Fan airflow calculator
A 0.4 m fan at 1500 rpm pushes air forward at 10 metres per second in the ideal model, a little over 1 cubic metre per second. Enter the impeller diameter and the speed to get the airflow in m³/s, m³/h and CFM. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Diameter
- 0.4
- Speed
- 1,500
- Swept area
- 0.1256637061 m³/s
- Axial velocity
- 10
- Airflow
- 1.2566370614
- Airflow m3 h
- 4,523.8934211693
A fan moves air by spinning a disk of blades, and the volume it can theoretically deliver follows from two geometric quantities you already know: the impeller diameter and the rotational speed. HVAC designers, makers, technicians, and students often need that airflow as a first-order check before they open a catalogue curve or pick a duct. This fan airflow calculator takes diameter in metres and rotational speed in revolutions per minute, treats the impeller as a circular swept disk with square pitch — axial travel of one diameter per revolution — and returns the ideal volumetric flow in cubic metres per second together with cubic metres per hour and cubic feet per minute.
What fan airflow means and which two quantities you need to send
A fan delivers airflow by sweeping a circular disk of blades through the surrounding fluid. The first geometric quantity is the impeller diameter D, which sets the swept area of that disk: A equals pi times D squared over four. The second is rotational speed N in revolutions per minute, which becomes revolutions per second when divided by sixty.
This calculator uses the ideal square-pitch model: each revolution is treated as advancing the air axially by one diameter, so the axial velocity is D times N over sixty. Volume flow Q is then area times axial velocity, which simplifies to Q equals pi over four times D cubed times N over sixty, with Q in cubic metres per second when D is in metres.
That identity is the theoretical displacement of an axial impeller with pitch equal to diameter — the same D-cubed scaling that appears in the fan affinity laws — not a catalogue curve, a CFD run, or a measured k-factor from a test chamber.
Real fans deliver less because of blade angle, hub blockage, leak paths, and the resistance of the duct they feed; the number here is the ideal geometric rate from diameter and speed alone, which is exactly what people search for when they type fan airflow calculator with those two inputs. Negative diameter or negative speed cannot describe a physical impeller, so those inputs are rejected rather than returning a signed volume.
Search intent clusters around fan airflow calculator, fan CFM from diameter and RPM, axial fan volume flow, and cubic metres per hour from impeller size. People want a numeric rate they can check against a nameplate, a homework key, or a first-pass exhaust size — not only a reminder that the formula exists.
Practical use, limits, pricing, and delivery channels
Use the browser tool when you want an immediate first-order cubic-metre or CFM check while reading a fan nameplate, sizing a workshop exhaust, comparing two impeller diameters at the same RPM, or verifying a homework problem on fan laws. Results are fully deterministic: the same diameter and speed always yield the same airflow. There is no language model, no external fan catalogue, and no randomness, so the capacity is safe to pin in continuous-integration checks and reproducible lesson materials.
Pair the result with a separate duct-size or pressure-drop calculator when you need installed performance rather than the ideal geometric rate; this tool does not estimate static pressure, brake horsepower, or a manufacturer k-factor. Keep requests small, pin the rounded airflow field in tests, and you get reproducible fan airflow for homework, design notebooks, and edge workers without standing up a turbomachinery stack of your own.
What you can do with it
HVAC first-order fan selection
Turn an impeller diameter and nameplate RPM into an ideal m³/s, m³/h, and CFM so duct and grille choices start from a shared airflow number before catalogue curves are applied.
Workshop exhaust and maker cooling checks
Makers sizing a booth fan, PC radiator, or greenhouse exhaust can call a pure diameter-and-RPM oracle instead of reimplementing the square-pitch identity in every spreadsheet.
FAQ
Which formula does the fan airflow calculator use?
Ideal square-pitch axial displacement: Q = (π/4) × D³ × (N/60), with D in metres and N in rpm. Equivalently Q = A × v with A = π D² / 4 and v = D × N / 60. Catalogue k-factors are not applied.
What happens if diameter or speed is negative?
A negative impeller diameter or a negative rotational speed is not allowed; those calls are not charged. Zero is allowed and yields zero airflow.
What units should I send for diameter and speed?
Diameter must be in metres and rotational speed in rpm. Divide a millimetre nameplate by 1000, or multiply inches by 0.0254, before calling. Airflow is returned in m³/s with m³/h and CFM companions.
Why does a real fan move less air than this result?
Because the result is the ideal displacement of the blade disk. Blade angle, the hub that blocks part of the disk, leaks and the resistance of the duct all reduce what a real fan delivers, so treat it as a first upper check.
How much more air does a bigger fan move?
At the same speed, flow grows with the cube of the diameter, so doubling the diameter gives eight times the ideal airflow. Doubling the speed, by contrast, only doubles it.
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/fan \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"diameter":0.4,"speed":1500}'const res = await fetch("https://api.kit.forhosting.com/phys/fan", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"diameter": 0.4,
"speed": 1500
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/fan",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"diameter": 0.4,
"speed": 1500
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/fan", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"diameter":0.4,"speed":1500}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"diameter":0.4,"speed":1500}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/fan", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"diameter": 0.4,
"speed": 1500
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.fan",
"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
Negative diameter or negative speed is rejected as invalid_input rather than producing a signed volume that has no meaning for a physical fan.
What fan airflow means and which two quantities you need to send
Delivering diameter, speed, swept_area, axial_velocity, airflow, airflow_m3_h, airflow_cfm, 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 arithmetic.
How this calculator validates input and applies Q = (π/4) D³ (N/60)
Numeric strings that parse to finite numbers are accepted so forms and CSV-style pipelines can pass values without an extra cast. Diameter and speed must not be negative; a signed impeller size or a reverse-signed RPM is rejected with a clear message because a physical fan does not deliver a negative volume in this geometric model. Zero diameter or zero speed is allowed and yields zero airflow, which is the honest result of a disk that does not exist or does not turn. There is no efficiency correction, no static-pressure derating, and no unit auto-conversion; convert millimetres to metres yourself by dividing by one thousand before sending. Send a JSON body with diameter and speed. 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: diameter also accepts d, D, diameter_m, dia, and fan_diameter; speed also accepts rpm, n, N, rotational_speed, speed_rpm, and revolutions_per_minute. After validation, swept_area is computed as pi times diameter squared over four, axial_velocity as diameter times speed over sixty, and airflow as their product — equivalently (pi/4) times diameter cubed times speed over sixty. Companions airflow_m3_h and airflow_cfm convert that SI rate with an exact 3600 factor and the international foot of 0.3048 metres, so cubic feet per minute never depend on a rounded 2118.88 shortcut. 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. Choose units consistently — if diameter is in metres and speed is in revolutions per minute, airflow is true SI cubic metres per second, airflow_m3_h is cubic metres per hour, and airflow_cfm is cubic feet per minute. Wire the endpoint into HVAC worksheets, contest answer checkers, or preprocessing steps where you already prefer explicit domain errors — such as rejecting a negative diameter — over opaque black-box widgets that cannot explain why a bad input was refused.
Integration use cases
Homework and lab fan-law drills
Students and graders confirm Q = (π/4) D³ (N/60) for given diameter and speed, with a clear invalid_input rejection when diameter or speed is negative.
Technical questions
How do I compute fan airflow with this API?
Send a JSON body with diameter in metres and speed in revolutions per minute to phys.fan. The response returns diameter, speed, swept_area, axial_velocity, airflow in m³/s, airflow_m3_h, airflow_cfm, unit, formula, and method.
What does the fan airflow calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.