Flow Rate Calculator
Find the flow rate of a fluid four ways: from cross-section area times velocity (Q = A·v), from a round pipe diameter, from a volume divided by the time it takes to pass, or solve in reverse for the velocity a given flow needs. Add a fluid density for mass flow rate, and an optional pump head for the energy cost of moving it.
Formula
Worked example
A pipe of area 0.05 m² carries water at 2 m/s: Q = 0.05 × 2 = 0.1 m³/s, which is 6,000 L/min. At 998 kg/m³ the mass flow is 99.8 kg/s, and lifting it 10 m at 65% efficiency needs about 15.1 kW.
What volumetric flow rate measures
Volumetric flow rate, written Q, is the volume of fluid that passes a chosen cross-section every second. Its SI unit is the cubic metre per second (m³/s), though litres per minute, cubic metres per hour and gallons per minute are common in plumbing, HVAC and irrigation. Because it tracks volume rather than mass, it is independent of the fluid density: a cubic metre of air and a cubic metre of water represent the same volumetric flow even though their masses differ enormously. This makes Q the natural quantity for sizing pipes, pumps and ducts, and this calculator reports it in all the everyday units at once.
Four ways to find Q, plus reverse solving
The first method comes from geometry: multiply the cross-section area A that the fluid flows through by its average velocity v, giving Q = A·v. If you only have a round pipe, pick the diameter mode and the calculator builds the area for you as A = π(d/2)². The third method is purely a definition: if a known volume V passes in a time t, then Q = V ÷ t. The fourth runs the algebra backwards, given a target flow rate and the pipe area it solves for the velocity the fluid must reach, v = Q ÷ A, which is how engineers check that a pipe is not undersized. Every input is converted to SI base units first, so you can freely mix metres, inches, gallons and hours.
Mass flow rate and continuity
Turn on mass flow to multiply the volumetric rate by the fluid density, ṁ = ρ·Q, giving the kilograms per second that matter for heating, dosing and combustion. For an incompressible fluid with no leaks or branches the volumetric flow rate is the same at every point along a pipe, the continuity equation A₁v₁ = A₂v₂. A practical consequence is that squeezing the pipe to a smaller area forces the fluid to speed up to carry the same Q, which is exactly why a thumb over the end of a garden hose produces a faster jet.
Estimating the energy to move the flow
Moving a flow costs energy whenever a pump has to lift it or push it through friction. The useful hydraulic power is P = ρ·g·Q·H, where H is the total head in metres (vertical lift plus friction losses) and g is 9.81 m/s². Dividing by the wire-to-water efficiency of the pump and motor gives the electrical power it actually draws. The calculator turns that into kilowatt-hours per day from your run hours, then a daily and monthly cost at your electricity price. These figures are planning estimates: real head loss depends on pipe size, length and fittings, so confirm with a proper pipe-friction calculation before specifying a pump.
Common flow-rate unit conversions
| From | To | Multiply by |
|---|---|---|
| 1 m³/s | L/min | 60,000 |
| 1 m³/s | m³/h | 3,600 |
| 1 m³/s | US gal/min | 15,850 |
| 1 L/min | m³/s | 0.0000167 |
| 1 US gal/min | m³/s | 0.0000631 |
| 1 ft³/s | m³/s | 0.02832 |
Multiply a value in the left unit by the factor to reach the unit on the right.
Frequently asked questions
What is the difference between volumetric and mass flow rate?
Volumetric flow rate (Q) measures the volume of fluid passing per second and is given in m³/s. Mass flow rate (ṁ) measures the mass per second in kg/s. They are linked by the fluid density: ṁ = ρ·Q. Turn on the mass flow option and enter a density to get both at once.
How do I find the flow rate from a pipe diameter?
Pick the pipe diameter mode and enter the inside diameter and the velocity. The calculator builds the area as A = π(d/2)², then multiplies by velocity for Q = A·v. If you already know the area, the area mode skips that step.
How do I work out the velocity a pipe needs for a given flow?
Choose the solve-for-velocity mode, enter the target flow rate and the pipe cross-section area, and the calculator returns v = Q ÷ A. For water, keeping that velocity below roughly 1.5 to 2.4 m/s limits noise, water hammer and pipe erosion.
How is the pumping cost estimated?
The useful power is P = ρ·g·Q·H, where H is the total head in metres. Dividing by the pump and motor efficiency gives the electrical power drawn; multiplying by run hours and your electricity price gives the daily and monthly cost. It is a planning estimate, since real head loss depends on pipe size, length and fittings.
Does flow rate stay the same all along a pipe?
For an incompressible fluid in a sealed pipe with no branches, yes, the continuity equation A₁v₁ = A₂v₂ keeps Q constant. Where the pipe narrows, the velocity rises to compensate; where it widens, the velocity falls.