Mass Flow Rate Calculator
Enter a fluid's density, the cross-sectional area, and the flow velocity to get the mass flow rate in kilograms per second — plus the volumetric flow rate.
Use SI units
Density in kg/m³, area in m², and velocity in m/s give the flow in kg/s — convert cm² to m² by dividing by 10,000 before you start.
What is mass flow rate?
How much mass moves per second
Mass flow rate is how much mass of a fluid passes through a given cross-section every second. This mass flow rate calculator turns three measurements — the density in kilograms per cubic metre, the cross-sectional area in square metres, and the flow velocity in metres per second — into the mass flow rate in kilograms per second, alongside the volumetric flow rate (area times velocity). It is the number behind pipe sizing, pump and fan selection, ventilation design, and engine fuel and air delivery: anywhere you need to know how much material is actually moving, not just how fast it travels.
Enter a density, a cross-sectional area, and a flow velocity to get the mass flow rate in kg/s and the volumetric flow rate instantly.
The mass flow rate is the density multiplied by the cross-sectional area and the flow velocity, and the volumetric flow rate is simply area times velocity.
ṁ = ρ × A × vBecause the three quantities are multiplied together, each one scales the result directly: double the density, the area, or the velocity and the mass flow rate doubles. Use kilograms per cubic metre, square metres, and metres per second, and the flow comes back in kilograms per second, with the volumetric flow rate in cubic metres per second.
Suppose water (density 1000 kg/m³) flows through a pipe with a 0.01 m² cross-section at 2 m/s.
Find the volumetric flow rate
0.01 × 2 = 0.02 m³/s — the volume passing each second.
Multiply by the density
1000 × 0.02 = 20 — density times the volume per second.
Read the result
The mass flow rate is 20 kg/s, and the volumetric flow rate is 0.02 m³/s.
The two outputs answer two different questions. The mass flow rate (20 kg/s for the pipe above) tells you how much actual mass moves per second — the figure you need to size a pump, balance an energy budget, or check that a process receives enough material. The volumetric flow rate (0.02 m³/s) tells you how much space the fluid occupies per second, which matters for pipe diameter and velocity limits. The two are linked by density: ṁ = ρ × Q. For incompressible liquids like water the density barely changes, so the two figures track each other closely. For gases, density rises with pressure and falls with temperature, so the same volumetric flow can carry very different masses — which is why engineers usually specify gas flows by mass. The continuity principle adds one more insight: in a closed pipe the mass flow rate stays constant, so where the pipe narrows the velocity must rise to compensate.
The formula is exact for a uniform flow, but a couple of practical points are worth keeping in mind.
Average velocity and consistent units
This calculator uses the average velocity across the cross-section. Real flows in pipes are faster in the centre than at the walls, so for precise work use the area-averaged velocity rather than a single point reading. Keep your units consistent — kg/m³ for density, m² for area, and m/s for velocity — or the result will be wrong: convert cm² to m² by dividing by 10,000 and km/h to m/s by dividing by 3.6 before you enter them.