Volumetric flow rate calculator
A pipe with a 0.01 m² cross-section and fluid moving at 1.5 m/s carries 0.015 m³/s. Enter the area and the mean speed and get the discharge in matching units, with reverse flow shown as a negative value. 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
- Precision
- 10
This volumetric flow rate calculator returns the discharge Q equals area times fluid speed for any consistent pair of units. In fluid mechanics and thermofluid design the product of internal cross-section area A and mean axial speed v is the volume of fluid that crosses a section per unit time, so a pipe with A equal to zero point zero one square metres and v equal to one point five metres per second carries zero point zero one five cubic metres per second. The identity is fully deterministic: there is no empirical friction factor, no compressibility correction, and no table lookup. Negative area is rejected because a geometric section cannot be negative; signed velocity is allowed so reverse flow appears as a negative Q.
What flow rate means and what you get back
Volumetric flow rate, often written Q or sometimes V-dot, is the volume of fluid that passes through a control surface per unit time. For a duct or circular pipe with a well-defined internal cross section that is filled with fluid, the simplest and most common definition is Q equals A times v, where A is the area of that section and v is the mean speed of the fluid normal to the section.
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. Zero area is valid and simply yields zero flow; zero velocity yields zero discharge as well. If you need mass flow rate, multiply Q by density in a separate step; if you need Reynolds number, friction factor, head loss, or compressible choked flow, use tools dedicated to those models.
Where Q equals A times v fits in study, plant design, and software
Students meet volumetric flow rate when a textbook introduces continuity, when a lab asks for discharge from measured diameter and 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 numbers without trusting opaque calculator apps that silently switch unit systems or drop signs on reverse flow.
Developers call the same contract from scripts to seed deterministic test vectors for HVAC sizing tools, to normalize user-entered pipe data before a larger thermofluid model, or to satisfy programming-challenge statements that demand Q rather than a hand-waved sketch. Plant and field engineers use the product for quick checks when a flowmeter reports speed and the internal area is known from the schedule diameter. Product and education tools use the rewrite when a learner types area and speed and the UI must show discharge with a clean formula string.
What you can do with it
Homework and lab discharge checks
Compute Q = A·v from measured pipe area and mean speed, and verify discharge before writing a lab report or continuity problem.
Quick pipe and duct sizing
Convert known cross-section and design velocity into volumetric discharge for early-stage layout, spreadsheet models, and teaching demos.
FAQ
What does the volumetric flow rate calculator cost?
It is free in your browser on this page.
How is Q defined?
For cross-section area A and mean fluid speed v, Q = A·v. Keep A and v in consistent units so Q is volume per time (for example m²·m/s = m³/s).
What happens if area is negative?
A geometric cross-section cannot be negative; zero area is allowed and yields zero flow rate.
Does this tool convert units or compute mass flow?
No. It only multiplies A and v. Convert units yourself first if needed, and multiply by density separately if you need mass flow rate.
Can the fluid speed be negative?
Yes. A negative speed stands for flow in the opposite direction, so the flow rate comes out negative too. The area, on the other hand, can never be negative and is rejected if it is.
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/thermo/flow-rate \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"area":0.01,"velocity":1.5}'const res = await fetch("https://api.kit.forhosting.com/thermo/flow-rate", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"area": 0.01,
"velocity": 1.5
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/thermo/flow-rate",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"area": 0.01,
"velocity": 1.5
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/thermo/flow-rate", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"area":0.01,"velocity":1.5}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"area":0.01,"velocity":1.5}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/thermo/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
{
"area": 0.01,
"velocity": 1.5
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "thermo.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_area | 1000000000000000 |
max_abs_velocity | 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
What volumetric flow rate means and what the response contains
This calculator returns the normalized area and velocity you supplied, the product flow_rate rounded to the requested precision, the precision used, a method tag volumetric_flow_rate, and a short formula string Q equals A times v. There is no approximate CFD path and no random sampling: the engine either multiplies two finite scalars inside the supported magnitude range or rejects the input with invalid_input. Rejected cases include missing area or velocity, non-finite values, magnitudes above the documented ceiling, and any area that is strictly negative, because a negative geometric section has no meaning for this definition of discharge.
How area and velocity are read and how Q stays reproducible
Optional leading plus signs and scientific notation on numeric strings are allowed when they parse as finite decimals; embedded spaces, hex prefixes, and non-numeric tokens are rejected with a clear message so a bad cell does not become a wrong discharge. The preferred fields are area for the internal cross-section area and velocity for the mean fluid speed, but aliases A, cross_section, cross_section_area, and section_area for area, and v, speed, fluid_speed, mean_velocity, and V for velocity are accepted so spreadsheets, query strings, and typed forms can reuse the same contract. Area must be non-negative: if area is less than zero, the request fails with invalid_input explaining that Q equals A times v is undefined for negative cross-section area in this calculator. 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. An optional precision field, with aliases decimals and dp, chooses how many decimal places to expose for area, velocity, and flow_rate, defaulting to ten and capped at fifteen so JSON goldens stay stable. Pair the free browser run on this page with the priced API when you need the identical mathematical result inside an automated pipeline without re-implementing Q equals A times v yourself.
Where Q equals A times v fits in study, plant design, 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. Pair it with unit converters and other thermofluid endpoints when you are building a small lab of free, deterministic engineering helpers, and keep A and v in consistent units so the returned Q is meaningful without hidden conversion steps.
Integration use cases
Deterministic test fixtures
Generate reproducible flow_rate values for unit tests, property checks, and CI assertions in HVAC or fluid-mechanics software.
Technical questions
Can velocity be negative?
Yes. A negative velocity returns a negative flow_rate so reverse or return flow can be represented without a separate direction flag.