PSI to GPM Calculator
Convert PSI to GPM Calculator between units instantly. Includes conversion tables, common equivalents, and calculation formulas.
PSI to GPM Calculator
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Formula: GPM = Cd x A x sqrt(2 x g x h) x 448.831
Worked example — Approximately 35.24 GPM at 60 PSI through a 0.5-inch orifice
Formula
GPM = Cd x A x sqrt(2 x g x h) x 448.831
This calculator uses the orifice flow equation. Pressure in PSI is first converted to head in feet (h = PSI x 2.31). The orifice area A is calculated from the diameter. The discharge coefficient Cd accounts for flow losses. Velocity is found from v = Cd x sqrt(2gh), and volumetric flow is converted from cubic feet per second to gallons per minute.
Worked Examples
Example 1: Residential Water Flow
Problem:A home has 60 PSI water pressure with a 0.5-inch supply line. What is the maximum flow rate?
Solution:Head = 60 x 2.31 = 138.6 ft Area = PI x (0.25)^2 = 0.1963 sq in = 0.001364 sq ft Velocity = 0.61 x sqrt(2 x 32.174 x 138.6) = 57.57 ft/s Flow = 0.001364 x 57.57 = 0.0785 cfs GPM = 0.0785 x 448.831 = 35.24 GPM
Result:Approximately 35.24 GPM at 60 PSI through a 0.5-inch orifice
Example 2: Fire Sprinkler Calculation
Problem:A sprinkler head operates at 25 PSI with a 0.375-inch orifice and Cd of 0.75.
Solution:Head = 25 x 2.31 = 57.75 ft Area = PI x (0.1875)^2 = 0.1104 sq in = 0.000767 sq ft Velocity = 0.75 x sqrt(2 x 32.174 x 57.75) = 45.73 ft/s Flow = 0.000767 x 45.73 = 0.03507 cfs GPM = 0.03507 x 448.831 = 15.74 GPM
Result:Approximately 15.74 GPM at 25 PSI through the sprinkler head
Frequently Asked Questions
How do you convert PSI to GPM?
PSI (pounds per square inch) measures pressure while GPM (gallons per minute) measures flow rate, so a direct conversion requires knowing the pipe or orifice diameter and a discharge coefficient. The method first converts PSI to a pressure head in feet using the factor 2.31 feet per PSI, then applies the orifice flow equation Q = Cd * A * sqrt(2gh) to get volumetric flow. Finally, the result is converted from cubic feet per second to gallons per minute using the factor 448.831.
What is the discharge coefficient and what value should I use?
The discharge coefficient (Cd) accounts for energy losses as fluid passes through an orifice or nozzle. A standard sharp-edged orifice has a Cd around 0.61, while a well-rounded nozzle can be 0.95 to 0.98. Fire hose nozzles typically use 0.97, and partially open valves range from 0.3 to 0.7 depending on the valve type and position. If you are unsure, 0.61 is the most common default for general orifice calculations.
Why does pipe diameter have such a large effect on flow rate?
Flow rate depends on the cross-sectional area of the pipe, which scales with the square of the diameter. Doubling the pipe diameter quadruples the area, which can roughly quadruple the flow rate at the same pressure. This is why even small increases in pipe size lead to significant increases in water delivery capacity, making pipe sizing one of the most important decisions in plumbing and hydraulic system design.
What is the relationship between PSI and water pressure head?
Water pressure head expresses pressure as the height of a column of water that would produce that pressure. One PSI equals approximately 2.31 feet of water head, or equivalently, a column of water 2.31 feet tall exerts a pressure of 1 PSI at its base. This conversion is derived from the density of water (62.4 lb/ft3) and is fundamental in hydraulic engineering for calculating pump requirements, flow through pipes, and sprinkler system design.
Why does flow rate rise with the square root of pressure instead of doubling when pressure doubles?
The orifice equation sets velocity as v = Cd x sqrt(2gh), so velocity, and therefore volumetric flow, follows the square root of the pressure head. Doubling the supply pressure multiplies flow by sqrt(2), roughly 1.41, not by two. Quadrupling pressure is what doubles GPM. This is why boosting pressure gives disappointing returns compared with enlarging the opening, whose area grows with the square of diameter.
What is the difference between static pressure and residual pressure in a water system?
Static pressure is the gauge reading with no water moving, and it reflects only elevation and supply head. Residual pressure is the reading while flow is occurring, after friction in pipe, fittings and meter has consumed part of that head. Flow calculations should use residual pressure at the outlet, because using static pressure assumes zero losses and overstates GPM, sometimes badly on long or undersized service lines.
How does the Hazen-Williams equation estimate friction loss along a pipe run?
Hazen-Williams models head loss in full-flowing water pipe as proportional to flow raised to about 1.852 and inversely proportional to the roughness coefficient C raised to 1.852 and to diameter raised to roughly 4.87. Because the diameter exponent is so large, a small increase in bore cuts friction loss dramatically. C values run high for smooth plastic and copper and lower for old, tuberculated steel or cast iron.
What is the difference between GPM, cubic feet per second and litres per minute?
All three measure volumetric flow and differ only in the unit of volume and time. One cubic foot per second equals 448.831 gallons per minute, and one US gallon per minute equals 3.78541 litres per minute. Engineers use cfs for streams and large mains, GPM for plumbing and pumps, and LPM for metric pump curves. Converting is pure arithmetic and needs no pressure or pipe data.
Why does pipe velocity matter as well as flow rate?
Velocity, not GPM alone, drives noise, water hammer and erosion of pipe walls, and it also sets how fast friction consumes head, since loss rises steeply with speed. Designers therefore size pipe so velocity stays within a moderate band rather than simply meeting a GPM target. A pipe that delivers the required flow at an excessive velocity will be noisy and will waste pressure over its length.
When should I use an orifice calculation instead of a full pipe-flow calculation?
Use the orifice form when the restriction dominates, such as a nozzle, sprinkler head, hose bib or a hole in a tank wall, where nearly all the pressure drop happens at one small opening. Use a pipe-flow method such as Hazen-Williams or Darcy-Weisbach when the run is long and friction along its length controls the result. Real systems often need both, added as losses in series.
References
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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