PSI to GPM Calculator

Related Calculators

Pressure (psi): Force per unit area, measured in pounds per square inch. In this calculator, it is the upstream gauge pressure for the chosen setup.

Flow rate (gpm): How many gallons of fluid move each minute.

Opening diameter (inches): The inside width of the nozzle, orifice, or pipe opening where water exits.

Outlet pressure (psi): The pressure at the exit side. For open discharge to air, gauge outlet pressure is usually 0 psi.

Discharge coefficient: A correction factor that reduces ideal nozzle flow to a more realistic estimate.

Fluid density (lb/ft^3): How heavy the fluid is for a given volume. Higher density lowers estimated speed and flow for the same pressure drop.

Exit speed (ft/s): The ideal pressure-derived speed before applying the discharge coefficient; it is not a measured jet speed or, when the coefficient differs from 1, flow divided by opening area.

Water horsepower (HP): The useful hydraulic power carried by the fluid stream, based on pressure and flow.

Mistake: Treating Pressure (psi) as enough by itself to get Flow rate .
Fix: Start with What are you calculating from? and choose the setup that matches your system before trusting the result.

Mistake: Entering the wrong size in Opening diameter (inches) , such as outside diameter instead of inside opening size.
Fix: Use the inside diameter where water actually leaves, because small diameter changes can strongly change Flow rate .

Mistake: Using Pipe exit when Outlet pressure (psi) is equal to or higher than Pressure (psi) .
Fix: Enter a lower outlet pressure than upstream pressure, or choose a different setup if the water is not exiting under a positive pressure drop.

Mistake: In Pump power mode, leaving Pump efficiency (%) blank or entering 0, 150, or another impossible value.
Fix: Enter a real efficiency between 0 and 100 so Flow rate and Water horsepower are meaningful.

Mistake: Choosing Custom density under Fluid but forgetting Fluid density (lb/ft^3) .
Fix: Enter a positive density value, or switch Fluid back to water if you want the default water assumption.

Mistake: Reading Flow per hour as a separate calculation instead of just another unit view.
Fix: Treat Flow per hour as the same flow converted from minutes to hours for tank filling or longer run-time comparisons.

• This calculator does not convert PSI to GPM directly without an assumed model. Results only apply to the selected setup.
• Nozzle or orifice mode assumes flow through an opening and uses the entered Discharge coefficient to account for losses.
• Pipe exit mode assumes negligible velocity in an upstream reservoir or plenum, an incompressible liquid, and no elevation change. It is not a general pressure-drop-to-flow model for a uniform pipe: pipe friction, fittings, roughness, valves and pump curves are not included.
• Pump power mode uses a power balance, not nozzle discharge physics, so it can differ from a real outlet-flow estimate.
• Water is used as the default fluid density. If your fluid is not close to water, use Custom density.
• Very small Opening diameter (inches) values make the estimate highly sensitive, so tiny measurement errors can noticeably change the result.
• Open air discharge is usually entered as Outlet pressure (psi) = 0 because the calculator uses gauge pressure, not absolute pressure.

How the calculator chooses the math

The first input is What are you calculating from?. That choice matters because pressure and flow are related in different ways depending on whether water leaves an opening, exits a pipe, or is limited by pump power.

Nozzle or orifice mode

This mode estimates flow through an opening using pressure drop, opening area, fluid density, and a discharge coefficient.

Q = Cd * A * sqrt(2 * DeltaP * g_c / rho)

A = pi * d^2 / 4

DeltaP = Pressure (psi) * 144

Here, Q is flow in cubic feet per second, Cd is Discharge coefficient, A is area in square feet, d is diameter in feet, DeltaP is pressure drop in pounds per square foot, rho is density in lb/ft^3, and g_c is the U.S. customary unit conversion constant 32.174 lb-ft/(lbf-s^2). The result is then converted to GPM using 448.831 gpm per ft^3/s. Default water density is 62.4 lb/ft^3 [1].

Flow rate (gpm) = Q * 448.831

Exit speed (ft/s) = sqrt(2 * DeltaP * g_c / rho)

This is ideal speed. Flow divided by the geometric opening area is Cd times this speed. A discharge coefficient can include jet contraction as well as velocity loss, so actual jet speed requires more information.

Water horsepower (HP) = Pressure (psi) * Flow rate (gpm) / 1714

Mini-example: with Pressure (psi) = 40, Opening diameter (inches) = 0.25, Discharge coefficient = 0.97, and water density 62.4 lb/ft^3, the calculator gives about 11.44 gpm and an ideal exit speed of 77.07 ft/s. Flow divided by opening area is about 74.76 ft/s for this coefficient.

Pipe exit mode

This mode uses an ideal pressure-drop-to-velocity estimate from an upstream reservoir or plenum with negligible approach speed to an outlet at the same elevation. It does not apply a discharge coefficient. Two pressure readings along a uniform pipe are not enough to determine flow with this model.

DeltaP = (Pressure (psi) - Outlet pressure (psi)) * 144

v = sqrt(2 * DeltaP * g_c / rho)

Q = A * v

Flow rate (gpm) = Q * 448.831

If Outlet pressure (psi) is equal to or greater than Pressure (psi), the calculator shows an error because there is no positive forward pressure drop to drive the estimate.

Pump power mode

This mode uses the standard hydraulic horsepower relation. Enter pump shaft input power and the pressure rise across the pump; the entered pump efficiency converts shaft power to hydraulic power. If the input is already hydraulic output power, set Pump efficiency (%) to 100. A pump curve is still needed to establish a real operating point.

Water horsepower (HP) = Pump horsepower (HP) * Pump efficiency (%) / 100

Flow rate (gpm) = Water horsepower (HP) * 1714 / Pressure (psi)

Equivalent form: Flow rate (gpm) = Pump horsepower (HP) * eta * 1714 / Pressure (psi)

Mini-example: with 5 HP, 85% efficiency, and 1000 psi, water horsepower is 4.25 HP and flow is about 7.28 gpm.

Extra displayed values

Flow per hour (gph) = Flow rate (gpm) * 60

Method used reports which formula family was applied so you can confirm the setup was correct. Important note appears when the estimate may be weak or very sensitive.

Assumptions used by the formulas

The nozzle and pipe-exit methods treat the fluid as incompressible and use pressure-drop relationships for flow speed. Real systems can differ because of pipe losses, bends, roughness, valves, and height changes. Pressure is a force per area measure [4], and pump systems often use pressure and flow together rather than as direct unit conversions [2][3].