Mass Flow Rate Calculator

Fluid density

Cross-sectional area

Flow velocity

Mass flow rate

Compare a second cross-section

Apply the continuity equation: enter a different flow area and see the new velocity.

Total the mass moved over time

Multiply the flow rate by a time window to get the mass transferred.

Enter any three of density, area, velocity, and mass flow rate. The calculator solves for the fourth.

Please input values into the fields

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Show the flow-vs-velocity chart

Plot how mass flow rate scales with velocity at your density and area.

Show the sample table

A table of mass and volumetric flow at a range of velocities.

Mass flow rate is the mass that passes through a given point per second. It's a useful quantity even when density changes and can be applied in situations where volume changes but mass remains constant, such as with compressed gases, steam flowing through a turbine or hot air rising up a duct. You can calculate mass flow rate if you know density, cross-sectional area of the stream and velocity, and you can leave one of these four fields blank to find the corresponding value.

What is mass flow rate?

Mass flow rate is the mass of a fluid passing through a given cross-sectional area in a certain amount of time and is denoted by "m-dot". For non-compressible liquids such as water, it is almost exactly equivalent to volumetric flow. With gases, however, density changes due to pressure or temperature changes so that the two values no longer match up. The mass flow rate remains important even under these conditions.

The SI unit is kilograms per second. Laboratories often use grams per second and factories quote prices in pounds per minute, and the calculator will convert these units on input.

How to use this calculator:

Enter three of four values: density, flow area, velocity or mass flow rate. Leave the fourth field blank and the tool will calculate that value for you. If water with a density of 1000kg/m3 passes through an opening with an area of 0.0005m2 at a speed of 2m/s then the result is 1kg/s. Reverse calculations are also possible. You can specify a target mass flow rate and enter the other two values to find the missing value. This can be useful for sizing a pipe or adjusting a pump to suit operating conditions. The units can be freely combined, so you could use square inches for area, feet per second for velocity, and kg/m3 for density, for example.

Understanding the formula.

You multiply the density by area and speed.

\dot{m} = \rho \, A \, v

Here m-dot is the mass flow rate, rho is density, A is cross-sectional area and v is average velocity. When you combine all of these units together, your result must have a dimension that represents mass divided by time.

\frac{kg}{m^3} \times m^2 \times \frac{m}{s} = \frac{kg}{s}

The cubic meters cancel each other out leaving kilograms per second at the end. The following table shows the individual symbols and example values.

Symbol	Meaning	Example
m-dot	Mass flow rate	result
rho	Fluid density	1000 kg/m3
A	Cross-sectional area	0.0005 m2
v	Flow velocity	2 m/s

Example calculation:

Assume the garden hose nozzle has an opening area of about 0.0005 m². If water with a density of 1000 kg/m³ flows through at a speed of 2 m/s, then the mass flow is 1 kg/s, which is the product of 1000, 0.0005 and 2, and corresponds to one liter of water per second. If we extend this to a jet engine in cruise mode, the air density at the intake tract is about 1.2 kg/m³, the area of the intake tract is approximately 2 m², and the air flows in with a speed of 250 m/s. The result of the calculation is 600 kg/s, which is the product of 1.2, 2 and 250. The intake of six hundred kilograms of air per second explains why a jet engine can generate such high thrust.

Mass flow and volume flow

The volume flow rate Q is the volume per unit time while the mass flow rate is the mass per unit time. The density relates the two quantities to each other.

\dot{m} = \rho \, Q

Since the volume flow rate is itself a product of area and velocity, these two equations are simply different perspectives on the same phenomenon. For liquids with constant temperature, density changes very little so either equation can be used. In gases, however, the volumetric value will change depending on pressure while the mass value remains constant. That's why engineers tend to set the scale for gas systems in terms of mass flow rate. Calculation tools report both values simultaneously.

Continuity equation - The flow velocity increases when the pipe narrows

In a steady flow through a tube whose cross-section varies, the mass flow rate is constant from one end to the other.

\rho_1 A_1 v_1 = \rho_2 A_2 v_2

For incompressible fluids the change in density is compensated for so that the flow rate is inversely proportional to the cross-sectional area. If the diameter of a pipe were halved, then the area would be reduced by a factor of four and the speed of the fluid would double. This is the principle behind nozzles and explains why water from a garden hose squirts out faster if you pinch it to reduce its cross-sectional area. The second option for cross-sectional area allows us to find the new velocity at any point in the flow.

In what situations is it used?

HVAC engineers determine the size of heating and cooling systems based on the mass flow rate of air in ducts because density changes due to temperature change are significant enough that considering only volume can lead to misunderstandings. In chemical plants, mass flow rates are tightly controlled to maintain reaction ratios; even a few percent deviation in one reactant's flow rate can ruin an entire production run. In aerospace engineering it is used to calculate fuel consumption and engine suction power. Even in residential ductwork the same principle applies when ensuring that required flow rates are achieved with minimal pressure drop.

Tips for correct calculations:

Adjust the density to match actual operating conditions. The density of water changes slightly with temperature while gases vary more dramatically in their densities. Air at sea level and 15 °C has a density of about 1.225 kg/m3, whereas a temperature of around 100 °C would correspond to a density of about 0.95 kg/m3. So you must use values that match the actual state of your fluid.

Use the actual cross-sectional area instead of nominal dimensions. For a cylindrical pipe, this is π times the square of the inner radius. In most cases, a one inch diameter pipe will not actually have an inside diameter of exactly one inch when you account for wall thickness. Calculation tools give the equivalent circular diameter for any given area which can be helpful in checking against actual piping.

Velocity varies across the cross section of a pipe. It is zero at the pipe wall and greatest in the middle. Calculations require the average velocity across the cross section. Most flow meters give this average value directly, while individual measurement points may not be as accurate.

General Density of Liquids

These are reference values that can be used as a starting point for entering the field of Density. For an accurate calculation use values based on temperature and pressure of the liquid.

Fluid	Density (kg/m3)
Air (sea level, 15 C)	1.225
Carbon dioxide (15 C)	1.98
Steam (100 C, 1 atm)	0.6
Engine oil	900
Water (20 C)	998
Seawater	1025

Frequently asked questions

What is the difference between mass flow and volumetric flow?

The volumetric flow rate is the volume per unit time, e.g. liters per second. The mass flow rate is the mass per unit time, e.g. kilograms per second. Density links both quantities together. For liquids with constant temperature, either quantity can be used. However for gases, the mass flow rate reflects the state of flow more accurately while the volumetric flow rate varies with pressure and temperature.

How can you determine the density of a liquid?

Please provide the temperature and pressure values for the fluid. Water has a density of about 1000 kg/m3 at 20 °C, and air at sea level has a density of about 1.225 kg/m3 at 15 °C. For gases, the density can be calculated using the ideal gas law with pressure, temperature, and molar mass. As liquids have only small changes in their densities due to temperature, usually a single reference value is sufficient.

Can this also be used for compressible fluids?

Yes it is possible by considering a particular cross section at each calculation and using the local density at that point. For compressible fluids, density, area and velocity change along the pipeline while mass flow rate remains constant from one end to another. So using specific values for each cross section will give you same result everywhere.

Why do the calculation results differ from the measured flow?

The formula used is based on average velocity, while the actual velocity distribution at pipe walls is zero and highest in the middle. These differences are further increased by bends, elbows and turbulence within the piping system. For more accurate calculation correction factors should be applied or a Coriolis flow meter or thermal mass flow meter used directly.

What happens if you decrease the diameter of a pipe?

In incompressible flows the velocity increases as the cross-sectional area decreases to keep mass flow constant. If the diameter is halved then the area becomes one quarter so the velocity must be quadrupled. This is the principle of operation of a nozzle and the second cut option shows this relationship varying with the inputted area.

Related calculators

Mass Flux CalculatorCalculate mass flux from density and velocity (G = rho v) or from a mass flow rate and pipe area (G = m_dot / A), and solve for any variable. Adds volumetric flow rate, equivalent pipe diameter, and the Reynolds number.

Pipe Velocity CalculatorCalculate the velocity of a fluid in a round pipe from the flow rate and inside diameter with v = Q/A, or solve for the diameter or flow rate instead. Reports the bore area and mass flow rate, in units from GPM to m³/s.

Mass CalculatorCalculate the mass of an object from its density and volume with m = ρV, or solve for the density or volume instead. Reports the weight under any gravity, in any unit from milligrams to tonnes.

Specific Thrust CalculatorCalculate specific thrust from thrust and air mass flow rate with Is = F / m-dot, and solve for any of the three. Read the result in several speed units, recover the jet exhaust velocity and propulsive efficiency from a flight speed, and benchmark it against real engine types.

Piston Displacement CalculatorFind piston and engine displacement from bore, stroke, and cylinders, plus the volumetric flow rate, compression ratio, bore-stroke ratio, and mean piston speed. Solve for any input.

Thermal Resistance CalculatorCalculate thermal resistance of a layer with R = L / (k A) and solve for any of the four quantities. Find the heat flow from a temperature difference, convert to R-value and U-value, and compare materials.

Disclaimer: This calculator is provided for general informational and educational purposes only. Our calculators are under active development, and results may be inaccurate, incomplete, or unsuitable for your situation. Always verify the figures independently and seek advice from a qualified professional before relying on them. We make no warranties and accept no liability for any loss or decision arising from use of this tool.

References

NASA Glenn: Mass Flow Rate
Definition and derivation of mass flow rate for fluid and gas flow.
Engineering ToolBox: Mass and Volume Flow
Reference relations between mass flow, volume flow, density, and velocity.