Flow Rate Calculator
Estimate pipe flow rate from pressure drop, dimensions, and viscosity, or use flow velocity with pipe shape. Helpful for quick fluid calculations.
Flow Rate Calculator
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What the flow rate calculator does
Flow rate is how much fluid moves past a point in a given time. This calculator finds it two ways: from the fluid's speed and the size of the pipe it flows through, or from the pressure pushing it along a narrow pipe against the fluid's own thickness. The first is the everyday method; the second applies the physics of slow, viscous flow.
Below is what flow rate means, the two methods the calculator uses, and a worked example.
How to use it
- Choose a method: from flow velocity and pipe shape, or from a pressure difference.
- Enter the values the method asks for, each with its own unit. The velocity method also lets you pick a round or rectangular pipe.
- Press Calculate for the flow rate, shown across several units, or Reset to clear it.
What flow rate is
Flow rate, usually written Q, is the volume of fluid that passes a cross-section each second. A garden hose might deliver a few litres a minute; a river, thousands of cubic metres a second. It is a measure of throughput, of how much is being moved, rather than how fast any single drop travels, though the two are closely related.
The distinction between flow rate and speed matters. A wide, slow river and a narrow, fast stream can carry the same flow rate, because the wide one makes up in area what it lacks in speed. This is why flow rate is the right quantity when you care about how much water reaches a field, fills a tank, or passes through a pump, and it is what this calculator is built around.
Flow rate from velocity and area
The most direct way to find flow rate is to multiply the fluid's speed by the area it flows through. If fluid moves at velocity v through a pipe of cross-sectional area A, the flow rate is:
Q = v × A
This is the equation of continuity, and it captures the wide-river idea exactly: throughput is speed times the area carrying it. The calculator works out the area for you from the pipe's shape, using the circle's area for a round pipe or width times height for a rectangular one, then multiplies by the velocity you enter.
Flow rate from pressure drop
The second method applies when a fluid is pushed through a narrow pipe by a pressure difference and held back by its own viscosity, its internal stickiness. For slow, smooth flow this is described by Poiseuille's law, which relates the flow rate to the pressure difference ΔP, the pipe radius r, the fluid's viscosity η, and the pipe length L:
Q = (π ΔP r⁴) ÷ (8 η L)
The striking feature here is the fourth power of the radius. Because flow rate depends on the radius to the fourth, a pipe twice as wide carries sixteen times the flow for the same push. This is why even a slight narrowing of a pipe, or an artery, chokes the flow so dramatically, and why pipe diameter is the single most powerful factor in viscous flow.
Units and precision
The calculator works in SI units, taking dimensions in metres, centimetres, or millimetres and reporting the flow rate in cubic metres per second alongside cubic metres per minute, litres per minute, and litres per second. The pressure method takes pressures in pascals and viscosity in pascal-seconds. Poiseuille's law assumes smooth, orderly flow, so it fits slow flow in narrow pipes; faster or wider flows become turbulent and need a different treatment. Results carry several decimal places.
A worked example
Suppose water flows at 2 metres per second through a round pipe 0.1 metres across.
The pipe's area is π times the square of its radius, π × 0.05² ≈ 0.00785 m². The flow rate is Q = v × A = 2 × 0.00785 ≈ 0.0157 m³/s, which is about 15.7 litres per second, or roughly 942 litres per minute. A wider pipe at the same speed would carry proportionally more.
Questions people ask
How do you calculate flow rate?
The simplest way is flow rate equals velocity times cross-sectional area, Q = vA. For pressure-driven viscous flow in a narrow pipe, Poiseuille's law relates flow rate to pressure, radius, viscosity, and length.
What is the difference between flow rate and flow speed?
Flow speed is how fast the fluid moves; flow rate is how much volume passes per second. A wide slow flow and a narrow fast one can have the same flow rate, since rate is speed times area.
Why does pipe radius matter so much?
In viscous flow, Poiseuille's law makes flow rate depend on the radius to the fourth power, so doubling the radius gives sixteen times the flow. A small narrowing reduces flow sharply.
When does Poiseuille's law apply?
For slow, smooth, orderly flow of a viscous fluid in a narrow pipe. Faster or wider flows turn turbulent and no longer follow it, needing a different model.
References
A quick note on where the physics comes from. Flow rate as velocity times area, and Poiseuille's law for viscous flow, are standard fluid mechanics, set out in OpenStax's University Physics and in Georgia State University's HyperPhysics. The SI units follow the US National Institute of Standards and Technology.
- OpenStax, University Physics Volume 1, Section 14.5, Fluid Dynamics. https://openstax.org/books/university-physics-volume-1/pages/14-5-fluid-dynamics
- OpenStax, University Physics Volume 1, Section 14.7, Viscosity and Turbulence (Poiseuille's law). https://openstax.org/books/university-physics-volume-1/pages/14-7-viscosity-and-turbulence
- National Institute of Standards and Technology (NIST), Special Publication 811, Guide for the Use of the International System of Units (SI). https://www.nist.gov/pml/special-publication-811
Bibek Lal Karna is a PhD student and graduate teaching assistant at the University of Mississippi, with deep interests in theoretical and gravitational physics. He is also the founder of NRCC and is strongly engaged in scientific teaching and communication. At Eon Tools, he reviews physics tools.