PSI to GPM Calculator

Why a direct PSI to GPM conversion is a myth

Search for a psi to gpm conversion and you will find charts offering a single multiplier. They are all wrong, and it is worth being precise about why, because the reason tells you what to measure instead.

PSI — pounds per square inch — is a pressure: force divided by area. It describes how hard the water is being pushed, and it says nothing at all about whether any water is moving. A sealed pipe with a closed valve can sit at 80 psi forever at exactly zero flow. GPM — gallons per minute — is a volumetric flow rate: volume divided by time. It describes how much water actually arrives, and it says nothing about how hard it was pushed to get there.

These are different dimensions in the strict physical sense, so no conversion factor links them any more than one links degrees Celsius to kilograms. What exists is a relationship, and it needs a third thing: the geometry the water passes through. Supply a diameter and the question becomes answerable. That is why every input box above asks for one, and why any PSI/GPM calculator that turns psi to gallons per minute without asking for a diameter is guessing on your behalf.

How to calculate GPM from PSI through a nozzle or orifice

When water leaves a hole into open air, the useful model is orifice discharge. Bernoulli's equation says the pressure energy converts into velocity, giving a jet speed of √(2P/ρ). Multiply that speed by the area of the hole and you have a volume per second; correct it for the fact that real jets contract and rub, and convert the units into inches, psi and US gallons, and the whole thing collapses to one line:

GPM = 29.83 × C_d × d² × √P

d is the orifice diameter in inches, P is the pressure in psi measured at the nozzle rather than back at the pump, and C_d is the discharge coefficient of that particular opening. That is how to calculate GPM with PSI — and note that the diameter is not an optional refinement, it is half the input.

The 29.83 is not a magic number; it is purely the unit conversion, and we derived it rather than copying it: (π/4) × (1 inch in metres)² × √(2 × 1 psi in pascals ÷ water density) × 60 ÷ (1 US gallon in cubic metres). With water at 60 °F that returns 29.831. Warmer, less dense water pushes it to 29.85, which is why handbooks print 29.84 — a difference of one part in a thousand, far below the uncertainty in C_d.

Fire-service tables print GPM = 29.7 × d² × √P with no coefficient visible. That is the same equation with C_d folded into the constant: 29.7 ÷ 29.83 implies 0.996, because a well-machined smooth-bore tip really is close to ideal. Pick that option above and it reproduces the handbook exactly — a 1⅛″ tip at 50 psi is 266 gpm either way.

The discharge coefficient is the input people get wrong

C_d is where a tidy formula meets a messy hole. A jet leaving a sharp-edged opening keeps narrowing for a short distance after it exits — the vena contracta — so the effective area is smaller than the area you drilled. The classical free-streamline solution puts that contraction at π/(π+2) = 0.611, and with a small further loss to friction the familiar figure of about 0.61 for a plain drilled hole falls straight out. Round the entry off and the contraction largely disappears, taking C_d up to roughly 0.98. Taper it properly, as a fire nozzle does, and you land between 0.96 and 0.99.

The practical consequence: assuming C_d = 1 because you do not know it will overstate the flow through a smooth nozzle by about 3 percent, and through a drilled hole by more than 60 percent.

A worked example

A ½″ hole drilled in a plate, sharp-edged, with 60 psi behind it. Work it in three steps. First the geometry: d² = 0.5² = 0.25. Then the pressure: √60 = 7.746. Then the combined constant: 29.83 × 0.61 = 18.20. Multiply through — 18.20 × 0.25 × 7.746 — and you get 35.2 gpm.

Change nothing but the edge, rounding it to a bell-mouth so C_d becomes 0.98, and the same hole at the same pressure passes 56.6 gpm — a 61 percent increase for a filing job. That is the single best demonstration of why pressure alone cannot tell you flow.

Running it backwards as a GPM to PSI calculator

Switch the toggle to GPM → PSI and the same equation solves the other way, P = (Q ÷ (29.83 × C_d × d²))². That is the sizing question rather than the measuring one: you know the flow you need and you want the pressure that delivers it. Pushing 250 gpm through a 1⅛″ smooth bore needs 47 psi at the tip, and because pressure goes as the square of flow, asking that same tip for 500 gpm needs four times as much — 186 psi. Whatever the hose and fittings lose on the way has to be added on top at the pump.

PSI to GPM chart

Every figure below was computed with the formula above at C_d = 0.97, a smooth nozzle. For a plain drilled hole, multiply by 0.63; for a fire-service tip, add about 3 percent. Read down for the orifice size, across for the nozzle pressure.

Two patterns are worth absorbing from that table, because they are the whole behaviour of the equation. Going down a column, doubling the diameter multiplies flow by four — compare the ½″ and 1″ rows. Going across a row, doubling the pressure multiplies flow by only 1.41, and quadrupling it is what doubles flow. Diameter is worth vastly more than pressure, which is why every practical fix is a bigger pipe rather than a bigger pump.

How to figure GPM from PSI in a pipe run

The nozzle formula answers "what comes out of this hole". A different question — "how much will this pipe carry" — needs a different model, because now the limit is friction along the walls rather than a single opening. The standard tool for water in the 40–200 °F range is the Hazen–Williams equation, which in US plumbing units is Q = 0.442 × C × d^2.63 × (ΔP/L)^0.54, with Q in gpm, d the inside diameter in inches, ΔP the pressure lost in psi and L the run length in feet. We derived that 0.442 from the underlying velocity form and got 0.4422.

C is a roughness factor, and unlike C_d it is not derivable from anything — it is measured and read from published tables. Plastic is smoothest at about 150, copper around 140, new steel about 130, galvanised steel about 120, and old tuberculated cast iron can fall to 100 or below. Your choice of C moves the answer more than any other input, and it is the reason this method gives an estimate rather than a guarantee.

A concrete case: 100 feet of ¾″ copper, and you are willing to give up 10 psi across it. The calculator returns 8.4 gpm. Swap to 1″ copper, changing nothing else, and it returns 17.9 gpm — 2.13 times as much, from a quarter-inch of extra diameter. Note also that the relationship is not symmetric: because flow appears to the power 1.852 in the loss term, doubling the flow through a fixed pipe multiplies the pressure drop by 3.61. Undersized pipe punishes you quickly.

Two honest caveats. Hazen–Williams covers only water, near room temperature, in full pipes — for other fluids or for compressed air you need Darcy–Weisbach instead. And no GPM/PSI calculator can see the elbows in your basement: this one counts the straight run only, so every tee, valve and meter adds losses, conventionally handled by adding "equivalent length" of pipe. A real 100-foot run with a dozen fittings may behave like 130 feet.

Common mistakes when converting PSI to GPM

Using static pressure, or reading it in the wrong place. The number you get with everything shut is static pressure — the highest the system will ever show. As soon as water moves, friction eats into it. The P in the equation is the pressure right at the opening, so a gauge back at the pump, upstream of 200 feet of hose, is reading a different number and will overestimate flow.

Using the nominal pipe size as the diameter. Nominal sizes are names, not measurements — ¾″ copper does not have a ¾″ bore. Since flow scales with d² or d^2.63, a small error here is amplified. Use the actual inside diameter.

Assuming pressure and flow rise together. On a pump curve they trade against each other: what you get is the operating point where the pump curve meets the system curve, and pushing for more of one generally costs you the other.

When to skip the gallons per minute calculator: PSI is only half the story

If the water is accessible, a bucket and a stopwatch beat every formula on this page, because they include all the losses a model can only approximate. The EPA rates fixtures this way for the same reason: a standard showerhead is quoted at 2.5 gpm and a WaterSense-labelled one at no more than 2.0 gpm — always a measured flow at a defined test pressure, never a pressure on its own.

Frequently asked questions

How do you calculate GPM from PSI?

You cannot, from pressure alone — you also need the size of the opening the water leaves through. For a nozzle or orifice the formula is GPM = 29.83 × Cd × d² × √P: d is the orifice diameter in inches, P the pressure in psi at the nozzle, and Cd the discharge coefficient of that opening (about 0.97 for a smooth bore, about 0.61 for a drilled hole). Double the diameter and flow quadruples; double the pressure and it rises only about 1.41 times.

Is there a direct PSI to GPM conversion factor?

No, and any chart offering one without asking for a diameter is wrong. PSI is force per unit area; GPM is volume per unit time. They are different physical quantities, so no single number converts between them — the same 60 psi gives roughly 14 gpm through a quarter-inch hole and roughly 224 gpm through a one-inch one. Pressure tells you how hard the water is pushed; geometry tells you how much of it gets through.

How do I figure GPM from PSI at a tap without using a formula?

Do not use a formula — measure it. Put a bucket of known volume under the outlet, open it fully, and time the fill. GPM is gallons divided by minutes, so a 5-gallon bucket filled in 40 seconds is 5 ÷ (40/60) = 7.5 gpm. This beats any calculation because it automatically includes every fitting, bend and partial blockage between the main and the tap — exactly the part a formula has to guess at.

Which discharge coefficient should I use?

Match it to the shape of the opening; it is the input people get most wrong. A well-machined smooth-bore nozzle is close to ideal at roughly 0.96 to 0.98. A sharp-edged hole drilled in a plate is only about 0.61, because the jet keeps contracting after it leaves. A rounded or bell-mouthed entry sits near 0.98. Defaulting to 1.0 overstates flow by about 3 percent for a smooth nozzle and by more than 60 percent for a drilled hole.

Does more PSI always mean more GPM?

Through the same fixed opening yes, but with sharply diminishing returns: flow scales with the square root of pressure, so you need four times the pressure to double the flow. Across a whole system it can even go the other way — high static pressure drops as soon as flow starts, and a long or narrow pipe run leaves you with good pressure at the meter and poor flow at the outlet. That is why plumbers size pipe rather than raise pressure.

Related tools

• Unit converter
• Percentage calculator
• Rule of three calculator
• All tools