Linear Flow Rate Calculator
Enter flow velocity and pipe inner diameter to get the volumetric flow rate in five units, or flip to reverse mode to find the velocity from a known flow rate and diameter. Diameter dominates: flow scales with the square of it.
Idealized: assumes uniform velocity across the section and incompressible flow. Real pipes have friction losses and velocity profiles.
Quick Answer
At a velocity of 2 m/s through a 100 mm inner-diameter pipe (area 0.007854 m²), the flow rate is 0.015708 m³/s, which is 15.708 L/s, 942.5 L/min, 56.55 m³/h or 249.0 GPM. Run the same numbers in reverse, 15.708 L/s through 100 mm, and the tool returns exactly 2.00 m/s. The calculator above is pre-filled with this example on both tabs.
Key takeaways
- Flow is velocity times area, Q = v × A, and for a round pipe A = πd²/4. Velocity enters once; diameter enters squared.
- Doubling the diameter quadruples the flow at the same velocity. Upsizing a pipe beats pushing velocity up, and it avoids the noise and pressure loss that come with speed.
- One run returns five units at once: m³/s, L/s, L/min, m³/h and GPM. No separate converter step.
- The result is the idealized rate: uniform velocity across the section, incompressible fluid, no friction. The badge under the result judges the velocity against real working bands.
- Quick Answer
- How to use the linear flow rate calculator
- The formula, and why diameter wins
- Worked examples, checked against this exact tool
- Typical velocities: judging the number you got
- What this tool assumes, stated plainly
- What competing calculators miss
- Frequently asked questions
- Add This Calculator to Your Website
- References
How to use the linear flow rate calculator
Stay on the Flow rate tab when you know the velocity and need the volume, and switch to Velocity (reverse) when you know the volume and need the speed. Results stay hidden until you click Calculate.
- Flow rate tab: enter the flow velocity in m/s and the pipe inner diameter in mm. The pre-filled 2 m/s and 100 mm return 0.015708 m³/s with the other four units and the cross-sectional area underneath.
- Velocity tab: enter the flow rate in L/s and the inner diameter in mm. The pre-filled 15.708 L/s and 100 mm return 2.00 m/s, the check that the two modes agree.
- Read the badge: every result carries a verdict on the velocity, typical supply range, suction band, too slow or too fast, based on the bands in the velocity section below.
- Use the inner diameter: pipe sizes are usually quoted as nominal or outside dimensions. A 110 mm outside-diameter plastic pipe might have an inner diameter near 100 mm, and that difference alone changes the flow by about a fifth.
The same Q = vA relationship drives most moving-water estimates on this site. Checking how much a garden hose actually delivers, for instance, is the same two inputs pointed at a smaller pipe, covered by the hose flow rate calculator.
The formula, and why diameter wins
The flow rate is the velocity multiplied by the cross-sectional area of the pipe: Q = v × A. For a circular pipe the area comes from the diameter, A = πd²/4, so the whole calculation is one line.
A = πd²/4, with d converted from millimetres to metres (d ÷ 1000)
Reverse: v = Q ÷ A, with Q converted from L/s to m³/s (Q ÷ 1000)
Conversions: 1 m³/s = 1,000 L/s = 60,000 L/min = 3,600 m³/h ≈ 15,850.32 GPM
This is the continuity relationship for incompressible flow: what flows into a section flows out, so the volume rate is the area times the average speed. OpenStax College Physics sets it out directly in its section on flow rate and its relation to velocity, and the University Physics treatment of fluid dynamics derives the same continuity equation, A₁v₁ = A₂v₂, for a pipe that changes size. The squared diameter is the part people underestimate. Velocity enters the formula once, so doubling velocity doubles flow. Diameter enters through d², so doubling diameter multiplies area, and flow, by four. That asymmetry decides most real sizing arguments: a pipe one size up usually moves far more water than the same pipe pushed harder, and it does so quietly, because pressure loss climbs steeply with velocity.
Worked examples, checked against this exact tool
Every row below was run through the calculator code on this page and copied from its output. Enter the matching numbers to reproduce these figures exactly.
| Mode | Inputs | Tool result | Badge |
|---|---|---|---|
| Flow rate | 2 m/s, 100 mm | 0.015708 m³/s (15.708 L/s, 942.5 L/min, 56.55 m³/h, 249.0 GPM); area 0.007854 m² | Typical supply |
| Flow rate | 1.5 m/s, 50 mm | 0.002945 m³/s (2.945 L/s, 46.7 GPM); area 0.001963 m² | Typical supply |
| Flow rate | 3 m/s, 200 mm | 0.094248 m³/s (94.248 L/s, 1,493.9 GPM); area 0.031416 m² | Typical supply (top of band) |
| Velocity | 15.708 L/s, 100 mm | 2.00 m/s; area 0.007854 m² | Typical supply |
| Velocity | 100 L/s, 300 mm | 1.41 m/s; area 0.070686 m² | Typical supply |
| Velocity | 10 L/s, 50 mm | 5.09 m/s; area 0.001963 m² | High velocity |
The last row is the one to learn from: 10 L/s is a modest flow, but forced through a 50 mm pipe it needs 5.09 m/s, well past the noisy, erosive band. The fix is the pipe, not the pump. The scaling table below shows why, holding velocity at the worked example's 2 m/s and changing only the diameter.
| Inner diameter at 2 m/s | Area (m²) | Flow (m³/s) | Flow (L/s) |
|---|---|---|---|
| 50 mm | 0.001963 | 0.003927 | 3.927 |
| 100 mm (worked example) | 0.007854 | 0.015708 | 15.708 |
| 200 mm | 0.031416 | 0.062832 | 62.832 |
Typical velocities: judging the number you got
A flow rate on its own says nothing about whether the pipe is well sized; the velocity does. The verdict badge in the results applies the bands below, which are the working ranges plumbers and pump engineers use for water.
| Velocity band | Where it fits | What to watch |
|---|---|---|
| Below 0.5 m/s | Oversized pipe or a trickle flow | Sediment settles in horizontal runs; air pockets collect at high points |
| 0.5 to 1.5 m/s | Pump suction lines | Kept low to protect the pump from cavitation |
| 1 to 3 m/s | Building water supply and general distribution | The normal design window: quiet, modest pressure loss |
| Above 3 m/s | Short runs only, if at all | Noise, water hammer on valve closure, erosion of the pipe wall over time |
Badge note: the verdict badge applies the supply framing, so it switches from Low to Typical supply at 1 m/s. The 0.5 to 1.5 m/s suction band in the table overlaps that range for pump suction use, but the badge labels 1 to 3 m/s as Typical supply.
If reverse mode hands you a velocity far outside the band for the job, reconsider the pipe size, not the flow: the flow is usually set by the fixtures or the process, while the diameter is the designer's free choice. Two follow-on questions sit just past this tool. What the velocity costs you in pressure is a head-loss problem, worked through by the flow rate pressure calculator, and open-channel or gravity drainage sizing follows different rules again, covered by the drain flow rate calculator.
What this tool assumes, stated plainly
The calculation is exact for the model it uses, and the model is deliberately simple. Knowing its edges is what separates a useful estimate from a wrong one.
- Uniform velocity: real pipes have a velocity profile, fastest at the centre and zero at the wall. The v in Q = vA is the average across the section, which is what a flow meter or a continuity check gives you.
- Incompressible flow: fine for water and most liquids at ordinary pressures. For gases, density changes with pressure, so the volumetric rate changes along the pipe and a single Q can mislead.
- Full, circular pipe: the area formula assumes the pipe runs full with a round bore. Partially full pipes, rectangular ducts and open channels need their own area formulas.
- No friction or fittings: nothing here computes pressure drop. Elbows, valves, roughness and length all eat head in a real system, which is why the note under the calculator names Darcy-Weisbach style losses as outside its scope.
- Inputs are fixed-unit: velocity only in m/s, diameter only in mm, reverse flow only in L/s, and every value must be greater than zero. A zero or negative input gets an explanatory message rather than a meaningless zero result.
What competing calculators miss
The formula is one line, so rivals compete on scope, and most either bury the simple case under a design tool or split it into one-way converters:
- Omni's Pipe Flow Calculator: a Hazen-Williams gravity-flow tool that wants pipe length, height drop and a roughness coefficient before it answers. Excellent for a draining pipeline, but it solves for gravity velocity, a different question from Q = vA, and the simple forward-and-reverse pair is not its headline.
- Omni's Flow Rate Calculator: broad and careful, with cross-section shapes and a density field that extends into mass flow. The cost is sprawl: a reader who just wants velocity and diameter turned into five units has to walk past shape pickers and density inputs to get there.
- GoodCalculators' Flow Rate Calculator: genuinely useful for open channels, with rectangular, trapezoidal and partially full circular formulas. Its worked examples run in feet and square feet, it has no reverse velocity mode, and the circular-pipe case this page is about is one shape among several.
- CalculatorDoc and KWCalc: imperial one-trick converters, inches and feet per second in, GPM or FPS out, built on the 0.408 constant. Accurate within their lane, but each does one direction in one unit system and leaves the rest to you.
- CalculatorsHub's Flow to Velocity Calculator: the reverse half of this page, done from a cross-sectional area you must supply yourself rather than from the diameter you actually measured.
- The gap this page fills: both directions from the two measurements people actually take, velocity and inner diameter, five units in a single run, the exact formula printed under every result, and a verdict on whether the velocity sits in a sensible band.
Frequently asked questions
Multiply the flow velocity by the pipe's cross-sectional area: Q = v × A, with A = π × (d/2)² for a round pipe. With velocity in m/s and diameter converted from mm to m, Q comes out in m³/s, and this tool also converts it to L/s, L/min, m³/h and GPM.
This tool reports five units from one run: cubic metres per second (m³/s), litres per second (L/s), litres per minute (L/min), cubic metres per hour (m³/h) and US gallons per minute (GPM). Inputs are fixed: velocity in m/s, diameter in mm, and flow in L/s in the reverse mode.
Divide the flow rate by the cross-sectional area: v = Q ÷ A. Use the Velocity (reverse) tab with the flow in L/s and the inner diameter in mm. For example, 15.708 L/s through a 100 mm pipe gives exactly 2.00 m/s.
Because area is πd²/4, area grows with the square of diameter. Double the diameter and the area, and so the flow at the same velocity, becomes four times larger. Halving the diameter cuts flow to a quarter, which is why small sizing errors matter so much.
Water in building supply pipes typically runs 1 to 3 m/s. Pump suction lines stay lower, 0.5 to 1.5 m/s, to avoid cavitation, and below about 0.5 m/s sediment can settle out. Above 3 m/s, noise, water hammer and erosion become real problems, and the verdict badge under the result flags which band your number falls in.
Velocity is how fast the fluid moves, in m/s. Flow rate is how much volume passes per unit of time, in m³/s or L/s. The pipe's cross-sectional area links them: the same velocity in a bigger pipe is a much bigger flow rate.
Exactly 1,000 L/s. The same flow is 60,000 L/min, 3,600 m³/h and about 15,850 GPM. The tool's GPM conversion uses the factor 15,850.32 per m³/s.
No. This is the idealized volumetric rate from Q = v × A, assuming the velocity is uniform across the section and the fluid is incompressible. Real systems lose pressure to wall friction and fittings, described by methods such as Darcy-Weisbach, so a pump or gravity head has to overcome those losses to actually deliver the velocity you enter.
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References
- OpenStax, Rice University. College Physics, Section 12.1: Flow Rate and Its Relation to Velocity. Accessed October 22, 2026.
- OpenStax, Rice University. University Physics Volume 1, Section 14.5: Fluid Dynamics. Accessed October 22, 2026.
- OpenStax, Rice University. University Physics Volume 1, Section 14.1: Fluids, Density, and Pressure. Accessed October 22, 2026.
- OpenStax, Rice University. College Physics, Section 12.2: Bernoulli's Equation. Accessed October 22, 2026.
- National Institute of Standards and Technology. SI Units: Volume. Accessed October 22, 2026.