Pneumatic cylinder force calculator
At 6 bar of shop air, a cylinder with a 0.05 m bore pushes out with about 1178.1 N. Enter supply pressure in pascals and bore in metres to get the extension force and the piston area, ready to compare with a catalogue table. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Pressure
- 600,000
- Bore diameter
- 0.05
- Area
- 0.0019634954 N
- Force
- 1,178.0972450962
A pneumatic cylinder turns compressed air into a linear push. The theoretical extension force on the piston is the product of supply pressure and the circular bore area, so two numbers you already have — air pressure and bore diameter — determine the newton rating of the out-stroke. Machine builders, maintenance technicians, students, and catalogue designers use that force to size actuators, check whether a six-bar shop-air supply can move a given load, and verify textbook problems of the form F equals P times pi times D squared over four.
What pneumatic cylinder extension force is and which two quantities you send
A double-acting pneumatic cylinder extends when compressed air fills the cap (piston) end and the rod travels out. The theoretical extension — or push — force is the gauge pressure acting on the full circular bore area: F equals P times A, and A equals pi times D squared over four. That is the identity this calculator implements.
Pressure is interpreted in pascals, which are newtons per square metre. Convert bar by multiplying by one hundred thousand, megapascals by multiplying by one million, and pounds per square inch by the conventional 6894.757293168 pascals per psi before sending. Bore diameter is in metres: divide millimetres by one thousand, or multiply inches by 0.0254.
Search intent clusters around pneumatic cylinder force calculator, air cylinder push force, newton force from bar and bore, and F equals P pi D squared over four. People want a numeric extension force they can check against a catalogue table, a homework key, or a machine-guarding load — not only a reminder that force equals pressure times area.
A fifty millimetre bore at six bar of shop air is a convenient check: 0.05 metres and 600000 pascals yield about 1178.1 newtons, which is six hundred thousand times pi times 0.0025, matching the textbook table that lists roughly one hundred twenty kilograms of push for that popular ISO 15552 size.
How this calculator validates input and applies F = P × π × D² / 4
Numeric strings that parse to finite numbers are accepted so forms and CSV-style pipelines can pass values without an extra cast. Bore diameter must be strictly positive; a value of zero or a negative bore is rejected with a clear message because a piston of vanishing or reversed diameter does not define a physical area. Zero pressure is allowed and simply yields zero force, which is the unloaded, unpressurised case.
There is no friction correction, no seal-drag allowance, no efficiency factor, and no unit auto-conversion; this is ideal theoretical push from the two known quantities. Keep pascals and metres consistent with the datasheet after you convert bar or millimetres yourself. Pair the result with a separate retract-force calculation when you also know rod diameter; this tool does not subtract rod area from the piston face.
Practical use, limits, pricing, and delivery channels
Use the browser tool when you want an immediate newton check while reading a cylinder datasheet, verifying a homework problem, sizing a clamp or ejector, or comparing two ISO 15552 bores that share a plant pressure but differ in diameter. Choose units consistently — if pressure is in pascals and bore is in metres, force is true SI newtons and area is square metres. Results are fully deterministic: the same pressure and bore always yield the same force.
There is no language model, no external cylinder catalogue, and no randomness, so the capacity is safe to pin in continuous-integration checks and reproducible lesson materials. Do not treat the theoretical push as the working load without a safety factor: friction, side load, and seal drag typically leave eighty-five to ninety-five percent of the ideal force, and catalogues publish those deratings separately.
Keep requests small, pin the rounded force field in tests, and you get reproducible extension force for homework, design notebooks, and edge workers without standing up a full pneumatics-modelling stack of your own.
What you can do with it
Actuator sizing from plant air pressure
Convert a cylinder's bore and the available shop-air pressure into newtons so clamp, ejector, and lift selections start from a shared theoretical push force.
FAQ
Which formula does the pneumatic cylinder force calculator use?
Theoretical push: F = P × A with A = π D² / 4, so F = P × π × D² / 4. Pressure is in pascals and bore in metres; the result is newtons. Retract force is not computed.
What happens if bore diameter is zero or negative?
A zero or negative bore is not allowed because it does not define a physical piston area; those calls are not charged.
What units should I send for pressure and bore?
Pressure must be in pascals and bore diameter in metres. Multiply a bar reading by 100000; divide a millimetre bore by 1000; convert psi with 6894.757293168 Pa per psi before calling.
How much force does a 0.05 m bore cylinder give at 6 bar?
About 1178.1 newtons of theoretical push. Six bar is 600 000 pascals, and multiplying that by the bore area, π × 0.05² / 4 square metres, gives the extension force.
Why is the retract force lower than the push force?
On the return stroke the rod covers part of the piston face, so less area feels the pressure. This calculator gives only the extension force and does not ask for the rod diameter.
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/pneumatic-cylinder-force \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"pressure":600000,"bore_diameter":0.05}'const res = await fetch("https://api.kit.forhosting.com/phys/pneumatic-cylinder-force", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"pressure": 600000,
"bore_diameter": 0.05
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/pneumatic-cylinder-force",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"pressure": 600000,
"bore_diameter": 0.05
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/pneumatic-cylinder-force", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"pressure":600000,"bore_diameter":0.05}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"pressure":600000,"bore_diameter":0.05}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/pneumatic-cylinder-force", 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": 600000,
"bore_diameter": 0.05
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.pneumatic_cylinder_force",
"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 pneumatic cylinder force calculator accepts pressure in pascals and bore diameter in metres, computes the piston area from the circular identity, and returns structured JSON with the echoed inputs, area, force in newtons, the unit, the formula, and the method. A bore diameter of zero or a negative bore is rejected as invalid_input because a piston of vanishing or reversed diameter is not a physical cylinder.
What pneumatic cylinder extension force is and which two quantities you send
Retract force is smaller because the rod occupies part of the piston face; this endpoint does not ask for rod diameter and does not compute retract force. Delivering pressure, bore_diameter, area, force, unit, formula, and method as JSON makes the result easy to paste into notes, pin in automated tests, or reuse across languages without reimplementing the circular-area identity.
How this calculator validates input and applies F = P × π × D² / 4
Send a JSON body with pressure and bore_diameter. Both fields are required and must be finite: missing either field, 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. Aliases are recognized for convenience: pressure also accepts P, pressure_pa, pa, air_pressure, and supply_pressure; bore_diameter also accepts bore, diameter, d, D, bore_m, and bore_diameter_m. After validation, area is computed as pi times bore_diameter squared divided by four, and force is pressure times that area. Results are rounded to twelve decimal places 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, so a classroom demo and a production script never disagree.
Practical use, limits, pricing, and delivery channels
Each successful request is one billable item at $0.002; failed validation does not consume balance. Wire the endpoint into actuator-sizing worksheets, contest answer checkers, or preprocessing steps where you already prefer explicit domain errors — such as rejecting a zero or negative bore — over opaque black-box widgets that cannot explain why a bad input was refused.
Integration use cases
Homework and lab pneumatics drills
Students and graders confirm F = P × π × D² / 4 for given pressure and bore, with a clear invalid_input rejection when bore diameter is zero or negative.
Deterministic fixtures for machine tests
Pipelines that seed unit tests or interactive pneumatics demos can call a pure pressure-and-bore oracle instead of reimplementing the circular-area identity in every language.
Technical questions
How do I compute pneumatic cylinder extension force with this API?
Send a JSON body with pressure in pascals and bore_diameter in metres to phys.pneumatic_cylinder_force. The response returns pressure, bore_diameter, area in m², force in N, unit, formula, and method.
What does the pneumatic cylinder force calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.