Volumetric Flow Rate Calculator

Volumetric flow rate, written Q, tells you how much volume of a fluid passes a given point per unit time. The SI unit is the cubic metre per second, but you will meet it in many forms: litres per minute (LPM) on pumps and taps, cubic metres per hour on water supply and process equipment, US gallons per minute (gpm) in North American plumbing, and cubic feet per minute (cfm) for air. Wikipedia's article on the volumetric flow rate gives the definition and the SI unit, and the same Q is used all through fluid mechanics, from a garden hose to a pipeline.

A few other quantities are easy to confuse with it. Velocity is how fast the fluid moves, in m/s or ft/s. Mass flow rate is how much mass passes per unit time, in kg/s or lb/min. Volumetric flow rate sits between them: it equals velocity times area, and mass flow is that multiplied by the density. This calculator moves between all of them. A single number such as 235.6 L/min is the same flow as 62.2 gpm, 14.14 m3/h or 8.32 cfm, and the results panel lists every unit side by side so you can match whatever your pump data sheet or standard uses.

The key equation is Q = A x v, often written Q = AV. A is the area of the flow, the cross-section the fluid goes through, and v is the average velocity across that cross-section. For a round pipe running full, A = pi x D² / 4, where D is the inside diameter. For a rectangular duct, A is width times height. The formula assumes a steady flow with a uniform average velocity. It is the same relationship Wikipedia gives as the alternative definition of volumetric flow rate.

The area depends on the square of the diameter, so small diameter changes matter a lot. A 100 mm pipe has four times the area of a 50 mm pipe, and at the same velocity it carries four times the flow. The table of flow rate by diameter and velocity shows the pattern: a 50 mm pipe at 2 m/s carries 235.6 L/min, and a 100 mm pipe at 2 m/s carries 942.5 L/min.

Use the inside diameter, not the nominal pipe size or the outside diameter. A pipe sold as 2 in has an actual inside diameter that depends on its wall thickness and material, so check the data sheet. The round pipe and rectangular duct modes above take the dimensions and the velocity and return Q in every unit.

Often you know the flow and need the velocity, for instance to check that water in a line is not moving too fast. Rearranging gives v = Q / A. For 100 gpm in a pipe with a 2 in (50.8 mm) inside diameter, the velocity is 3.113 m/s, or 10.21 ft/s. The table of velocities for 100 gpm shows how quickly velocity falls as the pipe gets larger.

The opposite question is which pipe to use. Choose a velocity that suits the fluid and the job, then solve for the diameter: D = √(4 Q / (pi v)). For 500 L/min at 2 m/s the inside diameter works out to 72.8 mm. Round up to the next standard size, and check the real inside diameter. Acceptable velocities depend on the fluid, the pipe material, noise, erosion and pump energy, and they differ between standards and manufacturers, so this page does not state a single correct value.

The velocity and diameter modes are built for exactly these two questions. Enter the flow in whichever unit you have, and the diameter or velocity appears in mm, inches, m/s and ft/s.

If you know how much fluid moved and how long it took, the flow rate is simply Q = V / t. A bucket test uses this to measure a tap or a pump: time how long a known container takes to fill. A 10 L bucket that fills in 20 seconds gives 0.5 L/s, which is 30 L/min or 7.93 gpm. A 200 L tank filled in 80 seconds gives 2.5 L/s, or 150 L/min. The table of bucket tests lists more cases.

The same relationship solved for time, t = V / Q, gives a fill time. A 15,000 US gallon pool filled at 30 gpm takes 500 minutes, or 8.33 hours. The fill time table shows common pool and tank sizes against typical flow rates. The calculation assumes the flow stays steady, so a falling supply pressure or a partly closed valve will make the real time longer.

For pools, the volume itself comes from the pool's dimensions, and the pool salt calculator linked below is one place to start. Enter the gallons or litres in the fill time mode, with the hose or pump flow, and read the time in seconds, minutes and hours.

Most mistakes in flow work are unit mistakes. The US gallon is exactly 3.785411784 litres (NIST), so 1 gpm is 3.7854 L/min and 0.06309 L/s. A cubic foot is exactly 0.028316846592 cubic metres, so 1 cfm is 28.317 L/min. One m3/h is 0.2778 L/s. The unit table lists the conversions between every pair of the units the calculator shows.

Watch out for the imperial gallon, which is about 20 percent larger than the US gallon. This page uses the US gallon only, so a UK flow figure in gallons per minute will not match. Also keep minutes and seconds apart: a flow of 60 L/min is 1 L/s, and mixing them is a factor of 60.

For a metric calculation, work in L/s, L/min or m3/h with lengths in mm or m and velocity in m/s. For a US calculation, work in gpm or cfm with inches or feet and ft/s. The calculator accepts either set and displays the results in both, so you can cross-check a metric specification against a US one.

Volumetric flow and mass flow are linked by density: m = rho x Q, and Q = m / rho. Wikipedia's article on the mass flow rate gives the same pair of relations. For water at 20 °C (998.21 kg/m3), 10 m3/h is 2.773 kg/s. For glycerol (about 1,261 kg/m3) the same volume flow is a higher mass flow, and for air (about 1.204 kg/m3) it is far lower. The table of mass flow compares them.

The density has to match the fluid and its temperature, so use the density at the operating conditions. For liquids the temperature effect is small but real: water at 60 °C has a density of 983.21 kg/m3, about 1.5 percent below the 20 °C value.

Gases are different, because their volume changes strongly with pressure and temperature. A volumetric flow of gas is meaningful only with its conditions stated, and many designers work in mass flow or in flow at standard conditions to avoid confusion. The mass to volume and volume to mass modes take a density in kg/m3 or lb/ft3, so you can supply the right value for the actual pressure and temperature.

Q = A v relates flow, size and velocity, and nothing else. It does not say how much pressure it takes to push the fluid through a pipe, and it cannot give a flow from a pipe diameter and a pressure alone. That needs pipe length, roughness, fittings, fluid viscosity, elevation and a friction or pump model. If you are sizing a pump, a sprinkler system, a fuel line or a gas line, use the proper method for it, follow the applicable standards and the manufacturer's data, and have a qualified engineer check anything that affects safety, cost or compliance.

The results here are exact for the numbers you enter, but real flows differ from the ideal case. Velocity varies across a pipe, pipes may be partly full, a fluid's density changes with temperature, and flows rise and fall over time. Treat the answers as engineering estimates.

A few related tools may help: the pool salt calculator for pool volume and dosing, the linear interpolation calculator for reading a value between two table entries, and the percentage calculator for percent differences between two flow rates.