# Flow Rate Calculator

Created by Hanna Pamuła, PhD
Reviewed by Bogna Szyk and Jack Bowater
Last updated: Jun 05, 2023

Believe it or not, our flow rate calculator is not only useful in fluid mechanics but also in everyday problems. It will not only help you if you want to find the flow rate of a garden hose or shower head but also if you're curious about how much blood your heart pumps every minute (what we met at the cardiac output calculator). It may also serve as a simple pipe velocity calculator.

For a complete understanding of the topic, you can find a section explaining what the flow rate is below, as well as a paragraph helping to understand how to calculate the flow rate. Be careful, as the term "flow rate" itself may be ambiguous! Luckily for you, we've implemented two flow rate formulas, so you're covered in both cases. This means that our tool may serve as both a volumetric flow rate calculator (i.e., we can use it to calculate the gallons per minute) and a mass flow rate calculator.

## What is flow rate? Volumetric and mass flow rate

When we talk about flow rate, you most likely picture the concept of volumetric flow rate (also known as rate of liquid flow, volume flow rate or volume velocity). The volumetric flow rate can be defined as the volume of a given fluid that passes through a given cross-sectional area per unit of time. It's usually represented by the symbol $Q$ (sometimes $\dot{V}$$V$ with a dot)

$Q = \frac{V}{t}$

Another related concept is mass flow rate, sometimes called mass flux or mass current. This time it's not the volume, but mass of a substance that passes through a given cross-sectional area per unit of time. It is an essential measure when purifying water in a wastewater plant.

We indicate it with a dot over the symbol $m$:

$\dot{m} = \frac{m}{t}$

Mass flow rate is commonly used in the specifications of fans and turbines, amongst other things.

## How to calculate flow rate? Flow rate formulas

TL;DR version

• Volumetric flow rate formula:
$\dot{V} = A\cdot v$

where,

• $A$ — The cross-sectional area; and

• $v$ — The flow velocity.

• Mass flow rate formula:

$\dot{m} = \rho\cdot\dot{V} =\rho\cdot A\cdot l$

where $ρ$ is the fluid's density.

Longer explanation:

The volumetric flow rate formula may be written in the alternative (read: way more useful) form. You can first calculate the volume of a portion of the fluid in a channel as:

$V = A\cdot l$

where A is a cross-sectional area of the fluid, and $l$ is the width of a given portion of the fluid. If our pipe is circular, it's just the formula for to calculate the cylinder volume. Substituting the above formula to the equation from the flow rate definition, we obtain:

$\dot{V} = \frac{V}{t} = \frac{A\cdot l}{t}$

As $l / t$ is the volume length divided by time, you can see that it's just the flow velocity. So, the volumetric flow rate formula boils down to:

$\dot{V} = A\cdot v$

Most pipes are cylindrical, so the formula for volumetric flow rate will look as follows:

$\dot{V}_{\mathrm{cyclinder}} =\pi\cdot \left(\frac{d}{2}\right)^2\cdot v$

where $d$ is the pipe's diameter.

The equation can be rearranged to find the formula for pipe velocity.

To find the mass flow rate formula, we need to remind ourselves of the density definition first:

$\rho = \frac{m}{V}$

As the mass flow rate is the mass of a substance passing per unit of time, we can write the formula as:

$\dot{m} = \frac{m}{t} = \frac{\rho\cdot V}{t} = \rho\cdot\dot{V} = \rho\cdot A\cdot v$

The last equality is the most refined one:

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

## How to use the flow rate calculator

Now that you know what the flow rate is, let's check it out with a simple example:

1. First, select a shape from the drop-down list. For this example, we'd like to know the flow rate of water in a circular pipe, so we will select the circular (full) option.

2. Input the measurements needed to compute cross-sectional area. If the cross-section is a circle or square/rectangle, you'll find that option on the list. In every other case, you can type the area value directly into the calculator (you can use our comprehensive area calculator to help you). Let's choose a pipe with an internal diameter of $3\ \mathrm{in}$.

3. Enter the average velocity of the flow. Let's pick $10\ \mathrm{ft/s}$.

4. And there it is, the first part of the calculations is done: the tool has worked as a volumetric flow rate calculator. We've found out that the volumetric flow rate is $0.4909\ \mathrm{ft^3/s}$. Remember, you can always change the units, so don't worry if you need to work in gallons/minute or liters/hour.

5. If you know the density, you can calculate the mass flow rate as well; just input the density of the flow material. In our example, water has a flow rate of approximately $998\ \mathrm{kg/m^3}$ (the density of water at $68\ \mathrm{\degree F}$, or $20\ \mathrm{\degree C}$). However, if you want to be super accurate, check out our water density calculator, as the density changes with temperature, salinity, and pressure.

6. The tool displayed a mass flow rate of $30.58\ \mathrm{lbs/s}$. Great!

Don't forget that our tools are flexible, so you can use this calculator as a pipe velocity calculator. You can, for example, determine the water velocity of your faucet, given the diameter (e.g., $0.5\ \mathrm{in}$) and flow rate of a kitchen faucet (the usual range is $1$ gallon - $2.2$ gallons per minute, depending on the aerator type). By the way, have you seen our tap water calculator, which shows your savings if you were to switch from bottled to tap water?

## FAQ

### What is flow rate?

Flow rate is a quantity that expresses how much substance passes through a cross-sectional area over a specified time. The amount of fluid is typically quantified using its volume or mass, depending on the application.

### How do I find mass flow rate from volumetric flow rate?

To find the mass flow rate, you need to multiply the volumetric flow rate by the density of the substance. This relation is easier to remember if you recall that density is the quotient of mass and volume.

### How do I calculate blood flow rate?

To calculate blood flow rate through a blood vessel:

1. Divide the diameter of the vessel by 2 to obtain the radius.
2. Find the circular cross-sectional area using A = π × r².
3. Determine the (average) velocity of blood in the vessel.
4. Multiply the area by the velocity to obtain the volumetric blood flow rate.

### What does maximum flow rate mean?

The maximum flow rate tells you the upper limit of how much fluid can be transferred through an object within a specific time interval. For example, the larger it is for a tap, the faster you can fill a bath.

### How do I calculate fluid velocity from flow rate?

To determine fluid velocity from the volumetric flow rate, you need to divide it by the cross-sectional area of the substance.

For the mass flow rate, perform an additional division by the fluid density.

Hanna Pamuła, PhD
Shape
circular (pipe) Diameter (d)
in
Velocity
ft/s
Density
lb/cu ft
Flow rate
(Volumetric) flow rate
ft³/s
Mass flow rate
lb/s
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