratio P1 / T1.
What happens if initial temperature T1 is zero?
Final pressure cannot be computed when T1 is zero because the formula divides by initial temperature.
Which units should I use?
Any consistent pair: keep P1 and the returned P2 in the same pressure unit and T1 and T2 on the same absolute temperature scale (kelvin recommended). The tool does not convert units or Celsius to kelvin.
Can it solve for final temperature instead of pressure?
No. This landing always solves for P2 given P1, T1, and T2. For other gas-law unknowns, use a dedicated calculator for that search intent.
What does it cost?
The browser tool is free and runs locally.
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/gay-lussac-final-pressure \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"p1":1,"t1":300,"t2":600}'const res = await fetch("https://api.kit.forhosting.com/chem/gay-lussac-final-pressure", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"p1": 1,
"t1": 300,
"t2": 600
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/gay-lussac-final-pressure",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"p1": 1,
"t1": 300,
"t2": 600
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/gay-lussac-final-pressure", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"p1":1,"t1":300,"t2":600}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"p1":1,"t1":300,"t2":600}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/gay-lussac-final-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
{
"p1": 1,
"t1": 300,
"t2": 600
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.gay_lussac_final_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
What you send and what you get back
Send three finite numbers: p1 for the initial pressure, t1 for the initial absolute temperature, and t2 for the final absolute temperature after the isochoric change. Classic textbook checks include doubling the absolute temperature of a one-atmosphere sample from three hundred kelvin to six hundred kelvin and recovering two atmospheres, or heating from two hundred seventy-three kelvin at one hundred kilopascals to five hundred forty-six kelvin and recovering two hundred kilopascals. All three fields are required. p1 must be non-zero and expressed in any consistent pressure unit. t1 must be non-zero; when initial temperature is zero the request fails with a clear message that final pressure cannot be computed under Gay-Lussac's law because the formula divides by T1. t2 may be any finite number including zero, which yields a zero final pressure under the ideal model. Missing fields, non-numeric strings, NaN, and Infinity also fail with invalid_input and are not charged. On success the response echoes cleaned p1, t1, and t2, reports the solved p2, includes ratio as P1 divided by T1, and documents formula P2 equals (P1 times T2) over T1 with method gay_lussac_final_pressure. Pricing for successful API calls is the published base of $0.002 per item; validation failures do not consume prepaid balance.
Where final-pressure Gay-Lussac 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.