What is the formula for volumetric flow rate?

Volumetric flow rate Q equals the cross-sectional area of the pipe or channel multiplied by the average flow velocity: Q = A times v. Q is measured in cubic metres per second (m3/s), A in square metres, and v in metres per second. For a circular pipe, A = pi times (D/2) squared, where D is the pipe diameter. Flow rate is also commonly expressed in litres per second (L/s) where 1 m3/s = 1000 L/s.

What is the difference between volumetric and mass flow rate?

Volumetric flow rate Q measures the volume of fluid passing a point per unit time (in m3/s or L/s) and does not account for the density of the fluid. Mass flow rate m-dot equals the density rho multiplied by the volumetric flow rate Q: m-dot = rho times Q. Mass flow rate is measured in kilograms per second and is the more fundamental quantity in energy and material balances because it is conserved even when density changes with temperature or pressure.

How do you find flow velocity from flow rate?

Rearrange Q = A times v to get v = Q divided by A. For a circular pipe, A = pi times (D/2) squared, so v = Q divided by (pi times r squared). This is useful when you know the flow rate from a meter or specification sheet and need to find the velocity at which the fluid moves through a particular pipe size.

Flow Rate Calculator

Flow rate is a measure of how much fluid passes through a pipe, channel, or opening per unit of time. It comes in two forms: volumetric flow rate, which measures volume per second, and mass flow rate, which measures mass per second. Volumetric flow rate Q is calculated using the simple formula Q equals the cross-sectional area A multiplied by the average fluid velocity v. For a circular pipe, the area is pi times the radius squared, which means the pipe diameter has a large effect: doubling the diameter quadruples the area and therefore quadruples the flow rate at the same velocity. Flow rate appears in almost every branch of engineering and science, from sizing water supply pipes and designing irrigation systems to calculating fuel delivery in engines, airflow through ventilation ducts, and blood flow in physiological research. Mass flow rate adds the fluid density to the equation: mass flow rate equals density multiplied by the volumetric flow rate. This is the more fundamental quantity for energy balances, heat exchangers, and chemical reactions, because mass is conserved even when the fluid changes density. This calculator accepts either a cross-sectional area directly or a pipe diameter (it will compute the circular area for you), along with the flow velocity and fluid density. It returns the volumetric flow rate in cubic metres per second, litres per second, and litres per minute, plus the mass flow rate in kilograms per second.

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Input mode

Cross-sectional area A

m²

Pipe diameter D

Flow velocity v

m/s

Fluid density ρ

kg/m³

0.0500 m³/s

volumetric flow rate Q

In L/s50.00 L/s

In L/min3,000 L/min

Mass flow rate50.00 kg/s

Area used0.0100 m²

Assumes uniform (plug) flow across the cross-section. Real pipe flow has a velocity profile; the average velocity is typically used in this formula.

How it works

Volumetric flow rate: Q = A × v, where A is the cross-sectional area in m² and v is the average velocity in m/s. For a circular pipe: A = π × (D/2)². Conversions: 1 m³/s = 1000 L/s = 60,000 L/min. Mass flow rate: ṁ = ρ × Q, where ρ is fluid density in kg/m³.

Worked example

A pipe has a cross-sectional area A = 0.01 m² and water flows through it at v = 5 m/s. Volumetric flow rate Q = A × v = 0.01 × 5 = 0.0500 m³/s = 50.00 L/s = 3,000 L/min. With water density at 1000 kg/m³, mass flow rate = 1000 × 0.05 = 50.00 kg/s. These match the default values pre-filled in the calculator above.

Related calculators

Reynolds Number Calculator: find whether flow is laminar or turbulent.
Hydrostatic Pressure Calculator: calculate pressure at a given depth in a fluid.
Velocity Calculator: find speed, distance, or time from motion equations.
Density Calculator: find density, mass, or volume.

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