- Home |
- About |
- Contact Us |
- Privacy |
- Newsletter |
- Shop |
- Donate

Welcome to our Volume of a Pipe Calculator page.

We explain how to find the volume of a pipe and provide a quick calculator to work it out for you, step-by-step.

There are also some worked examples so you can see how to find the volume of a pipe for yourself.

Quicklinks to ...

This calculator from omnicalculator.com finds the volume of a pipe when the inner diameter and pipe length are known.

You can also change any of the units of measurement so you can convert the volume into liters or gallons or cubic cm if you wish.

Volume of a Pipe Calculator

- Choose a value for the inner diameter (d) and select the required measurement units.
- Choose a value for the pipe length (l) and select the required measurement units.
- Choose your units of measurement for the volume result.

The volume of a pipe is the amount of space inside it, or the amount of liquid it can hold when full.

A pipe is basically the same shape as an open cylinder. So the formula for the volume of a pipe is the same as the formula for the volume of a cylinder.

The main difference is the fact that some pipes can be quite thick, and to get an accurate result, we have to look at the inner diameter of the pipe rather than the outer diameter.

The volume of a pipe is: \[ V = \pi r^2 l \]

where r is the inner radius of the pipe and l is the length of the pipe.

To find the inner radius of the pipe, we need to halve the inner diameter (d).

If you would like to see where the formula comes from, then we hope you will find the explanation below useful.

The volume of a pipe is the amount of space inside the pipe.

To find the amount of space inside the pipe, we need to find the area of the circular cross-section of the pipe and multiply this amount by the length of the pipe.

The area of the circular cross-section of the pipe is: \[ A = \pi r^2 \] where A is the area and r is the inner radius of the pipe.

This means that the volume of the pipe is: \[ V = \pi r^2 l \; where \; r \; is \; the \; inner \; radius \; and \; l \; is \; the \; length \; of \; the \; pipe \]

A pipe has an inner diameter of 5 cm and a length of 32 cm. Find the volume to 1 decimal place.

The inner diameter of the pipe is 5cm, so the inner radius is 5 ÷ 2 = 2.5 cm.

The formula for the volume of a pipe is: \[ V = \pi r^2 l \]

If we substitute the values of the radius and length into this equation, we get: \[ V = \pi \cdot 2.5^2 \cdot 32 = \pi \cdot 6.25 \cdot 32 = 200 \pi \]

This gives us a final answer of: \[ V = 628.3 \;\ cm^3 \; to \; 1 \; decimal \; place \]

A pipe has an inner diameter of 1.5 inches and a length of 18 inches. Find the volume to 1 decimal place.

The inner diameter of the pipe is 1.5 inches, so the inner radius is 1.5 ÷ 2 = 0.75 inches.

The formula for the volume of a pipe is: \[ V = \pi r^2 l \]

If we substitute the values of the radius and length into this equation, we get: \[ V = \pi \cdot 0.75^2 \cdot 18 = \pi \cdot 0.5625 \cdot 18 = 10.125 \pi \]

This gives us a final answer of: \[ V = 31.8 \;\ in^3 \; to \; 1 \; decimal \; place \]

A ½ inch thick pipe has an outer diameter of 8 inches and a length of 24 foot. Find the volume to the nearest cubic inch.

First we need to find the inner diameter of the pipe.

If the outer diameter is 8 inches and the pipe is ½ inches thick, then we need to subtract twice the thickness of the pipe from the outer diameter to find the inner diameter (see diagram below).

This gives us an inner diameter of 7 inches.

This means that the inner radius = 7 ÷ 2 = 3.5 inches

Next we need to convert the length of the pipe into inches, so that both measurement units are the same. 1 ft = 12 inches.

1 ft = 12 inches, so 24 ft = 24 x 12 = 288 inches.

The formula for the volume of a pipe is: \[ V = \pi r^2 l \]

If we substitute the values of the radius and length into this equation, we get: \[ V = \pi \cdot 3.5^2 \cdot 288 = \pi \cdot 12.25 \cdot 288 = 3528 \pi \]

This gives us a final answer of: \[ V = 11,084 \;\ in^3 \; to \; the \; nearest \; cubic \; inch \]

A pipe has an inner diameter of 3.2 cm and a length of 4.8 m. How many liters of water will it hold? Give your answer to 2 decimal places.

First we need to convert the length of the pipe into cm.

1 m = 100 cm. So 4.8 m = 480 cm.

The inner diameter of the pipe is 3.2 cm. This means that the inner radius = 3.2 ÷ 2 = 1.6 cm

The formula for the volume of a pipe is: \[ V = \pi r^2 l \]

If we substitute the values of the radius and length into this equation, we get: \[ V = \pi \cdot 1.6^2 \cdot 480 = \pi \cdot 2.56 \cdot 480 = 1228.8 \pi = 3860.39 cm^3 \; to \; 2 \; decimal \; places \]

Next we need to convert from cm^{3} into liters.

1 liter = 1000 cm^{3} so 3860.39 cm^{3} = 3.86039 liters

This gives us a final answer of: \[ V = 3.86 \; liters \; to \; 2 \; decimal \; places \]

Take a look at some more of our resources similar to these.

We have a range of other area calculators to help you find the area of a range of different 2d and 3d shapes.

We have a range of other area worksheets and support pages for a range of different 2d shapes.

We have a wide range of free math calculators to help you.

Most of our calculators show you their working out so that you can see exactly what they have done to get the answer.

Our calculator hub page contains links to all of our calculators!

How to Print or Save these sheets 🖶

Need help with printing or saving?

Follow these 3 steps to get your worksheets printed perfectly!

How to Print or Save these sheets 🖶

Need help with printing or saving?

Follow these 3 steps to get your worksheets printed perfectly!

Sign up for our newsletter and get free math support delivered to your inbox each month. Free seasonal math grab pack included.

The Math Salamanders hope you enjoy using these free printable Math worksheets and all our other Math games and resources.

We welcome any comments about our site or worksheets on the Facebook comments box at the bottom of every page.

## New! Comments

Have your say about the Math resources on this page! Leave me a comment in the box below.