Hoop stress calculator
A pipe at 1 MPa with a 0.2 m bore and a 5 mm wall carries a hoop stress of 20,000,000 Pa, the circumferential pull that tries to split it along a seam. Compare the result with the allowable stress of your pipe or tank wall. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Pressure
- 1,000,000
- Inner diameter
- 0.2
- Wall thickness
- 0.005
- Hoop stress
- 20,000,000 Pa
Hoop stress is the circumferential tensile stress that develops in the wall of a pressurized cylinder as internal fluid tries to split the vessel along a longitudinal seam. In the thin-walled approximation used throughout introductory mechanics of materials, that stress equals internal pressure times inner diameter divided by twice the wall thickness—sigma hoop equals P D over 2 t—and the result is reported in pascals when pressure is in pascals, diameter in metres, and thickness in metres. Students checking homework, piping engineers screening a pipe schedule, vessel designers comparing a first-pass hoop value to allowable stress, and automated worksheets all need that number without opening a finite-element model.
What hoop stress means and when PD/(2t) applies
A closed cylindrical pressure vessel carries internal pressure on every square millimetre of the inner wall. Cutting the cylinder along a longitudinal plane and writing equilibrium on a half-cylinder shows that the force trying to split the wall apart is pressure times the projected rectangle of inner diameter times length, while the wall resists with hoop stress times twice the thickness times length. Cancel length and you obtain the textbook thin-wall hoop formula: hoop stress equals P times D divided by 2 t.
Search intent clusters around hoop stress calculator, Barlow formula, thin-walled pressure vessel circumferential stress, and pipe hoop stress from internal pressure—people who already have P, D, and t and want a numeric stress in pascals they can compare to allowable limits, homework keys, or a spreadsheet, not only a reminder that the formula exists. Keep units consistent: if P is in pascals, D in metres, and t in metres, stress comes out in pascals; any other coherent system works the same way.
The thin-wall model assumes t is small compared with D, typically t over r less than about one tenth, so through-thickness variation of stress can be neglected. Thick-wall Lame solutions, thermal gradients, and nozzle discontinuities need a different analysis path. Longitudinal axial stress in a closed cylinder is half the hoop value under the same assumptions; this capability reports hoop stress only.
Practical use, limits, pricing, and delivery channels
Use the browser tool when you want an immediate hoop stress check while grading a strength-of-materials homework set, comparing a hand calculation of P D over 2 t, verifying a preliminary pipe or tank wall against an allowable stress, or teaching how circumferential stress grows with diameter and pressure and falls as the wall thickens. Results are fully deterministic: identical inputs always produce the same hoop stress and the same formula and method labels.
There is no language model, no external structural analysis service, and no randomness, so the capacity is safe to pin in continuous-integration checks and reproducible course materials. For average axial stress of a bar rather than vessel hoop stress, use the separate stress calculator; that is a different search intent and a different formula.
What you can do with it
Preliminary pipe and vessel screening
Engineers and makers estimate circumferential hoop stress in a thin-walled cylinder before opening a full FEA model or selecting a catalog pipe schedule.
FAQ
What units should I use for pressure, diameter, and thickness?
Use any mutually consistent set. Pascals, metres, and metres yield hoop stress in pascals. The engine does not convert units; convert millimetres or bar to SI first if you want a pascal result.
Is the hoop stress calculator free?
The browser tool runs free on your device.
Does this also compute longitudinal or spherical membrane stress?
No. This capability evaluates only the thin-walled cylindrical hoop formula PD/(2t). Longitudinal stress PD/(4t) and spherical membrane stress are different formulas and different search intents.
When is the thin-wall formula accurate enough?
When the wall is thin compared with the diameter, typically a thickness under about one tenth of the radius. Thicker walls, thermal gradients and nozzle openings need a thick-wall or more detailed analysis.
Can I enter a negative pressure for a vacuum vessel?
No. The pressure must be the internal gauge pressure, zero or above. A negative value would describe external pressure and buckling, which this hoop formula does not cover, so it is refused.
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/hoop-stress \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"pressure":1000000,"inner_diameter":0.2,"wall_thickness":0.005}'const res = await fetch("https://api.kit.forhosting.com/phys/hoop-stress", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"pressure": 1000000,
"inner_diameter": 0.2,
"wall_thickness": 0.005
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/hoop-stress",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"pressure": 1000000,
"inner_diameter": 0.2,
"wall_thickness": 0.005
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/hoop-stress", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"pressure":1000000,"inner_diameter":0.2,"wall_thickness":0.005}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"pressure":1000000,"inner_diameter":0.2,"wall_thickness":0.005}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/hoop-stress", 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": 1000000,
"inner_diameter": 0.2,
"wall_thickness": 0.005
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.hoop_stress",
"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
This capability takes those three finite numbers, rejects zero or negative wall thickness with a clear invalid_input error, and returns hoop stress plus echoed inputs and a formula label as structured JSON.
What hoop stress means and when PD/(2t) applies
Delivering hoop_stress, pressure, inner_diameter, wall_thickness, formula, and method as JSON makes the result easy to paste into notes, pin in automated tests, or reuse across languages without reimplementing the arithmetic.
How this calculator validates input and applies σ = PD/(2t)
Pressure is the internal gauge pressure and must be non-negative: a negative value would describe external pressure or vacuum buckling, which this hoop formula does not treat. Inner diameter must be strictly positive because a zero or negative bore is not a vessel. Extremely small thickness magnitudes that would not solve stably on floating-point hardware are also rejected. There is no longitudinal-stress mode, no spherical-vessel mode, no unit conversion, and no material-allowable lookup; this is the pure P D over 2 t evaluation only. Send a JSON body with the three required fields pressure, inner_diameter, and wall_thickness. Every field must be a finite number or a numeric string that parses to one; missing fields, empty strings, non-numeric text, NaN, and Infinity all fail immediately with invalid_input before any result is returned, and failed validation is not charged. Wall thickness must be strictly positive: zero or negative thickness is explicitly rejected as invalid_input because it would divide by zero in the classic formula, matching the product contract for this capability. Optional aliases such as P, internal_pressure, D, diameter, di, t, and thickness are accepted when documented so forms and scripts can use textbook symbols. After validation the engine computes hoop stress as pressure times inner diameter divided by twice the wall thickness, then rounds to a stable precision so the same input always yields the same JSON across JavaScript engines. The same pure function powers the free in-browser tool and the API path, with no network, no random seed, and no wall clock in the computation path.
Practical use, limits, pricing, and delivery channels
Each successful request is one billable item at $0.002; failed validation does not consume balance. Choose units consistently and stay within the published magnitude bounds so intermediate products remain finite on a Worker isolate. Wire the endpoint into mechanics drills, contest answer checkers, early-stage vessel worksheets, or preprocessing steps where you prefer explicit domain errors—such as rejecting zero or negative wall thickness—over opaque widgets that cannot explain why a bad input was refused.
Integration use cases
Homework and exam verification
Students and graders compute σ = PD/(2t) for a known internal pressure, inner diameter, and wall thickness, and get a clear invalid_input error when thickness is zero or negative.
Deterministic fixtures for mechanics tests
Pipelines that seed unit tests or interactive vessel demos call a pure PD/(2t) oracle instead of reimplementing the thin-wall hoop formula in every language.
Technical questions
How do I calculate hoop stress with this tool?
Send JSON with pressure (P), inner_diameter (D), and wall_thickness (t). The response returns hoop_stress equal to P times D divided by 2 t, in pascals when those SI units are used, plus echoed inputs and formula labels.
What happens if wall thickness is zero or negative?
The request fails with invalid_input. Zero or negative thickness would divide by zero in σ = PD/(2t); validation rejects it and the request is not charged.