How do I convert volumetric flow rate to mass flow rate?

Multiply by the fluid density: mass flow = ρ × Q. For water at 20 °C (998 kg/m³), 10 L/s is 9.98 kg/s. For gases, use the density at the actual line pressure and temperature, not the density at standard conditions.

How do I calculate mass flow rate from pipe diameter and velocity?

Find the flow area A = πD²/4, then ṁ = ρ × A × v. Water at 2 m/s in a 50 mm pipe has A = 1.963×10⁻³ m², Q = 3.927 L/s, and a mass flow of 3.919 kg/s.

What is the difference between mass flow and volumetric flow?

Volumetric flow is the volume of fluid passing a section per second, and mass flow is the mass. For a liquid they differ by a nearly constant density. For a gas the density changes with pressure and temperature, so volumetric flow changes along the line but mass flow stays constant in steady flow.

How do I convert kg/s to lb/hr?

Multiply kg/s by 7,936.6 to get lb/hr. One kg/s is 3,600 kg/h, which is 7,936.6 lb/hr, because 1 kg = 2.20462 lb.

Why does mass flow stay constant in a pipe when the diameter changes?

Mass cannot accumulate in a steady flow, so ρAv is the same at every section. If the area shrinks, the velocity rises to compensate. For a liquid, ρ is constant, so Av is constant too.

Mass Flow Rate Calculator

Mass flow rate from density and volumetric flow, or from pipe diameter and velocity, with fluid presets and results in kg/s, kg/h, and lb/hr.

Scratchpad (not saved)

Save to create a persistent, shareable workspace.

What This Calculator Does

Mass flow rate is the mass of fluid crossing a section each second, $\dot m = \rho Q$. It is the quantity that stays constant along a pipe in steady flow, even when the fluid is a gas whose density and volumetric flow change with pressure and temperature. This calculator works from either a volumetric flow $Q$, or a pipe diameter and mean velocity, and it takes the density from a preset or your own value. Results are given in kg/s, kg/h, and lb/hr, alongside the volumetric flow and velocity. For volumetric flow from pressure, use the flow rate calculator; this page covers the step that follows it.

It combines Calculate From, Pipe Inside Diameter D, Diameter Unit, Mean Velocity v to estimate Mass flow rate ṁ, Mass flow rate, Volumetric flow Q.

Formula & Method

Mass flow rate:

\dot m = \rho\,Q = \rho\,A\,v, \qquad A = \frac{\pi D^2}{4}

where

\dot m

is mass flow (kg/s),

\rho

is fluid density (kg/m³),

Q

is volumetric flow (m³/s),

A

is the flow area,

D

is the inside diameter, and

v

is mean velocity. Given

Q

and

D

, velocity follows from

v = Q/A

. Continuity for steady flow requires

\dot m

to be the same at every section:

\rho_1 A_1 v_1 = \rho_2 A_2 v_2

Notation used in the formulas: $R$ = Mass flow rate ṁ; $x_{1}$ = Calculate From; $x_{2}$ = Pipe Inside Diameter D; $x_{3}$ = Diameter Unit; $x_{4}$ = Mean Velocity v; $x_{5}$ = Velocity Unit; $x_{6}$ = Volumetric Flow Q.

Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.

Use it to size a fuel or coolant line, convert between volumetric and mass flow for process data, or check a flow meter that reports one when the specification gives the other. For gases, use the density at the actual line pressure and temperature.

Worked Examples

Water in a 50 mm pipe at 2 m/s (metric)

Given: D = 50 mm, v = 2 m/s, water at 20 °C (ρ = 998 kg/m³) Method: find the flow area, then Q = Av, then ṁ = ρQ. A = π(0.050)² / 4 = 1.963×10⁻³ m² Q = 1.963×10⁻³ × 2 = 3.927×10⁻³ m³/s = 3.927 L/s ṁ = 998 × 3.927×10⁻³ = 3.919 kg/s = 14,109 kg/h = 31,105 lb/hr

Air from a volumetric flow in cfm (imperial)

Given: Q = 600 ft³/min = 10 ft³/s, air at 20 °C and 1 atm (ρ = 1.204 kg/m³ = 0.0752 lb/ft³) Method: ṁ = ρQ, with density and flow in matching units. ṁ = 0.0752 lb/ft³ × 10 ft³/s = 0.752 lb/s = 2,707 lb/hr In SI: Q = 0.2832 m³/s, so ṁ = 1.204 × 0.2832 = 0.341 kg/s, the same flow. If the same 600 cfm were measured at 5 bar absolute, the density would be about five times larger, and the mass flow with it.

Typical Fluid Densities

Approximate values near atmospheric pressure. Density changes with temperature, and for gases with pressure, so use a datasheet value when accuracy matters.

Fluid	Density (kg/m³)	Density (lb/ft³)
Water at 0 °C	999.8	62.42
Water at 20 °C	998	62.3
Water at 60 °C	983	61.4
Seawater	1025	64.0
Light oil	870	54.3
Diesel fuel	830	51.8
Gasoline	740	46.2
Air at 20 °C, 1 atm	1.204	0.0752

Reference

The continuity relation and its use in pipe flow are covered in Çengel and Cimbala, Fluid Mechanics: Fundamentals and Applications, and in White, Fluid Mechanics. Crane Technical Paper 410 is the standard industry reference for flow of fluids in pipes.

Common Mistakes

Using liquid density for a gas, or the density at standard conditions for a gas at line conditions. A gas at 5 bar has about five times the density it has at 1 bar.
Entering the outside diameter of a pipe instead of the inside diameter. The flow area comes from the bore.
Mixing pounds-mass and pounds-force in lb/hr. Mass flow in lb/hr is pounds-mass per hour.
Treating a standard-flow reading (SCFM, Nm³/h) as an actual volumetric flow. Those are referenced to standard conditions and need the standard density, not the line density.
Assuming volumetric flow is constant along a gas line. Only mass flow is conserved when density changes.

When Not To Use This Calculator

Two-phase flow, such as steam-water mixtures or gas-liquid slugs, where density is not a single value.
Compressible flow near sonic velocity, where density varies strongly along the pipe. Compute at each section from local conditions.
Unsteady flow, where mass accumulates in the pipe and mass flow differs from section to section.
Non-uniform velocity profiles that are not captured by a single mean velocity, as in very short entrance regions.

Frequently Asked Questions

How do I convert volumetric flow rate to mass flow rate?: Multiply by the fluid density: mass flow = ρ × Q. For water at 20 °C (998 kg/m³), 10 L/s is 9.98 kg/s. For gases, use the density at the actual line pressure and temperature, not the density at standard conditions.
How do I calculate mass flow rate from pipe diameter and velocity?: Find the flow area A = πD²/4, then ṁ = ρ × A × v. Water at 2 m/s in a 50 mm pipe has A = 1.963×10⁻³ m², Q = 3.927 L/s, and a mass flow of 3.919 kg/s.
What is the difference between mass flow and volumetric flow?: Volumetric flow is the volume of fluid passing a section per second, and mass flow is the mass. For a liquid they differ by a nearly constant density. For a gas the density changes with pressure and temperature, so volumetric flow changes along the line but mass flow stays constant in steady flow.
How do I convert kg/s to lb/hr?: Multiply kg/s by 7,936.6 to get lb/hr. One kg/s is 3,600 kg/h, which is 7,936.6 lb/hr, because 1 kg = 2.20462 lb.
Why does mass flow stay constant in a pipe when the diameter changes?: Mass cannot accumulate in a steady flow, so ρAv is the same at every section. If the area shrinks, the velocity rises to compensate. For a liquid, ρ is constant, so Av is constant too.

Inputs Used

Calculate From: Used directly in the calculation.
Pipe Inside Diameter D: Needed for the diameter-and-velocity mode. Optional in the volumetric mode, where it also gives the velocity.
Diameter Unit: Unit for the value entered above.
Mean Velocity v: Used in the diameter-and-velocity mode.
Velocity Unit: Unit for the value entered above.
Volumetric Flow Q: Used in the volumetric flow mode.
Flow Unit: Unit for the value entered above.
Fluid (Density ρ): Used directly in the calculation.
Custom Density ρ: Used only when the fluid is set to Custom.
Custom Density Unit: Unit for the custom density.

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