Flow Rate Calculator
Volumetric flow rate from velocity and pipe diameter, or velocity from flow and diameter
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What this calculator computes
Flow rate is the volume of fluid passing a given point per unit time, expressed in units like gallons per minute (gpm), litres per minute (lpm), cubic feet per second (cfs), or cubic metres per second (m³/s). The calculator solves the relationship Q = A × v (volumetric flow equals cross-sectional area times average velocity) for any of the three variables given the other two, with the cross-sectional area derived from the pipe inside diameter using the cylinder formula A = π × (d/2)². Common inputs and outputs include flow in gpm or lpm, velocity in feet per second (ft/s) or metres per second (m/s), and pipe inside diameter in inches or millimetres. The relationship matters in plumbing fixture-unit calculations (where the per-fixture flow demand sums to a total system demand that determines pipe sizing), pump sizing for irrigation and hydronic systems (where the head curve specifies flow at a given pressure), HVAC duct and chilled-water sizing (where velocity limits prevent noise and erosion), and process-engineering applications across the chemical, water-treatment, and food-processing industries. The calculator assumes turbulent flow in a clean round pipe with no fittings; real-world calculations need to add pressure drop from fittings, valves, and pipe-roughness effects to reach a complete system design.
Calculator
The formula
Formula
Q = A × v = π × (d/2)² × v
Worked example
When to use this calculator
Use this calculator at the design stage of any plumbing, irrigation, hydronic, or process-piping system to verify that the chosen pipe size delivers the required flow within acceptable velocity limits. Residential plumbing typically targets 4–8 ft/s velocity in copper supply lines and 3–5 ft/s in PEX; commercial water mains can run 5–10 ft/s; HVAC chilled-water lines target 4–10 ft/s depending on pipe size and noise constraints; irrigation drip-systems run much slower, often under 5 ft/s, to limit pressure-drop on long lateral runs. The calculator does not handle pressure drop from fittings, friction losses, or pump-head requirements — those need a full hydraulic analysis with friction-factor calculations and a system-curve plot against the pump curve. It also does not handle two-phase flow or compressible-gas flow, which obey different governing equations.
Common input mistakes
- Using nominal pipe size instead of actual inside diameter. A "1-inch" PVC Schedule 40 has an ID of 1.049 inches, not 1.000 inches, and the area difference (10% larger than nominal) translates directly into a flow-rate error. Always look up the actual ID for the specific pipe type and schedule.
- Confusing volumetric flow rate (gpm, lpm) with mass flow rate (lb/min, kg/min). The two are related by fluid density and are interchangeable for liquids near reference conditions, but they diverge for gases, hot liquids, and any fluid whose density varies meaningfully with temperature. Process-engineering calculations specify which flow type is meant.
Frequently asked questions
What is a typical residential plumbing flow rate?
Residential peak flow demand typically ranges from 4 to 12 gpm depending on the number of simultaneous fixture uses. A single shower at full flow draws 2 to 2.5 gpm; a kitchen sink draws 1 to 2 gpm; a washing-machine fill peaks around 3 to 4 gpm. The fixture-unit method in the International Plumbing Code aggregates these into a peak-demand figure that determines main-line pipe sizing.
Why does pipe velocity matter?
Excessive velocity in metal pipes causes erosion of the inner wall over time, especially at fittings and elbows where flow direction changes induce turbulence. Copper supply lines typically limit velocity to 8 ft/s or less to prevent erosion and reduce noise from water hammer; PEX and PVC tolerate higher velocities. Below the lower limit, slow velocity contributes to sediment buildup and biofilm growth, particularly in long runs of dead-end piping where stagnation can support pathogens.
How do I convert gpm to lpm?
One US gallon equals 3.785 litres, so multiply gpm by 3.785 to get lpm. A 5 gpm flow is 18.93 lpm; a 10 gpm flow is 37.85 lpm. The same factor applies to gallons-per-hour to litres-per-hour conversions and any other gpm-to-lpm ratio with consistent time units.
What is the difference between gpm and cfs?
Gallons per minute (gpm) is the standard unit in residential and commercial plumbing; cubic feet per second (cfs) is the standard unit in civil engineering, hydrology, and large-scale water-supply work. The conversion is 1 cfs = 448.83 gpm, so a 1 cfs stream-flow figure equals about 450 gpm. Municipal water mains and irrigation canals typically use cfs because the flow magnitudes (hundreds to thousands of cfs) read more cleanly than the equivalent gpm figures.
How does temperature affect flow rate calculations?
Temperature affects flow rate primarily through fluid viscosity, which influences the friction factor and resulting pressure drop at a given velocity. Hot water (140°F / 60°C) has about 60% of the viscosity of cold water (50°F / 10°C), reducing pressure drop in hydronic systems compared to cold-water systems. The Q = A × v relationship itself is temperature-independent for incompressible fluids, but the velocity achievable at a given pump head changes with viscosity.