Flow Rate Calculator
Solve Q = v × A for flow rate, velocity or pipe diameter in L/s, m³/h, gpm, cfm or bbl/day, with mass flow from density and velocity in other bores.
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About this toolWhat is the Flow Rate Calculator?
Most pipe questions start with one relationship: flow equals velocity times area. Know two of the three and you have the third. This calculator solves Q = v × A in whichever direction you need. Enter a bore and a velocity to get the flow, a flow and a bore to get the velocity, or a flow and a target velocity to find the inside diameter a line should have. The default case, an 80 mm bore at 2 m/s, carries 10.05 L/s or 36.2 m³/h.
Flow units are where mistakes creep in, so every common one is here and converts in place: m³/s, m³/h, L/s, L/min, US gpm, UK (imperial) gpm, cubic feet per minute and per second, and oil barrels per day. Velocity works in m/s, ft/s or ft/min, and diameters in mm, cm, m, inches or feet. Add a density and you also get mass flow in kg/s, kg/h, lb/h and tonnes per hour.
Under the result, a table shows the same flow in fourteen common bores from 15 mm to 300 mm and shades the ones that land in the 0.6 to 3 m/s band that designers often use for pumped water. That turns a single sum into a quick line-sizing check.
- Solves for flow rate, velocity or inside diameter from the other two
- Nine flow units including UK gpm, cfm and oil barrels per day, with exact conversion factors
- Mass flow from density in kg/s, kg/h, lb/s, lb/h and t/h
- Velocity table across fourteen common bores with the typical water band shaded
- Velocity head, flow area, copy-ready summary and shareable link
How to use the Flow Rate Calculator
- Choose what to solve for: flow rate, velocity or diameter. The field you are solving becomes the shaded result box.
- Enter the other two values and pick their units. Use the actual inside diameter of the pipe or tube, not its nominal size.
- Optionally enter the fluid density to get mass flow. Water at 20 °C is 998.2 kg/m³.
- Read the result, the flow area, velocity head and mass flow. Switch any unit picker to see the same value converted.
- Scan the bore table to see what velocity the same flow would have in a larger or smaller pipe, then copy the results or share a link.
Worked examples
Flow from bore and velocity
Input
80 mm inside diameter, 2 m/s
Output
Q = 10.05 L/s = 36.19 m³/h = 159.3 US gpm
Area is 5,026.5 mm². With water density the mass flow is 10.04 kg/s, about 36.1 tonnes per hour.
Velocity in 2 inch Schedule 40 steel
Input
100 US gpm, 2.067 in inside diameter
Output
v = 9.56 ft/s (2.91 m/s)
Using the 2.000 in nominal size would give 10.21 ft/s, about 7% high. The bore matters.
Sizing a line for a target velocity
Input
50 m³/h at 1.5 m/s
Output
D = 108.6 mm inside diameter
A DN100 pipe would run slightly faster than 1.5 m/s and a DN125 slower. The bore table shows both at a glance.
Background and insight
The equation is continuity for an incompressible fluid: what goes in must come out, so the volume passing a cross-section each second equals the mean velocity times the flow area. For a full round pipe A = πD²/4, which is why velocity falls with the square of the diameter. Halve the bore and the same flow moves four times as fast.
The unit factors are exact by definition. One US gallon is 231 cubic inches, or 3.785411784 L; one imperial gallon is 4.54609 L; one cubic foot is 28.316846592 L; and an oil barrel is 42 US gallons, 158.987 L. US engineers often use the shortcut v (ft/s) = 0.4085 × gpm / d², with d in inches, which falls straight out of those definitions.
Velocity limits are judgment, not law. Many water designers aim for roughly 1 to 2.5 m/s (3 to 8 ft/s) in pumped lines, keep suction lines slower, and avoid going far above 3 m/s (10 ft/s) because of noise, erosion and water hammer. Plumbing codes and owners often set their own caps, so check the one that governs your job.
Common use cases
Pipe and tube sizing
Find the bore that keeps a design flow inside your velocity limits before you look at pressure drop.
Reading meters and pump plates
Convert a flow from gpm to L/s or m³/h and back, including imperial gallons and barrels per day.
Process and HVAC water loops
Turn a heat-load flow into a velocity, or check that a chilled-water branch is not running too fast.
Mass balances
Get kg/s or lb/h from a volumetric reading and a density for energy or material balances.
Tips and limitations
- Always use the inside diameter. Schedule 80 steel, SDR plastic and copper type K, L and M all have different bores for the same nominal size.
- Q = vA uses the mean velocity across the section. In laminar flow the centreline runs at twice the mean, so a point reading from a probe is not v.
- For gases, volume flow changes with pressure and temperature. Convert to standard conditions or use mass flow before comparing two points.
- A partly full pipe or open channel has a smaller flow area and needs Manning or similar methods, not this full-pipe formula.
- Once you have a velocity, check the friction loss with the pipe pressure drop calculator; a pipe can be fine for velocity and still too long for the pump.
Frequently asked questions
How do you calculate flow rate from pipe diameter and velocity?
Multiply the flow area by the mean velocity: Q = v × πD²/4. For a 100 mm bore at 1.5 m/s, A = 0.007854 m² and Q = 0.01178 m³/s, which is 11.78 L/s or 42.4 m³/h.
How do I convert gpm to velocity in a pipe?
Use v (ft/s) = 0.4085 × gpm / d², with d the inside diameter in inches. 100 gpm in a 2.067 in bore gives 0.4085 × 100 / 4.272 = 9.56 ft/s.
What is the formula for pipe diameter from flow rate?
Rearrange Q = vπD²/4 to D = √(4Q / (πv)). Pick a design velocity first, then round the answer up to the next available inside diameter.
What is a good water velocity in a pipe?
A common design range for pumped water is about 1 to 2.5 m/s (3 to 8 ft/s), lower on pump suction and higher only for short runs. Below about 0.6 m/s solids may settle; above about 3 m/s noise, erosion and surge pressure become concerns. Your governing code or client standard may set specific limits.
What is the difference between US and UK gallons per minute?
A US gallon is 3.785 L and an imperial (UK) gallon is 4.546 L, so 1 UK gpm equals 1.201 US gpm. Pump curves from British and Commonwealth makers sometimes use imperial gallons, so check which one a sheet means.
How do you convert volumetric flow to mass flow?
Multiply by density: ṁ = ρQ. Ten litres per second of water at 998.2 kg/m³ is 9.98 kg/s. For gases use the density at the actual pressure and temperature.
Is there an in-depth guide to the Flow Rate Calculator?
Yes. “Pipe Flow Rate, Velocity and Diameter: Using Q = vA Properly” covers the background, how it works, common pitfalls and worked examples. Read the full guide.
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