Flow rate calculator
A section of 0.01 square metres with fluid moving at 1.5 metres per second carries 0.015 cubic metres per second. Enter the mean velocity and either the cross-section area or the internal pipe diameter to get the flow rate. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Area
- 0.01
- Mean fluid speed
- 1.5
- Flow rate
- 0.015 m3/s
This flow rate calculator returns volumetric discharge in cubic metres per second from a mean fluid velocity and either a measured pipe cross-sectional area or a circular internal diameter. Continuity says the volume that crosses a filled section per unit time is Q equals A times v; when only a diameter is known, the engine first forms A as pi D squared over four, then multiplies by velocity. A two-hundred-millimetre circular pipe at one and a half metres per second therefore carries pi times zero point zero one five cubic metres per second.
What volumetric flow rate is and how area or diameter enter the product
Volumetric flow rate, written Q in SI, is the volume of fluid that crosses a control surface per unit time, and its coherent unit is the cubic metre per second. For a duct or circular pipe that is running full, the kinematic definition is Q equals A times v, where A is the internal cross-section area in square metres and v is the mean speed of the fluid normal to that section in metres per second.
When the velocity profile is not uniform, v is understood as the area-averaged speed so that the product still equals the true integrated discharge. Diameter that is zero or negative is rejected because a circular pipe cannot have a non-positive diameter, while a missing pair of area and diameter is also rejected. Zero area is allowed and yields zero flow.
The engine is a handful of arithmetic operations on finite scalars, fully deterministic, with no Date, no random sampling, and no network.
Where Q from velocity and area or diameter is used in study, plant, and software
Students meet volumetric flow rate when a textbook introduces continuity, when a lab asks for discharge from a measured internal diameter and an average velocity, or when an energy balance needs volume per second before density converts it to mass flow. Teachers can pre-generate answer keys for modest SI numbers without trusting opaque calculator apps that silently switch unit systems, drop signs on reverse flow, or treat a zero millimetre bore as a valid pipe.
Developers call the same contract from scripts to seed deterministic test vectors for HVAC sizing tools, to normalize user-entered circular-pipe data before a larger thermofluid model, or to satisfy programming-challenge statements that demand Q in cubic metres per second rather than a hand-waved sketch. Plant and field engineers use the product for quick checks when a flowmeter reports speed and the internal diameter is known from the schedule, or when a rectangular duct already has a tabulated area.
Product and education tools use the rewrite when a learner types diameter and speed and the UI must show discharge with a clean formula string that names pi D squared over four. Keep v in metres per second and A or D in metres so the returned Q is a true cubic metre per second, and pair this page with dedicated converters when you need gallons per minute or litres per hour after the SI discharge is known.
What you can do with it
Circular-pipe discharge from diameter and speed
Turn a measured internal diameter and mean fluid velocity into Q in cubic metres per second for lab reports, continuity homework, and first-pass pipe checks.
Duct and known-area flow checks
When the cross-section is already tabulated in square metres, multiply by mean speed to get volumetric discharge without converting diameter first.
FAQ
What does the flow rate calculator cost?
It is free in your browser on this page.
How is Q defined when I supply a diameter instead of an area?
For a circular section the engine sets A = π D² / 4 with D in metres, then Q = A · v with v in metres per second.
What happens if diameter is zero or negative?
A physical circular pipe cannot have a non-positive diameter; the calculator will not invent a default bore.
Do I have to provide both area and diameter?
No. Provide velocity plus at least one of area or diameter. If both area and diameter are sent, diameter defines the circular section and the returned area is π D² / 4.
Which units should I use, and can velocity be negative?
Use SI: velocity in m/s, area in m², diameter in m. The result is m³/s. The tool does not convert GPM, L/h, or CFM.
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/flow-rate \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"velocity":1.5,"area":0.01}'const res = await fetch("https://api.kit.forhosting.com/phys/flow-rate", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"velocity": 1.5,
"area": 0.01
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/flow-rate",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"velocity": 1.5,
"area": 0.01
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/flow-rate", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"velocity":1.5,"area":0.01}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"velocity":1.5,"area":0.01}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/flow-rate", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"velocity": 1.5,
"area": 0.01
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.flow_rate",
"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.
Limits
max_abs_velocity | 1000000000000000 |
max_abs_area | 1000000000000000 |
max_abs_diameter | 1000000000000000 |
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
Diameter that is zero or negative is rejected as invalid_input because a physical circular section cannot have a non-positive diameter. Successful API calls cost $0.002.
What volumetric flow rate is and how area or diameter enter the product
Many field notes, catalogues, and homework statements record an internal diameter rather than an area: for a circular section the geometric identity A equals pi D squared over four converts that diameter in metres into square metres, after which the same product Q equals A times v applies without further empirical factors. This calculator returns that SI discharge and nothing else. It does not convert US gallons per minute, litres per hour, or cubic feet per minute; it does not apply a Darcy friction factor; and it does not solve compressible mass flow or Bernoulli head.
Inputs, SI units, response fields, and why diameter must be positive
If both area and diameter are present, diameter defines the section and the returned area is the computed pi D squared over four rather than the extra area field. Area alone must be non-negative; a negative geometric section is rejected, while zero area yields zero flow. Magnitudes above one quadrillion are rejected as outside the supported range. Failed validation is not billed. POST a JSON body with a required finite velocity in metres per second and at least one of area in square metres or diameter in metres. Preferred names are those canonical fields; aliases v, speed, fluid_speed, and mean_velocity are accepted for velocity, aliases A, cross_section, cross_section_area, and section_area for area, and aliases d, pipe_diameter, inner_diameter, and inside_diameter for diameter, so spreadsheets and typed forms can reuse the same contract. Each value may arrive as a JSON number or as a decimal numeric string, including scientific notation; booleans, objects, arrays, empty strings, NaN, and infinities are rejected. Diameter, when supplied, must be strictly positive: zero and negative D fail with invalid_input naming diameter, because A equals pi D squared over four is not a physical circular section for a non-positive D, and this tool does not invent a default bore. Velocity may be positive or negative; a negative speed returns a negative flow_rate so reverse or return flow can be represented without a separate direction flag. On success the body echoes velocity, the working area, the flow_rate in cubic metres per second, unit m3/s, a formula string, and a method tag; diameter is included only when it was the source of area.
Where Q from velocity and area or diameter is used in study, plant, and software
On this page the work runs entirely in your browser; through the API each successful lookup costs $0.002, failed validation is not charged, and nothing is stored after the response returns. That split — free interactive exploration and a priced, identical API — matches the rest of the KIT tier-A catalog and lets you move from a classroom demo to an automated pipeline without changing the mathematical result.
Integration use cases
Deterministic SI fixtures for software
Pin reproducible flow_rate values in unit tests, property checks, and CI assertions for HVAC or fluid-mechanics libraries that must not invent unit conversions.