Pipe Flow Rate Calculator
The volumetric flow rate through a pipe is calculated from the continuity equation Q = A v, where Q is the flow rate (m^3/s), A is the cross-sectional area of the pipe (m^2), and v is the average fluid velocity (m/s). For a circular pipe, A = pi d^2 / 4. This calculator can solve for flow rate (given diameter and velocity), velocity (given diameter and flow rate), or diameter (given velocity and flow rate). Pipe flow calculations are fundamental to plumbing, civil engineering, chemical process design, and HVAC system sizing.
Pipe flow formula
Q = A × v = (pi d² / 4) × v
Q is volumetric flow rate (m^3/s), A is cross-sectional area (m^2), v is average velocity (m/s), d is inner diameter (m). For a change in pipe diameter: A1 v1 = A2 v2 (continuity). Mass flow rate = rho Q where rho is fluid density.
Common conversions
- 1 m^3/s = 1,000 L/s = 15,850.3 US gal/min (GPM)
- 1 L/s = 15.8503 GPM
- 1 inch = 0.0254 m (pipe diameter conversion)
Frequently asked questions
What is the continuity equation for pipe flow?
The continuity equation for incompressible flow states that the volumetric flow rate Q = A v is constant along a pipe, where A is the cross-sectional area and v is the average fluid velocity. This means A1 v1 = A2 v2 at any two cross sections.
How is cross-sectional area related to diameter?
For a circular pipe, A = pi d^2 / 4, where d is the inner diameter. If you enter diameter in meters, A will be in m^2. The flow rate Q = A v will then be in m^3/s.
What units does this calculator use?
Diameter in meters (m), velocity in m/s, area in m^2, and flow rate in m^3/s. To convert m^3/s to liters per second, multiply by 1,000. To convert to US gallons per minute, multiply by 15,850.3.
What is a typical water pipe velocity?
For water distribution systems, typical velocities are 0.6 to 3.0 m/s to prevent excessive pressure drop or erosion. Above 3 m/s, erosion and noise become significant. Below 0.3 m/s, sediment can deposit in the pipe.
How does this relate to the Reynolds number?
The Reynolds number Re = rho v d / mu determines whether flow is laminar (Re below 2,300) or turbulent (Re above 4,000). At typical pipe velocities and diameters, water flow is almost always turbulent.
Official sources
- NIST: NIST Special Publication 1038 (SI Units).
- OpenStax University Physics: 14.5 Fluid Dynamics.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.