This calculator links average fluid velocity, volumetric flow rate, and pipe inside diameter through the continuity equation. Choose the variable to calculate and enter the other two. It can find velocity from a known flow and pipe size, flow from velocity and diameter, or the diameter required for a target flow and velocity.
The formulas
For a full circular pipe, cross-sectional area is A = πD²/4. Continuity gives Q = A · Vf, so Vf = Q/A and D = √[4Q/(πVf)]. The calculator converts every input to SI internally before solving, then displays the result in the selected units.
Use actual inside diameter
Enter the pipe’s actual internal diameter, not just nominal pipe size. Schedule, material, and wall thickness change the bore. Because velocity varies with 1/D², a modest diameter difference can materially change the answer. If the nominal size and schedule are known, use the Pipe Size & Velocity Calculator to look up the inside diameter.
Solve in any direction
- Fluid velocity (Vf) — enter volumetric flow and actual pipe inside diameter.
- Volumetric flow (Q) — enter average velocity and actual inside diameter.
- Pipe inside diameter (D) — enter volumetric flow and the target average velocity.
Worked example
A full 4 in inside-diameter pipe carrying 100 gpm has an area of 12.566 in². The average velocity is 2.553 ft/s (0.7782 m/s). Reversing the calculation with 2.553 ft/s and a 4 in diameter returns approximately 100 gpm.
Assumptions and limits
- The pipe is full and has a circular, constant inside diameter.
- Flow is steady, and Vf is the bulk average velocity across the section rather than the local centerline velocity.
- Q is actual volumetric flow at the pipe conditions. For gases, do not mix standard flow with actual pipe volume without correcting for pressure and temperature.
- The calculation does not determine pressure drop, friction loss, or whether the resulting velocity is suitable for the service.