Flow Rate Calculator

Background.

Volumetric flow rate answers a simple, practical question: how much fluid passes a given cross-section of pipe every second, minute, or hour? This calculator applies the continuity equation, Q = A·v, where A is the pipe's cross-sectional area and v is the mean flow velocity, converting a single pipe-diameter-and-velocity pair into seven different flow-rate expressions at once — cubic meters per second, liters per second, liters per minute, cubic meters per hour, US gallons per minute, and cubic feet per minute — so you never have to hunt for a separate unit-conversion tool after getting your answer.

The underlying idea is one of the oldest and most useful results in fluid mechanics: for an incompressible fluid moving steadily through a pipe, the same volume must pass every cross-section per unit time, so as a pipe narrows, the fluid speeds up, and as it widens, the fluid slows down — the volume swept per second, A·v, stays constant along the pipe (this is the same principle that makes water shoot out faster when you partially cover a garden hose's nozzle with your thumb). This calculator only asks for a single diameter and velocity because it computes Q at one cross-section; if you need to find the velocity at a second, differently-sized cross-section downstream, you can set A₁v₁ = A₂v₂ and solve for the unknown.

Engineers, plumbers, and HVAC technicians reach for flow-rate calculations constantly: sizing a pump to deliver a target GPM, checking whether an existing pipe can carry a required flow without excessive velocity (which drives up both pressure drop and erosion risk), or converting a manufacturer's rated flow velocity into a number that matches a water bill, an irrigation schedule, or a fire-sprinkler code requirement. Because the industries that use flow rate rarely agree on units — plumbing codes in the US commonly specify gallons per minute, European and scientific contexts use liters per minute or cubic meters per hour, and HVAC airflow is usually rated in cubic feet per minute — this calculator computes every common unit from the same two inputs rather than forcing you to pick one and convert by hand.

It is worth being explicit about what this calculator is not. Quanta already has a dedicated Bernoulli's equation calculator, which solves a completely different physical relationship: the energy balance between pressure, velocity, and elevation along a streamline (P + ½ρv² + ρgh = constant). Continuity (Q = Av, this page) and Bernoulli's equation (energy conservation) are complementary tools that are almost always used together in a real problem — continuity is what lets you relate the velocity at two different pipe diameters in the first place, and Bernoulli's equation then tells you what that velocity change does to the pressure — but they answer different questions and this page deliberately keeps its scope to the flow-rate question alone.

What is flow rate calculator?

Volumetric flow rate (commonly denoted Q) is the volume of fluid that crosses a given surface — almost always a pipe's cross-section — per unit time, with SI units of cubic meters per second. For steady flow of an incompressible fluid through a cross-section of area A at mean velocity v, the volume swept past that cross-section in one second is exactly a cylinder of length v and cross-sectional area A, giving the simple relationship Q = A·v, sometimes written with an overbar on v to emphasize that it is an average velocity across a cross-section where the real velocity profile varies (fastest at the pipe's centerline, zero at the pipe wall due to viscous no-slip).

This relationship is the practical, single-cross-section form of the continuity equation, which more generally states that for steady incompressible flow, A₁v₁ = A₂v₂ between any two cross-sections along the same flow path — mass (and, for an incompressible fluid, volume) cannot appear or disappear inside the pipe, so whatever flows past one point must flow past every other point at the same rate. The assumption of incompressibility is excellent for liquids like water under normal conditions, and reasonable for gases at low Mach numbers, but breaks down for compressible high-speed gas flow, where density itself changes along the flow path and a mass-flow-rate formulation (ṁ = ρAv) is more appropriate.

How to use this calculator.

1. 01Enter the pipe's internal diameter in millimeters.
2. 02Enter the mean flow velocity in meters per second.
3. 03Read the flow rate in liters per minute (the default primary result).
4. 04Scroll the results panel for the same flow rate expressed in m³/s, L/s, m³/h, US GPM, and CFM.
5. 05If you need pressure effects from a velocity or elevation change, follow up with the Bernoulli's equation calculator.

The formula.

The calculator first converts the entered pipe diameter from millimeters to meters, then computes the cross-sectional area of the (assumed circular) pipe as A = π(D/2)², the familiar area-of-a-circle formula applied to a pipe's internal radius. Multiplying that area by the mean flow velocity gives the volumetric flow rate in the SI base unit, cubic meters per second: Q = A·v. This is dimensionally exact — area (m²) times velocity (m/s) gives m³/s — and requires no additional physical assumption beyond incompressibility and a (reasonably) circular, fully-flowing pipe.

From that single SI value, every other displayed unit is a straightforward multiplication or division by an exact conversion factor: liters per second and liters per minute follow from 1 m³ = 1000 L exactly; cubic meters per hour follows from 1 hour = 3600 seconds exactly; US gallons per minute uses the exact 1959 international definition 1 US gallon = 3.785411784 liters; and cubic feet per minute uses the exact relationship 1 foot = 0.3048 meters, so 1 cubic foot = 0.3048³ = 0.028316846592 cubic meters. None of these conversions introduces rounding error beyond the display precision — they are exact rational multiples of the underlying SI result.

A worked example.

Frequently asked questions.

References& sources.

1. [1]State University of New York (SUNY), via OpenStax College Physics. "Flow Rate and Its Relation to Velocity." Q = Av̄, derived from Q = V/t with V = Ad.
2. [2]U.S. Department of Energy. DOE Fundamentals Handbook: Thermodynamics, Heat Transfer, and Fluid Flow, DOE-HDBK-1012/3-92 (June 1992). Continuity equation, Q = A·v, mass flow rate ṁ = ρQ.
3. [3]National Institute of Standards and Technology (2008). Special Publication 811: Guide for the Use of the International System of Units (SI), Appendix B — Conversion Factors.