PSI to GPM Calculator
Convert pressure drop (PSI) to water flow rate (GPM) through an orifice or nozzle, or work backwards from a target flow rate to the pressure you need. Built on the industry-standard orifice formula GPM = 29.81 × Cd × d² × √ΔP.
Honest scope, read this first. The constant 29.81 is for water near 60°F through an ideal opening (Cd = 1.00). A real sharp-edged orifice plate flows about 38% less (Cd ≈ 0.62) - many online calculators hide this, so this one lets you pick the orifice type. Not for gases, steam, oils, or slurries. And note: PSI to GPM is not a unit conversion - it needs the orifice diameter, because flow depends on the opening, not just the pressure.
Calculator
0 GPM
0Liters / minute
0Cubic ft / second
0K-factor (GPM per √PSI)
0Orifice velocity (ft/s)
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0 PSI
0Kilopascals
0Bar
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Common orifice flow table (ideal opening, Cd = 1.00)
GPM of water at the given pressure drop. Multiply by your Cd (e.g. ×0.62 for a sharp-edged plate).
| Orifice diameter | 40 PSI | 60 PSI | 100 PSI |
|---|---|---|---|
| 1/16 in (0.0625) | 0.74 | 0.90 | 1.16 |
| 1/8 in (0.125) | 2.95 | 3.61 | 4.66 |
| 3/16 in (0.1875) | 6.63 | 8.12 | 10.48 |
| 1/4 in (0.25) | 11.78 | 14.43 | 18.63 |
| 5/16 in (0.3125) | 18.41 | 22.55 | 29.11 |
| 3/8 in (0.375) | 26.51 | 32.47 | 41.92 |
| 1/2 in (0.5) | 47.13 | 57.73 | 74.53 |
| 5/8 in (0.625) | 73.65 | 90.20 | 116.45 |
| 3/4 in (0.75) | 106.05 | 129.89 | 167.68 |
| 1 in (1.0) | 188.53 | 230.91 | 298.10 |
Worked examples
Example 1: 100 PSI, 1/4 in ideal orifice
GPM = 29.81 x 1.00 x 0.25^2 x sqrt(100)
= 29.81 x 0.0625 x 10
= 18.63 GPM (= 70.53 L/min)
= 29.81 x 0.0625 x 10
= 18.63 GPM (= 70.53 L/min)
Example 2: 60 PSI, 1/2 in ideal orifice
GPM = 29.81 x 0.5^2 x sqrt(60)
= 29.81 x 0.25 x 7.7460
= 57.73 GPM
= 29.81 x 0.25 x 7.7460
= 57.73 GPM
Example 3 (reverse): 50 GPM through 1/2 in, find PSI
dP = (GPM / (29.81 x Cd x d^2))^2
= (50 / (29.81 x 0.25))^2 = (50 / 7.4525)^2
= 45.01 PSI
= (50 / (29.81 x 0.25))^2 = (50 / 7.4525)^2
= 45.01 PSI
Example 4: 80 PSI, 1/8 in ideal orifice
GPM = 29.81 x 0.125^2 x sqrt(80)
= 29.81 x 0.015625 x 8.9443
= 4.17 GPM
= 29.81 x 0.015625 x 8.9443
= 4.17 GPM
Example 5: same as Ex.1 but sharp-edged plate (Cd = 0.62)
GPM = 29.81 x 0.62 x 0.25^2 x sqrt(100)
= 18.63125 x 0.62
= 11.55 GPM (38% less than ideal)
= 18.63125 x 0.62
= 11.55 GPM (38% less than ideal)
Example 6: 45 PSI, 3/8 in smooth nozzle (Cd = 0.98)
GPM = 29.81 x 0.98 x 0.375^2 x sqrt(45)
= 29.81 x 0.98 x 0.140625 x 6.7082
= 27.56 GPM
= 29.81 x 0.98 x 0.140625 x 6.7082
= 27.56 GPM
Methodology
Where 29.81 comes from
Start from the orifice equation Q = Cd × A × √(2ΔP/ρ). Plug in ΔP in PSI (1 PSI = 6,894.76 Pa), orifice area from diameter in inches, water density near 60°F, and convert m³/s to US gallons per minute. The result for an ideal opening (Cd = 1) is about 29.84; 29.81 is the rounded constant published in industry references (under 0.1% difference).
Discharge coefficients
| Opening type | Cd | Effective constant |
|---|---|---|
| Ideal theoretical | 1.00 | 29.81 |
| Smooth tapered nozzle | 0.98 | 29.21 |
| Rounded entry | 0.90 | 26.83 |
| Short tube | 0.82 | 24.44 |
| Sharp-edged orifice plate | 0.62 | 18.48 |
Effective constant = 29.81 × Cd.
Metric form
With diameter in millimeters and pressure drop in kPa: L/min = 0.06661 × Cd × d² × √ΔP.
Related tools and scope boundaries
- PSI conversion calculator - pure pressure unit conversion (PSI to bar, kPa, MPa...). Use it when you only need to change pressure units; use this page when you need flow rate from pressure plus an orifice size.
- Orifice flow calculator - the full Q = Cd·A√(2ΔP/ρ) orifice equation in SI units, with Torricelli and compressible gas modes. Use it for a first-principles calculation; use this page for the ready-made PSI↔GPM 29.81 shortcut with US units.
- Cv flow calculator - valve sizing with flow coefficients (Q = Cv√(ΔP/SG)). Use it for control valves; use this page for plain orifices and nozzles.
- Friction loss calculator - pressure lost to hose and pipe friction. Use it when the pressure drop comes from the pipe run itself rather than a single orifice.
Frequently asked questions
Can you convert PSI directly to GPM?
No. PSI measures pressure and GPM measures flow rate, so there is no fixed conversion between them. To get GPM from PSI you also need the size of the opening the water flows through. For a circular orifice the standard formula is GPM = 29.81 x Cd x d^2 x sqrt(dP), where d is the orifice diameter in inches, dP is the pressure drop in PSI, and Cd is the discharge coefficient of the opening.
What is the PSI to GPM formula?
GPM = 29.81 x Cd x d^2 x sqrt(pressure drop in PSI). The constant 29.81 is the theoretical value for water at about 60 F with an ideal opening (Cd = 1.00). Multiply by the discharge coefficient Cd of your actual orifice or nozzle: 1.00 ideal, 0.98 smooth tapered nozzle, 0.90 rounded entry, 0.82 short tube, 0.62 sharp-edged orifice.
Where does the constant 29.81 come from?
It comes from the orifice equation Q = Cd x A x sqrt(2 x dP / rho), with the units converted: pressure in PSI, diameter in inches, water density at about 60 F, and the result in US gallons per minute. Working it out from first principles gives about 29.84 for an ideal opening; 29.81 is the rounded constant published in industry references, a difference of under 0.1 percent.
What discharge coefficient (Cd) should I use?
Use 1.00 for the textbook ideal, 0.97 to 0.98 for a smooth tapered nozzle, 0.90 for a rounded entry, 0.82 for a short tube, and 0.61 to 0.65 for a sharp-edged orifice plate. If you are unsure and want the theoretical maximum, use 1.00. The calculator above lets you pick a preset or enter your own Cd.
Worked example: 100 PSI through a 1/4 inch orifice?
GPM = 29.81 x 1.00 x 0.25^2 x sqrt(100) = 29.81 x 0.0625 x 10 = 18.63 GPM. With a sharp-edged orifice plate (Cd = 0.62) the same setup gives 18.63 x 0.62 = 11.55 GPM.
How do I calculate PSI from GPM (reverse)?
Rearrange the formula: dP = (GPM / (29.81 x Cd x d^2))^2. Example: 50 GPM through a 1/2 inch ideal orifice needs (50 / (29.81 x 0.25))^2 = (50 / 7.4525)^2 = 45.01 PSI of pressure drop.
Does this work for fluids other than water?
Only with a correction. For another liquid, divide the result by the square root of its specific gravity: GPM_fluid = GPM_water / sqrt(SG). Viscous fluids such as oils also need a Reynolds-number correction because the discharge coefficient drops at low Reynolds numbers. The 29.81 constant is for water near 60 F.
Can I use this for air or compressed gas?
No. Gases are compressible, so the simple orifice formula does not apply; you need the expansion factor Y and the specific-heat ratio of the gas. Use a compressible-flow orifice calculator for air, natural gas, or steam instead.
What is the K-factor and how does it relate to PSI and GPM?
The K-factor is shorthand for everything except the pressure term: K = 29.81 x Cd x d^2, so GPM = K x sqrt(dP). A 1/4 inch ideal orifice has K = 1.863125. Fire protection uses the same idea: sprinkler K-factors relate flow to the square root of pressure.
Why does the calculator also show velocity?
Velocity through the orifice is Q/A. Very high velocity causes erosion, noise, and water hammer. As a rule of thumb, keep water velocity under about 5 ft/s in piping; the orifice throat itself is much faster (for example 121.77 ft/s in the 100 PSI, 1/4 inch example), which is normal for an orifice but hard on downstream piping.
Should I use gauge or absolute pressure?
Use the pressure DROP across the orifice (upstream minus downstream). If the orifice discharges to atmosphere, the upstream gauge PSI is the pressure drop. Do not use absolute pressure unless the downstream side is a vacuum.
Why do different PSI to GPM calculators give different answers?
Because they assume different discharge coefficients without saying so. A calculator using Cd = 0.65 has an effective constant of 29.81 x 0.65 = 19.38, so it reports about 35 percent less flow than the ideal 29.81 formula. Always check which Cd a calculator assumes before comparing results.
How big is the difference between a sharp orifice and a smooth nozzle?
Large. At the same pressure and diameter, a smooth tapered nozzle (Cd = 0.98) flows about 58 percent more than a sharp-edged orifice plate (Cd = 0.62), because 0.98 / 0.62 = 1.5806. This is why the orifice-type selector on this calculator matters.
Is there a metric version of the formula?
Yes. With diameter in millimeters and pressure drop in kPa: L/min = 0.06661 x Cd x d_mm^2 x sqrt(dP_kPa). Example: 100 kPa through a 6.35 mm (1/4 inch) ideal orifice gives 0.06661 x 40.3225 x 10 = 26.86 L/min, which matches the imperial calculation of 7.10 GPM x 3.78541.
What are the limits of this calculator?
It assumes liquid water near 60 F, fully turbulent flow, a thin-plate orifice or nozzle with a stable discharge coefficient, and pressure drop measured close to the orifice. It is not for gases, steam, slurries, very viscous oils, or laminar flow, and it is an estimate, not a substitute for engineered flow measurement.
Is PSI to GPM the same as a PSI unit converter?
No. A PSI converter changes pressure units (PSI to bar, kPa, MPa) with exact constants and needs no other input. PSI to GPM needs the orifice diameter and a discharge coefficient because flow depends on the opening, not just the pressure. For pure pressure unit conversion, use our PSI conversion calculator.
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