PSI to GPM Calculator — Pressure to Flow Rate (Orifice Discharge)
Pressure (PSI) alone does not give flow rate — you also need the orifice size. Enter gauge pressure, orifice diameter and geometry type, and the calculator applies the standard discharge formula to give GPM, L/min and m³/h.
psi
inches
Orifice geometry (Cd)
US gallons per minute — formula: Q = 29.84 × Cd × d² × √P
- 1
Orifice area factor (d²)
0.5 × 0.5 = 0.25 - 2
Pressure head (√P)
√40 = 6.3246 - 3
Flow rate (Q = 29.84 × Cd × d² × √P)
29.84 × 0.61 × 0.25 × 6.3246 = 28.78
How does this calculator work?
Flow rate through a water orifice: Q (GPM) = 29.84 × Cd × d² × √P, where d is orifice diameter in inches and P is gauge pressure in psi. Sharp-edged orifice Cd = 0.61; smooth nozzle Cd ≈ 0.82–0.98. Double the diameter to quadruple the flow; doubling pressure increases flow by √2 ≈ 1.41×.
Formula
How this is calculated
This calculator uses the orifice discharge formula derived from Bernoulli's equation and Torricelli's theorem for incompressible fluids. Starting from Q = Cd × A × √(2ΔP/ρ), where A is the orifice area (m²), ΔP is the pressure difference across the orifice (Pa), and ρ = 1 000 kg/m³ for water, the formula is rearranged and unit-converted to yield Q (GPM) = 29.84 × Cd × d² × √P, where d is in inches and P is the upstream gauge pressure in psi.
The discharge coefficient Cd accounts for the fact that real jets contract (vena contracta) and have friction losses. A sharp-edged circular orifice has Cd ≈ 0.61; a square-edged hole ≈ 0.70; a well-rounded entrance nozzle ≈ 0.82; a smooth converging nozzle ≈ 0.98. Fire hydrant flow testing typically uses Cd = 0.90. Irrigation nozzle manufacturers often publish their own Cd values.
Limitations: the formula assumes turbulent, incompressible, steady water flow with no back-pressure downstream. It is not suitable for gases, steam, two-phase flow, or very small Reynolds numbers (Re < ~1 000). At very high pressures (> 500 psi) compressibility corrections may apply. Pipe flow with significant length and friction requires the Hazen-Williams or Darcy-Weisbach equation instead.
Frequently asked questions
PSI is potential energy (pressure) per unit volume. To get flow rate you need to know how fast the fluid can escape — which depends on the orifice area and the discharge coefficient of the opening. The orifice formula Q = 29.84 × Cd × d² × √P combines both.
Use 0.61 for a sharp-edged plate orifice (the most common textbook case), 0.82–0.98 for smooth nozzles, and 0.90 for fire hydrant butt nozzles. When in doubt, err low (0.61) for a conservative estimate.
Not directly. The formula uses ρ = 1 000 kg/m³ (water). For air or other gases the density changes with pressure and temperature, and compressibility must be accounted for using the isentropic flow expansion factor. Use a dedicated gas-flow calculator for those cases.
Also known as
TG we-Calculate Editorial Team. (2026). PSI to GPM Calculator — Pressure to Flow Rate (Orifice Discharge) [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/psi-to-gpm-calculator
TG we-Calculate Editorial Team. "PSI to GPM Calculator — Pressure to Flow Rate (Orifice Discharge)." TG we-Calculate. 2026. https://we-calculate.com/calculator/psi-to-gpm-calculator.
TG we-Calculate Editorial Team, "PSI to GPM Calculator — Pressure to Flow Rate (Orifice Discharge)," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/psi-to-gpm-calculator
@misc{wecalculate_psi_to_gpm_calculator, title = {PSI to GPM Calculator — Pressure to Flow Rate (Orifice Discharge)}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/psi-to-gpm-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?