The flow rate calculator above ties together the four quantities that describe fluid moving through a pipe: the cross-sectional area available, the velocity of the fluid, the volume passing per second, and the mass passing per second. Give it any two of the geometric and kinematic ones and it derives the rest, and it states plainly at the top of the result which quantity it solved for — so there is never any doubt about which number was an input and which was computed.
Arb Digital builds free calculators that make the relationship visible rather than hiding it behind a single answer. Every result on this page shows all four quantities together, because the useful insight in flow problems is almost always the trade-off between them. This page also states the boundary against the converters already on the site: a converter rescales an existing flow figure between units, while this one derives flow from geometry and velocity.
What This Flow Rate Calculator Does
In its default mode it takes a pipe diameter and a fluid velocity and returns the volumetric flow rate. Switch the solve-for selector and it will instead find the velocity implied by a known flow through a known pipe, or the pipe diameter needed to carry a known flow at a chosen velocity. That third mode is the one engineers actually use most, because pipe sizing is usually driven by a target velocity rather than by anything else.
Mass flow is derived in every mode from volumetric flow and density. The two are not interchangeable and the distinction matters: a compressor moves a roughly constant mass of air per second while its volumetric flow changes with pressure, and a gas meter reading volume at the wrong temperature reports the wrong quantity of gas. Whenever the fluid is compressible, mass flow is the quantity that is actually conserved.
The cross-section selector handles square ducts as well as round pipes, because ventilation work uses rectangular sections far more often than circular ones. For a square duct the diameter field is read as the side length. Everything else in the calculation is unchanged, since the equation cares only about the area.
How to Use It
- Choose what you are solving for. The hero label updates to name the quantity being computed, and the remaining fields become the inputs it reads.
- Enter the inside diameter, in millimetres. Nominal pipe sizes are not bore sizes. A pipe sold as 50 mm may have an inside diameter several millimetres smaller, and area error scales with the square.
- Enter velocity or flow in your preferred unit. The flow unit dropdown covers litres per second and minute, cubic metres per second and hour, and US gallons per minute.
- Set density if you need mass flow. Volumetric flow is unaffected by density; mass flow is directly proportional to it.
- Check the velocity against practical limits. Water above roughly 3 m/s in a domestic pipe becomes noisy and accelerates erosion, and the note under the results flags where your figure sits.
The Formula: How Flow Rate Is Calculated
The core relation is Q = Av: volumetric flow equals cross-sectional area times velocity. OpenStax University Physics Volume 1, section 14.5 on fluid dynamics, states the volume flow rate as Q equals dV/dt equals Av, where A is the cross-sectional area of the pipe and v is the magnitude of the velocity. Mass flow follows as ṁ = ρQ, and for a round pipe the area is πd2 ÷ 4.
Work the default values. A 50 mm bore gives an area of π × 0.052 ÷ 4 = 1.9635 × 10−3 m2. At 2 m/s the volumetric flow is 1.9635 × 10−3 × 2 = 3.927 × 10−3 m3/s, which is 3.927 litres per second or 235.6 litres per minute. With water at 998 kg/m3 the mass flow is 3.919 kg/s.
The same page gives the continuity equation, A1v1 = A2v2 for an incompressible fluid, and the more general ρ1A1v1 = ρ2A2v2 when density varies. That is the statement that whatever goes into a pipe must come out of it, and it is what lets you solve for velocity at one point given conditions at another.
Continuity: What Happens Where a Pipe Changes Size
Volumetric flow is the same at every point along a pipe carrying an incompressible fluid with no branches. Velocity is not. Where the bore narrows, the same volume per second must pass through less area, so the fluid speeds up in exact inverse proportion to the area. Halve the diameter and the area falls to a quarter, so the velocity quadruples.
This is worth running through the calculator directly. Solve for velocity with a fixed flow rate, then change the diameter and watch the velocity move by the square of the ratio. It explains why a partially blocked pipe erodes fastest at the constriction, why a hose nozzle produces a fast jet from a slow supply, and why a sudden expansion in a duct is a good place for particles to drop out of the airstream.
Continuity also underlies pressure changes in a flow. Faster fluid at a constriction has lower static pressure, which is Bernoulli's principle — the mechanism behind venturi meters, carburettors and aspirators. Our Bernoulli equation calculator handles that step once you have velocities from this page.
Volumetric Flow and Mass Flow Are Not the Same Number
For liquids the distinction rarely bites, because water's density barely moves across normal temperatures. For gases it matters constantly. Air at sea level is 1.225 kg/m3; the same air at three atmospheres is around three times denser. A duct passing one cubic metre per second is passing three times the mass in the second case, which is why compressed-air systems are always specified in mass flow or in volume referred to a stated standard condition.
The convention you will meet is normal or standard cubic metres — volume that the gas would occupy at a defined reference temperature and pressure. That is really a mass measurement wearing volumetric clothing. If a specification quotes flow in standard units, convert it to mass flow before comparing it with a measurement taken at actual conditions, or the comparison is meaningless. The coherent SI unit underneath all of this is the cubic metre per second for volume and the kilogram per second for mass, as set out in the SI Brochure published by the BIPM; litres per minute and gallons per hour are conveniences layered on top.
This tool reports both numbers side by side for exactly that reason. Whichever quantity you solved for, you can see the other and decide which one your problem actually cares about. The mass flow rate converter rescales the mass figure into pounds per hour or tonnes per day if your specification uses those.
Choosing a Velocity Rather Than Guessing a Pipe Size
The pipe-sizing mode exists because sizing by trial and error is slow and sizing by target velocity is quick. Designers work backwards: pick a velocity appropriate to the fluid and the application, then compute the bore that delivers the required flow at that velocity. The velocity choice encodes a trade-off between pipe cost and pumping cost, since friction losses climb steeply with velocity while pipe cost climbs with diameter.
Typical practice puts domestic water somewhere below 2 m/s to limit noise, industrial water pumping in the 1.5 to 3 m/s range, and low-pressure ventilation air in the 3 to 8 m/s range. Those are conventions rather than physical limits, and they vary between codes and applications, so treat them as orientation rather than as design rules. What matters is that you choose the velocity deliberately instead of inheriting it from whatever pipe happened to be nearby.
Average Velocity and the Real Velocity Profile
The velocity in Q equals Av is an average across the whole cross-section, and no fluid particle in a real pipe actually travels at it. Viscosity holds the fluid at the wall to zero velocity, and the speed climbs toward a maximum at the centre line. In fully developed laminar flow the profile is a parabola and the centre-line speed is exactly twice the average. In turbulent flow the profile is much flatter, with the centre-line speed only around twenty per cent above the average.
This matters whenever you measure velocity rather than calculating it. A pitot tube or an insertion probe placed on the centre line reads the maximum, not the average, so using that reading directly in the flow equation overstates flow by up to a factor of two in laminar conditions. Measurement standards handle this either by traversing the section and averaging, or by applying a profile factor appropriate to the flow regime.
The regime itself is set by the Reynolds number, which combines velocity, diameter, density and viscosity. Below roughly 2,000 the flow is laminar, above roughly 4,000 it is turbulent, and in between it is unpredictable. Most engineering flows of water and air in ordinary pipes are comfortably turbulent, which is convenient: the flatter profile makes the average velocity a reasonable stand-in for a point measurement.
How This Differs From the Flow Rate Converter
The boundary in one sentence: a converter rescales an existing flow figure between units, while this calculator derives flow from pipe geometry and fluid velocity. The flow rate converter turns litres per minute into gallons per hour; it does not know how big your pipe is. This page starts from a bore and a speed and produces a flow figure that never existed as an input.
The two work well in sequence. Derive the flow here, then rescale it into whatever units your specification demands. The same pairing applies to mass flow rate converter for the mass figure, the density converter for the density input, the speed converter for velocity, and the volume converter if you are working out how long a tank takes to fill. For that last question, the cylinder volume calculator and pool volume calculator give the volume and this page gives the rate.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Using nominal pipe size as the bore — wall thickness reduces the inside diameter, and area error scales with the square of that difference.
- Confusing volumetric and mass flow — for gases they diverge with pressure and temperature, and only mass flow is conserved through a compressor.
- Assuming uniform velocity across the pipe — real flow is slower at the wall and faster at the centre, so the velocity in this equation is the average.
- Ignoring the velocity you end up with — a bore that delivers the flow may do it at a speed that is noisy, erosive or expensive to pump.
- Mixing millimetres and metres — the diameter field expects millimetres, and entering metres there inflates the area by a factor of a million.
Related Free Tools From Arb Digital
Rescale results with the flow rate converter or the mass flow rate converter, and prepare inputs with the density converter and the speed converter. For pressure and velocity relationships use the Bernoulli equation calculator or the hydrostatic pressure calculator. To turn a flow rate into a fill time, get the volume from the cylinder volume calculator or the pool volume calculator and divide. The full free online tools hub lists everything.
Frequently Asked Questions
Volumetric flow is the volume passing per second and mass flow is the mass passing per second. They are linked by density. For liquids the two track each other closely; for gases they diverge with pressure and temperature, and only mass flow is conserved through a compressor.
Whichever one the solve-for selector names. The hero label states it directly, and the result grid always shows all four quantities so you can see which figures were inputs and which were derived from them.
Inside diameter, always. Nominal size is a naming convention rather than a measurement, and the wall thickness it hides can remove several millimetres of bore. Because area depends on diameter squared, that error is magnified in the flow result.
No. Real flow is slowest at the wall and fastest at the centre, with the profile depending on whether the flow is laminar or turbulent. The velocity in this equation is the average across the section, which is what area times velocity requires.
No. It is a continuity calculation, which relates geometry, velocity and flow but says nothing about the pressure needed to sustain that flow. Friction losses depend on pipe roughness, length, fittings and Reynolds number, all of which are outside this equation.
Yes. Select the square-duct option and the diameter field is read as the side length. For a rectangular section of unequal sides, compute the area yourself and back out an equivalent side length, since the equation depends only on area.
The flow rate converter rescales a flow figure you already have between litres per minute, gallons per hour and other units. This calculator derives a flow figure that did not exist as an input, from pipe geometry and fluid velocity. One reformats, the other computes.
This tool is provided for educational and estimating use. It performs a continuity calculation only and does not model friction, pressure drop, cavitation, compressibility or code requirements, so treat its output as a physics result rather than a piping design.
