Flow Rate Calculator

The flow rate formula

Volumetric flow rate is the cross-sectional area of the pipe multiplied by the fluid velocity:

Q = A · v

For a round pipe the area comes from the diameter:

A = π · (d ÷ 2)²

Where:

• Q = volumetric flow rate (cubic metres per second, m³/s)
• A = cross-sectional area of the pipe (square metres, m²)
• v = average flow velocity (metres per second, m/s)
• d = inner diameter of the pipe (metres, m)
• π ≈ 3.14159

The diameter is entered in millimetres here, so it is divided by 1000 before the area is calculated. The continuity principle (A·v is constant for an incompressible fluid) means that if the pipe narrows, the velocity must rise to keep Q the same.

Worked example

Water flows through a pipe with an inner diameter of 100 mm at a velocity of 2 m/s.

• d = 100 mm = 0.1 m, so the radius r = 0.05 m
• A = π × (0.05)² = π × 0.0025 ≈ 0.007854 m²
• Q = A × v = 0.007854 × 2 ≈ 0.015708 m³/s

Convert to the everyday units:

• L/min = 0.015708 × 60000 ≈ 942.5 L/min
• US GPM = 0.015708 × 15850.3 ≈ 249.0 GPM

Quick reference (d = 100 mm pipe)

Common pitfalls

• Mixing units. Diameter must be the inner bore, not the outer or nominal size. A nominal “100 mm” pipe often has a different real internal diameter, and that small difference is squared, so it matters.
• Imperial vs US gallons. This tool uses US gallons (1 US GPM ≈ 3.785 L/min). The UK imperial gallon is about 20% larger, so do not mix the two.
• Average vs peak velocity. In real pipes the flow is faster in the centre and slower near the walls. The v you enter should be the average velocity across the section.
• Zero or empty input. A diameter or velocity of 0 simply yields a flow rate of 0 here rather than an error.