PSI to GPM Calculator
This calculator converts water pressure (PSI) to flow rate (GPM) using two industry-standard methods: the Hazen-Williams equation for pipe flow (choose pipe size, material, and length) and the orifice equation (Q = K * sqrt(P)) for nozzles, hydrant outlets, and sprinkler heads. Switch modes to solve in reverse, entering GPM to find the required pressure. Results update as you type.
Formula
Worked example
A 1-inch PVC pipe (C = 150) that is 100 feet long with 60 PSI inlet pressure and free discharge: dP = 60 - 0 = 60 PSI; Q = 0.442 * 150 * 1^2.63 * (60/100)^0.54 = 0.442 * 150 * 1 * 0.781 = 51.8, which gives approximately 7.3 GPM. Water velocity in the 1-inch pipe: 7.3 / (7.48 * pi * (1/24)^2 * 60) = about 3.7 ft/s, within the safe 2 to 8 ft/s range.
PSI and GPM measure different things
PSI (pounds per square inch) measures pressure, meaning the force the water exerts on the walls of the pipe or container. GPM (gallons per minute) measures flow rate, meaning the volume of water moving past a point each minute. These two quantities are related but not directly interchangeable. To find GPM from PSI you also need to know the pipe diameter, the pipe length, the pipe material, and whether you are dealing with a long pipe run or a short nozzle or orifice opening. That is why this calculator asks for those additional inputs.
Two calculation methods: Hazen-Williams vs orifice (Bernoulli)
The Hazen-Williams equation is the industry standard for pipe flow. It accounts for pipe friction through the roughness coefficient C (150 for smooth PVC, 100 for old corroded steel) and models how pressure drops along the length of the pipe. Use it for supply lines, irrigation mains, domestic plumbing, and any situation where the pipe run is the dominant factor. The orifice equation (Q = 29.84 * Cd * d^2 * sqrt(P)) comes from Bernoulli's principle and is used for short openings like nozzles, fire hydrant outlets, sprinkler heads, and hose bibs where the pipe length is negligible. The discharge coefficient Cd (0.7 to 0.9) accounts for energy lost at the outlet edge.
How to read the velocity output
Water velocity in the pipe is a key design check. Below 2 ft/s, sediment and biofilm can accumulate. Above 8 ft/s, you risk erosion of the pipe wall, water hammer when valves close, and noise. Most plumbing codes recommend 2 to 4 ft/s for return lines and up to 8 ft/s for pressure supply lines. If your velocity is outside this range, try a larger pipe diameter (which raises velocity at low flow or lowers it at high flow) or adjust the pressure to match your target flow.
Pipe material and the Hazen-Williams C factor
The Hazen-Williams C coefficient is a single number that summarises how smoothly water flows through a pipe. New PVC and HDPE score around 150, the highest common rating. New copper and ductile iron score 130 to 140. Steel drops from about 120 when new to 100 or below when corroded. Older concrete can fall below 110. Choosing the wrong material in this calculator will shift your GPM estimate by 20 to 50 percent, so match the material to what is actually installed. When in doubt, use a lower C to be conservative and size up your pipe.
Typical GPM by pipe size and pressure (PVC, 100 ft run)
| Pipe diameter | 20 PSI | 40 PSI | 60 PSI | 80 PSI | 100 PSI |
|---|---|---|---|---|---|
| 1/2 in (0.5") | 1.0 | 1.5 | 2.0 | 2.4 | 2.7 |
| 3/4 in (0.75") | 2.0 | 3.1 | 4.0 | 4.8 | 5.5 |
| 1 in (1") | 3.7 | 5.7 | 7.3 | 8.8 | 10.0 |
| 1-1/2 in (1.5") | 9.2 | 14.1 | 18.1 | 21.5 | 24.5 |
| 2 in (2") | 18.0 | 27.5 | 35.4 | 42.1 | 48.1 |
| 3 in (3") | 52.5 | 80.3 | 103.3 | 122.9 | 140.2 |
| 4 in (4") | 110.8 | 169.4 | 218.1 | 259.5 | 296.1 |
Flow rates calculated using the Hazen-Williams equation with C = 150 (PVC), 100-foot pipe, free discharge. Use these as a quick sanity check only; your actual result depends on pipe condition and fittings.
Frequently asked questions
Can I convert PSI directly to GPM without knowing the pipe size?
No. PSI and GPM measure fundamentally different things (pressure vs. volume flow), so you cannot convert one to the other without at least knowing the pipe or orifice diameter. For a pipe system you also need the pipe length and material. For a nozzle or sprinkler, you need the orifice diameter and discharge coefficient. Enter those values and this calculator does the rest.
What is the Hazen-Williams equation?
The Hazen-Williams equation is Q = 0.442 * C * D^2.63 * (dP / L)^0.54, where Q is flow in GPM, C is the roughness coefficient (150 for PVC), D is inside diameter in inches, dP is the pressure drop across the pipe in PSI, and L is the pipe length in feet. It was developed in the early 1900s specifically for water in pipes and is widely used in civil and plumbing engineering because it is simpler to apply than the Darcy-Weisbach equation while being accurate enough for most practical work.
What is the orifice formula Q = K * sqrt(P)?
This is a simplified form of Torricelli's theorem (derived from Bernoulli's equation). For a circular orifice, the full form is Q = 29.84 * Cd * d^2 * sqrt(P), where Cd is the discharge coefficient (0.7 to 0.9 depending on outlet shape), d is the orifice diameter in inches, and P is the pressure in PSI. It is commonly used to size fire hydrant outlets, sprinkler nozzles, and hose connections from a pitot gauge pressure reading.
What is a good water velocity in a pipe?
For domestic water supply, 2 to 4 ft/s is typical for return or low-pressure lines, and up to 8 ft/s is generally acceptable for pressurised mains. Industrial and fire protection systems sometimes allow higher speeds, but above 8 ft/s you risk noise, erosion, and water hammer. Below 2 ft/s, sediment can settle and biofilm can grow. Use the velocity output in this calculator to check whether your pipe is sized correctly.
How do I account for fittings and valves?
This calculator uses the Hazen-Williams equation for straight pipe only and does not include minor losses from elbows, tees, valves, or reducers. A common rule of thumb is to add 10 to 30 percent to the calculated pipe length as an allowance for fittings (known as the equivalent length method). For critical designs, use published K-values or equivalent lengths for each fitting and add them to the total pipe length before entering it here.
What is the discharge coefficient (Cd)?
The discharge coefficient Cd accounts for real-world energy losses at an orifice or nozzle exit, which are not captured by ideal Bernoulli flow. A smooth, rounded edge allows water to exit with minimal turbulence and has Cd = 0.9 (10 percent energy loss). A square or sharp-edged orifice has Cd = 0.8, and an orifice that projects into the barrel (such as a re-entrant tube) drops to Cd = 0.7. The lower the Cd, the less flow you get at the same pressure.
Why does my GPM seem low compared to what my supplier told me?
Several factors reduce real-world flow below the calculated ideal: fittings and bends add pressure loss, partial pipe scale or corrosion reduces effective diameter and lowers the C factor, and the pressure at the meter may be lower than the static pressure reading when flow is occurring. Try setting a lower C (simulating an older pipe) or adding 20 to 30 percent to your pipe length to approximate fitting losses, and check whether your pressure was measured under flowing or static conditions.