What this calculator does
This flow rate calculator works out how much fluid moves through a pipe or channel per second, in two related ways: volumetric flow rate, the volume passing per unit time, and mass flow rate, the mass passing per unit time. Both come from the same three measurements: the cross-sectional area the fluid is flowing through, how fast it is moving, and the fluid's density.
Volumetric flow rate answers "how much volume per second", while mass flow rate answers "how much mass per second", and the two only match numerically for a fluid with a density of exactly 1. For water, whose density sits close to 1,000 kg/m³, mass flow rate in kilograms per second is roughly 1,000 times the volumetric flow rate in cubic metres per second; for a lighter fluid such as oil, the same volumetric flow carries less mass.
The formula
Volumetric flow rate is area multiplied by velocity (Q = A × v): a wider pipe or a faster-moving fluid both push more volume through per second. Mass flow rate is then that volumetric flow rate multiplied by the fluid's density (ṁ = ρ × Q), converting a volume-per-second figure into a mass-per-second figure for whatever fluid is actually flowing.
| Term | Meaning |
|---|---|
| Q | Volumetric flow rate, the volume of fluid passing a point per unit time, in cubic metres per second (m³/s), also shown in litres per second and per minute. |
| ṁ | Mass flow rate, the mass of fluid passing a point per unit time, in kilograms per second (kg/s), also shown in kilograms per hour. |
| A | Cross-sectional area of the pipe or channel the fluid is flowing through, in square metres. |
| v | Flow velocity, the average speed of the fluid through that cross-section, in metres per second. |
| ρ | Fluid density, in kilograms per cubic metre; water is close to 1,000 kg/m³ at room temperature. |
The inputs explained
| Field | What to enter |
|---|---|
| Cross-sectional area (m²) | The cross-sectional area the fluid flows through. For a round pipe, this is π × radius², not the pipe's diameter. |
| Flow velocity (m/s) | The average flow velocity of the fluid through that cross-section. |
| Fluid density (kg/m³) | The density of the fluid flowing, in kg/m³. Water is close to 1,000 kg/m³ at room temperature; use the water density calculator for a more precise figure at a specific temperature, or your fluid's own known density for anything else. |
When to use it
Sizing a pipe for a target flow
Given a desired volumetric flow rate and a chosen fluid velocity, cross-sectional area, and from it pipe diameter, can be worked backwards from the same relationship.
Converting a measured velocity into a delivery rate
A flow meter or estimate often reports velocity directly; multiplying by the known cross-sectional area turns that into a volume or mass delivered per second, minute or hour.
Comparing flows of different fluids through the same pipe
The same pipe and velocity produce the same volumetric flow rate regardless of fluid, but a very different mass flow rate depending on how dense that fluid is.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How flow rate changes with velocity, at a fixed pipe area
A fixed 0.01 m² cross-sectional area and water at 1,000 kg/m³, across a range of flow velocities.
| Flow velocity | Volumetric flow rate | Mass flow rate (kg/s) |
|---|---|---|
| 1 m/s | 0.0100 m³/s | 10.000 kg/s |
| 2 m/s | 0.0200 m³/s | 20.000 kg/s |
| 3 m/s | 0.0300 m³/s | 30.000 kg/s |
How mass flow rate changes with fluid density, at a fixed area and velocity
A fixed 0.01 m² area and 2 m/s velocity, across a range of fluid densities.
| Fluid density | Volumetric flow rate | Mass flow rate (kg/s) |
|---|---|---|
| 800 kg/m³ | 0.0200 m³/s | 16.000 kg/s |
| 1,000 kg/m³ | 0.0200 m³/s | 20.000 kg/s |
Questions
What is the difference between volumetric and mass flow rate?
Volumetric flow rate measures volume moved per unit time, regardless of what the fluid weighs. Mass flow rate measures the actual mass moved per unit time, which depends on the fluid's density as well as its volumetric flow rate.
How do I find the cross-sectional area of a round pipe?
Use A = π × r², where r is the pipe's internal radius, not its diameter. Halving the radius used by mistake, instead of halving the diameter, is a common source of a wildly wrong area.
Why does mass flow rate matter if I already know volumetric flow rate?
Mass flow rate matters wherever the fluid's weight is what counts, such as sizing structural supports, calculating heat transfer, or billing by weight rather than volume. The two figures only tell the same story for a fluid with a density of exactly 1,000 kg/m³ measured in the matching units.
Does this calculator assume a specific fluid?
No. Density is a free input, so this works for water, air, oil or any other fluid once its density is known. The default of 1,000 kg/m³ is a convenient water approximation at room temperature, not a fixed assumption.
For a precise water density figure at a specific temperature, see the water density calculator. For the viscosity figures relevant to more detailed pipe-flow calculations, see the water viscosity calculator.