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Pipe Flow Velocity Calculator

Find the flow velocity in a pipe.

How it is calculated

The tool assumes a full, circular pipe and SI units: the volumetric flow rate Q in cubic metres per second and the inside diameter d in metres. First it finds the cross-section, then the mean velocity:

A = π × (d / 2)²
v = Q ÷ A

It reports v in m/s with four decimals and A in m² with six. Flow can be 0 or more (zero gives zero velocity); the diameter must be above 0. Since the result is an average over the cross-section, the velocity at the pipe wall is lower and at the centre higher. Use the inside diameter, not the outside one, and convert litres per second or gallons per minute to m³/s first (1 L/s = 0.001 m³/s).

Worked example

Water flows at 5 litres per second through a pipe with an inside diameter of 50 mm. Convert: Q = 0.005 m³/s and d = 0.05 m. Area: A = π × (0.025)² = 0.001963 m². Velocity: v = 0.005 ÷ 0.001963 = 2.5465 m/s. If the same flow went through a pipe of half the diameter, the area would be four times smaller and the velocity four times higher, about 10.19 m/s.

Try this example →

Common mistakes

  • Entering the diameter in millimetres, such as 50. The field expects metres: 50 gives an area of nearly 2,000 m² and a velocity of 0.0025 m/s. Enter 0.05.
  • Entering flow in litres per second or gallons per minute without converting. The flow field is in m³/s, so 5 L/s must be typed as 0.005.
  • Using the outside diameter of the pipe. The fluid only occupies the bore, so use the inside diameter, which is smaller by twice the wall thickness.
  • Entering the radius where the diameter is expected. Velocity then comes out four times too high, because area depends on the square of the diameter.
  • Treating the result as a limit check. It is an average for a full pipe running at steady flow; part-full pipes and fittings are not modelled.

About this calculator

This calculator finds flow velocity using v = Q/A, where Q is the volumetric flow rate and A is the pipe's cross-sectional area (πr² for a circular pipe) — a direct application of the continuity principle, which states that for an incompressible fluid, velocity must increase in a narrower pipe to keep the same volume moving through per unit time.

Plumbers and HVAC technicians sizing pipes to avoid excessive noise or erosion from high velocity, civil and mechanical engineers designing water distribution or irrigation systems, and engineering students working through fluid mechanics problems use this.

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Comments (1)

  • Editorial team

    Use the pipe's inside diameter, not the nominal size stamped on it, because the real bore is often noticeably different and the diameter enters the formula squared. The result is a mean velocity for a full pipe only and says nothing about pressure loss. Compare it with the velocity limit given in your own design guide or standard. What fluid and pipe material are you sizing for?

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