Flow Rate Calculator
Continuity — narrow the pipe, speed up the fluid.
Work out Flow Rate. Continuity — narrow the pipe, speed up the fluid. Names the assumption that breaks it.
Speed at point 2
8 m/s
4× faster · 20 L/s
A₁v₁ = A₂v₂. Mass is conserved, so narrowing a pipe must speed the fluid up in exact proportion to the area lost. Because area goes as the square of radius, halving a pipe's diameter quarters the area and therefore quadruples the speed. That is why a thumb over a hose produces a jet, and why the flow accelerates through any restriction whether you want it to or not.
How the Flow Rate Calculator works
Enter the cross-section and speed at one point and the cross-section at another for the speed there, plus volumetric and mass flow. Area goes as the square of radius, so halving a pipe's diameter quadruples the speed.
Also known as: continuity equation calculator · pipe flow velocity calculator · a1v1 = a2v2 calculator · volumetric flow rate calculator
Frequently asked questions
What is the continuity equation?
A₁v₁ = A₂v₂ for an incompressible fluid. Mass is conserved, so whatever passes one cross-section per second must pass every other one too.
Why does a thumb over a hose make a jet?
You cut the area dramatically, and the same volume per second has to get through, so the speed rises in exact proportion. The flow rate barely changes; the velocity changes enormously.
How do I convert to litres per minute?
Multiply the volumetric flow in m³/s by 60,000. A flow of 0.001 m³/s is 60 L/min.
Does this apply to gases?
Only at low speeds, where the gas is effectively incompressible. Above roughly a third of the speed of sound, density changes along the pipe and the compressible form is needed.
Put this calculator on your own site
Free to use, on any site, commercial or not. Paste this where you want it to appear. It is a plain iframe, so it works in WordPress, Squarespace, Wix, Webflow, Ghost and anything else that accepts HTML.
<iframe src="https://www.thecalclibrary.com/embed/flow-rate-calculator" width="100%" height="640" style="border:1px solid #e2e8f0;border-radius:12px" loading="lazy" title="Flow Rate Calculator"></iframe>
<p style="font:13px/1.5 system-ui,sans-serif;margin:6px 0 0;color:#64748b">Powered by <a href="https://www.thecalclibrary.com/flow-rate-calculator" style="color:#64748b">Flow Rate Calculator</a> from The Calc Library</p>The only condition is that the credit line below the frame stays in place. That one line is what pays for the tool being free — it is how anyone else finds it.
Related calculators
Bernoulli Equation Calculator
Pressure along a streamline — and why faster means lower.
OpenPoiseuille's Law Calculator
The fourth power on radius that dominates everything.
OpenReynolds Number Calculator
Laminar, transitional or turbulent.
Open