The continuity equation
Flow rate is area times velocity. That is the whole relationship, and it is the same one that gives velocity from flow:
Q (GPM) = cross-sectional area (sq in) × velocity (ft/s) × 3.1169- where
area = π × (inside diameter ÷ 2)²
That constant 3.1169 is worth understanding rather than trusting. One square inch of cross-section carrying water at one foot per second moves 1/144 of a cubic foot per second; over a minute that is 60 ÷ 144 = 0.4167 cubic feet; and a cubic foot is 7.48052 gallons, so the result is 3.1169 gallons per minute.
You can cross-check it against the velocity form of the same relationship: v = 0.4085 × GPM ÷ d². Rearranged, GPM = v × d² ÷ 0.4085. For a 2 inch bore at 1 ft/s: both routes give 9.79 GPM. If a calculator gives you a different figure, one of the two constants is wrong — a factor sometimes published as 0.0408 is a unit slip and is not correct.
Three worked examples
- 2 inch Schedule 40 (2.067 in bore) at 5 ft/s. Area = π × (2.067 ÷ 2)² = 3.356 sq in. Q = 3.356 × 5 × 3.1169 = 52.3 GPM, or about 3,138 gallons per hour.
- 3/4 inch (0.824 in bore) at 5 ft/s. Area = 0.533 sq in. Q = 0.533 × 5 × 3.1169 = 8.3 GPM.
- 1 inch (1.049 in bore) at 5 ft/s. Area = 0.864 sq in. Q = 0.864 × 5 × 3.1169 = 13.5 GPM.
At a fixed velocity, flow scales with the square of the diameter, which is why a modest increase in pipe size transforms what a line can carry.
Flow at common velocities
| Nominal size (Sch 40 ID) | @ 4 ft/s | @ 5 ft/s | @ 6 ft/s |
|---|---|---|---|
| 1/2" (0.622") | 3.8 GPM | 4.7 GPM | 5.7 GPM |
| 3/4" (0.824") | 6.6 GPM | 8.3 GPM | 10.0 GPM |
| 1" (1.049") | 10.8 GPM | 13.5 GPM | 16.2 GPM |
| 1-1/2" (1.61") | 25.4 GPM | 31.7 GPM | 38.1 GPM |
| 2" (2.067") | 41.8 GPM | 52.3 GPM | 62.8 GPM |
Read that table sideways and you get the design logic: if you need 12 GPM quietly, 3/4 inch at 5 ft/s gives only 8.3, so you go to 1 inch, where 12 GPM is about 4.4 ft/s.
Checking a real line: the bucket method
The calculator works from pipe size and velocity. When you want to know what an existing line actually delivers, measure it:
- Fill a container of known volume — a 5-gallon bucket marked at a known level is the usual choice.
- Time how long it takes to fill at the fixture, with everything else off.
GPM = gallons ÷ minutes. A bucket that fills in 30 seconds is 10 GPM.
This is also the honest way to check a flow rate you have calculated: measure, then compare. Real systems lose flow to friction, fittings, partially closed valves and pressure that is lower than you assumed.
Flow rate, velocity and pressure are not the same thing
The three are related but not interchangeable, and confusing them causes most sizing arguments:
- Flow (GPM) — how much water moves per minute.
- Velocity (ft/s) — how fast it moves, set by flow and pipe area.
- Pressure (psi) — the force available to push it. Raising pressure raises flow and therefore velocity; it does not independently quiet a line.
A fixture rated in GPM tells you the flow it wants. The pipe size decides the velocity at which that flow travels, and velocity decides whether the line is quiet and durable.
Common mistakes
- Using the wrong unit constant. The correct factor is 3.1169 GPM per (sq in · ft/s). Cross-check against 0.4085 × GPM ÷ d² before trusting any published figure.
- Using nominal size as the bore. It is squared into the area, so the error compounds.
- Confusing GPM with GPH. Multiply by 60. Irrigation is often quoted in GPH; pumps and plumbing in GPM.
- Assuming the calculated flow is the delivered flow. Friction, fittings and valves all take a share.
- Measuring with other fixtures running. Time a single draw.
- Ignoring that velocity limits still apply. A pipe can carry 12 GPM; whether it should depends on the resulting velocity.
Where the demand number comes from
The calculator answers "what flow does this pipe carry at this velocity". The more common real question is the reverse: how much flow does the job need in the first place?
For plumbing, demand is usually built up from water supply fixture units (WSFU) — each fixture type carries a unit value, the values are summed, and the total is looked up against a demand table to get a design GPM. The method is probabilistic, which is why a whole-house service can be far smaller than the arithmetic sum of every fixture: not everything runs at once.
Where flow is dictated by the load rather than by a fixture count — an irrigation zone, equipment cooling, a hose station, a water feature — you start from the required GPM instead and size the pipe to keep velocity inside the band. Either way the end of the calculation is the same: pick a bore where the needed flow lands at a comfortable velocity.
Two things are worth remembering about pump selection specifically. Pump curves are quoted in GPM against head, so a flow figure alone is not enough — you need the head the system presents. And for any fluid other than water, density and viscosity change the pump duty even though the continuity equation itself still holds.
Measuring flow instead of assuming it
Calculated flow and delivered flow are different numbers. These are the tools that close the gap, plus the pump side of the equation.
- Inline flow meter — The simplest way to read GPM continuously and compare it against what you calculated from pipe size and velocity.
- Ultrasonic clamp-on flow meter — Measures an existing pipe without cutting into it. Useful when you want to check a line before deciding whether it needs upsizing.
- Graduated measuring container — The bucket-and-stopwatch method, done properly. A marked container of known volume and a stopwatch is a legitimate flow measurement.
- Transfer pump — If the job is moving a known volume in a known time, the pump gets chosen from the flow rate — and pump curves are quoted in GPM against head, so know both.
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Sources and standards
Where these figures come from
Every formula on this page is implemented from the published reference material below. Where a value depends on the equipment manufacturer, the page says so instead of guessing one.
- ASHRAE — hydronic and plumbing flow, velocity and pipe sizing practice.
- NIST — weights and measures: gallon, cubic foot and unit conversions.
- Copper Development Association — tube dimensions used for the inside diameters in the tables above.
Figures, formulas and reference tables last verified: 21 September 2026.