Enter the outside diameter, the inside diameter and the length of the pipe. Besides the volume of the pipe wall (the material), you get the volume of the outer cylinder, the volume of the hollow and unit conversions.
Enter the outside diameter, the inside diameter and the length in the same unit, as numbers only (no units. For example, for an outside diameter of 10 cm enter "10"). The inside diameter must not be larger than the outside diameter.
Result and figure
Enter the outside diameter, the inside diameter and the length in the fields on the left and press "Calculate". The result will appear here.
Table of Contents
-
What you can do on this page
-
What is this calculation used for?
-
How to Use
-
Formulas and figures
-
Symbols and terms
-
Good to know before you start
-
How to calculate it in Excel
-
How to calculate it in Google Sheets
-
How to calculate it in Python
-
How to write it in LaTeX and other math languages (copy and paste)
-
How to have ChatGPT do the calculation
-
DataChef Features
-
Related Features
-
NumberChef Calculators List
What you can do on this page
- Enter the outside diameter, the inside diameter and the length, and you get the volume of the pipe itself (the pipe wall, which is the material) on the spot
- It also shows the volume of the outer cylinder and the volume of the hollow inside (how much water or other liquid fits in the pipe)
- It shows the exact value with \(\pi\) left in (for example, \(900\pi\)) and converts the volume to gallons and ft³. Switch "Units" to Metric to get liters and m³ instead
- The result is also shown as a 3D shape that you can turn by dragging to check the shape
- A plain-language explanation of the formulas and copy-and-paste formulas for Excel, Google Sheets and Python are all on this page
Enter the outside diameter, the inside diameter and the length in the same unit (enter inches and the volume is in in³). This page finds the volume of the pipe wall (the material). For how much water fits inside the pipe, see the "hollow" volume in the result.
What is this calculation used for?
Estimating the weight of steel pipe and scaffold tube (construction and DIY)
1-1/2 inch Schedule 40 steel pipe, the same size as standard scaffold tube, has an outside diameter of 1.900 in and a wall of 0.145 in (an inside diameter of 1.610 in). For 1 ft (12 in) of it, the wall volume is \(\pi \times (0.95^2 - 0.805^2) \times 12 \approx 9.59\,\mathrm{in^3}\). Steel weighs about 0.2836 lb per in³, so it comes to about 2.72 lb per foot (the same as the value in pipe charts).
You can check "how many can we carry?" or "will it fit in the truck?" with numbers before you lift anything.
How much cold water runs before the hot water arrives (home and saving water)
The volume of the hollow in the pipe from the water heater to the faucet is how much cold water flows out before the hot water arrives. For 30 ft (360 in) of 1/2 inch Type L copper pipe (inside diameter 0.545 in, radius 0.2725 in), the hollow is \(\pi \times 0.2725^2 \times 360 \approx 84\,\mathrm{in^3}\), or about 0.36 gallons.
The longer the pipe run in a house, the more water you waste waiting. This formula puts a number on that everyday experience.
Weight and shipping of PVC or metal pipe (DIY and shopping)
When you buy pipe at a home center or online, you can estimate its weight as "wall volume × density of the material". For example, a 10 ft (120 in) length of 1 inch Schedule 40 PVC pipe (outside diameter 1.315 in, inside diameter 1.049 in) has a wall volume of \(\pi \times (0.6575^2 - 0.5245^2) \times 120 \approx 59.3\,\mathrm{in^3}\). Rigid PVC weighs about 0.05 lb per in³, so that is about 3 lb.
You can check whether you can carry it home, or which shipping rate applies, before you order.
Concrete and weight of a storm or sewer pipe (civil engineering)
Concrete pipes buried under roads for sewers and storm drains are designed and made by working out the amount of concrete with this formula. For example, a 36 inch reinforced concrete pipe (inside diameter 36 in, wall 4 in thick, so outside diameter 44 in) 8 ft (96 in) long has a wall volume of \(\pi \times (22^2 - 18^2) \times 96 \approx 48{,}255\,\mathrm{in^3}\), about 27.9 ft³. At about 150 lb per ft³ of concrete, one section weighs about 4,190 lb, more than 2 tons.
Choosing a crane and planning the delivery both start from a volume calculation like this.
Estimating material cost in metalworking (manufacturing)
Stainless steel and copper tubing is often priced by weight, so a quote is "wall volume × density × price per pound". For example, a stainless steel tube with an outside diameter of 2.5 in, an inside diameter of 2 in and a length of 20 in has a wall volume of \(\pi \times (1.25^2 - 1^2) \times 20 \approx 35.3\,\mathrm{in^3}\). At about 0.29 lb per in³, it weighs about 10.2 lb.
This formula lets you estimate the material cost from the dimensions while the part is still being designed.
Formulas and figures
The idea behind the volume of a pipe (outside minus the hollow)
Figure
Standard notation
(the usual math form)
\(V\)
\(=\)
\(V_1\)
\(-\)
\(V_2\)
In words
(symbols replaced with words)
③
\(V\): volume of the pipe
\(=\)
①
\(V_1\): volume of the outer cylinder
\(-\)
②
\(V_2\): volume of the hollow
The formula in words
①
From the
\(V_1\): volume of the outer cylinder
②
subtract the
\(V_2\): volume of the hollow
(the inner cylinder)
③
and you get the
\(V\): volume of the pipe
Quick example
For a pipe with an outside diameter of 10 in, an inside diameter of 8 in and a length of 100 in
\(V\): volume of the pipe
\(=\)
outer volume (2500π in³)
\(-\)
hollow volume (1600π in³)
\(2500\pi - 1600\pi = 900\pi \approx 2827.43\,\mathrm{in^3}\)
Key idea
A pipe (tube) is a cylinder with a hole through it. The volume of a shape with a hole is hard to find directly, so take the volume of the outer cylinder as if it were solid, and subtract the volume of the hollow. This is the most important idea on this page.
What is left after the subtraction (the pipe wall, which is the material) is the volume of the pipe itself. The hollow you subtracted is how much water or air fits inside the pipe.
Volume of a cylinder (the basic formula)
Figure
Standard notation
(the usual math form)
\(V\)
\(=\)
\(\pi\)
\(\times\)
\(r\)
\(2\)
\(\times\)
\(h\)
In words
(symbols replaced with words)
⑤
\(V\): volume of the cylinder
\(=\)
①
\(\pi\): pi
\(\times\)
②
\(r\): base radius
③
squared (the number times itself)
\(\times\)
④
\(h\): height
The formula in words
①
Take
\(\pi\): pi
②
multiply it by the
\(r\): base radius
③
squared (the number times itself)
to get the area of the base circle (the base area)
④
multiply by the
\(h\): height
⑤
and you get the
\(V\): volume of the cylinder
Quick example
For a cylinder with a radius of 5 in and a height of 100 in (the outer cylinder of the pipe above)
\(V\): volume of the cylinder
\(=\)
\(\pi\): pi
\(\times\)
base radius (5 in)
squared
\(\times\)
height (100 in)
\(\pi \times 5^{2} \times 100 = 2500\pi \approx 7853.98\,\mathrm{in^3}\)
Key idea
The volume of a cylinder is "base area × height". The base is a circle, so the base area is "π × radius squared" (the area of a circle).
For a pipe, you use this formula twice: once for the outer cylinder and once for the inner cylinder (the hollow). For a pipe lying on its side, the "height" is the length of the pipe.
Formula for the volume of a pipe (the one this calculator uses)
Figure
Standard notation
(the usual math form)
\(V\)
\(=\)
\(\pi\)
\(\times\)
\((\)
\(r_1\)
\(2\)
\(-\)
\(r_2\)
\(2\)
\()\)
\(\times\)
\(l\)
In words
(symbols replaced with words)
⑥
\(V\): volume of the pipe
\(=\)
④
\(\pi\): pi
\(\times\)
\((\)
①
\(r_1\): outer radius
③
squared
\(-\)
②
\(r_2\): inner radius
③
squared
\()\)
\(\times\)
⑤
\(l\): length of the pipe
The formula in words
①
Take the
\(r_1\): outer radius
②
and the
\(r_2\): inner radius
③
square
each of them and subtract (\(r_1^2 - r_2^2\))
④
multiply by
\(\pi\): pi
⑤
and by the
\(l\): length of the pipe
⑥
and you get the
\(V\): volume of the pipe
Quick example
For a pipe with an outside diameter of 10 in, an inside diameter of 8 in and a length of 100 in (as radii, \(r_1 = 5\) and \(r_2 = 4\))
\(V\): volume of the pipe
\(=\)
\(\pi\): pi
\(\times\)
\((\)
outer radius (5 in)
squared
\(-\)
inner radius (4 in)
squared
\()\)
\(\times\)
length (100 in)
\(5^{2} - 4^{2} = 25 - 16 = 9\)
\(\pi \times 9 \times 100 = 900\pi \approx 2827.43\,\mathrm{in^3}\)
Key idea
Take the subtraction from formula 1, \(\pi r_1^2 l - \pi r_2^2 l\), factor out the common \(\pi\) and \(l\), and you get this single formula.
When you only know the diameters (the outside diameter \(d_1\) and inside diameter \(d_2\)), as in a catalog or a drawing, put radius = diameter ÷ 2 into it and you can also write \(V = \pi \times \dfrac{d_1^2 - d_2^2}{4} \times l\). (This calculator turns the diameters you enter into radii automatically.)
Diameter and radius
Figure
Standard notation
(the usual math form)
\(r\)
\(=\)
\(d\)
\(\div\)
\(2\)
In words
(symbols replaced with words)
③
\(r\): radius
\(=\)
①
\(d\): diameter
\(\div\)
②
\(2\): to take half
The formula in words
①
Take the
\(d\): diameter
②
divide it by
\(2\): to take half
③
and you get the
\(r\): radius
Quick example
For a pipe with an outside diameter of 10 in, the outer radius is
\(r_1\): outer radius
\(=\)
outside diameter (10 in)
\(\div\)
to take half (2)
\(10 \div 2 = 5\,\mathrm{in}\)
Key idea
In catalogs and drawings, the size of a pipe is normally given as the outside and inside diameters, not the radii. The cylinder formula, on the other hand, uses the radius, so divide each diameter by 2 before putting it into the formula. The most common mistake is to square the diameter as is, so watch out for it. (The "nominal size" printed on US pipe, such as "1-1/2 inch", is a name, not a measurement; look up the actual OD and wall thickness in a pipe chart.)
The volume of a pipe is "the volume of the outer cylinder minus the volume of the hollow (the inner cylinder)". The volume of a cylinder is "π × radius squared × height (length)". The key is to divide the outside and inside diameters from a catalog by 2 to get the radii before using them.
Symbols and terms
Symbols
| \(V\) | vee | A common symbol for volume, from the first letter of "volume". On this page it is the volume of the pipe (the pipe wall) you want to find. |
| \(V_1\) | V sub one | The volume of the outer cylinder, as if the pipe were solid all the way through. |
| \(V_2\) | V sub two | The volume of the hollow (the inner cylinder). It is how much water or air fits inside the pipe. |
| \(d_1\) | d sub one | The outside diameter (OD), the diameter of the outside of the pipe. Catalogs and drawings normally give the size of a pipe as the outside and inside diameters. |
| \(d_2\) | d sub two | The inside diameter (ID), the diameter of the hole inside the pipe. It equals the outside diameter minus two wall thicknesses. |
| \(r_1\) | r sub one | The outer radius, half the outside diameter (\(r_1 = d_1 \div 2\)). |
| \(r_2\) | r sub two | The inner radius, half the inside diameter (\(r_2 = d_2 \div 2\)). |
| \(l\) | ell | The length of the pipe, from the first letter of "length". It plays the same role as the height of a cylinder standing upright. |
| \(\pi\) | pi | The number that tells how many times the circumference of a circle is its diameter, about 3.14159. It appears in every calculation for circles and cylinders. |
| \(r^2\) | r squared | The number \(r\) multiplied by itself (\(r \times r\)). The small 2 at the upper right is an exponent that says "use it as a factor twice". |
| \(\mathrm{in^3}\) | cubic inch | A unit of volume. A cube 1 in on each side has a volume of 1 in³. Exactly 231 in³ make 1 US gallon, and 1728 in³ make 1 ft³. |
Terms
| pipe | A cylinder with a hole through it (also called a tube). Water pipes, gas pipes and scaffold tubes carry water or gas or serve as frames. In math terms, it is a hollow cylinder. |
| cylinder | A solid with a circular base that runs straight with the same thickness all the way, like a soda can or the tube inside a roll of paper towels. |
| volume | The amount of space a solid takes up, given as a number. It is measured by how many unit cubes (such as 1 in³ cubes) would fill it. |
| base area | The area of the face at the bottom of a solid. For a cylinder it is the area of the base circle (π × radius squared), and the volume is base area × height. |
| pi | The number that tells how many times the circumference (the distance around a circle) is the diameter. It is about 3.14159 and is written with the symbol \(\pi\). |
| hollow | Empty inside. A pipe is a hollow cylinder, so it is lighter and uses less material than a solid rod of the same thickness. |
Good to know before you start
Here is what helps you use the calculation on this page with real understanding, not just by pressing the button.
| Radius and diameter (Grade 7) |
|
| Area of a circle (Grade 7) |
|
| Volume of a cylinder (Grade 8) |
|
| Exponents (Grade 6) |
|
| Multiplying and dividing decimals (Grades 5–6) |
|
How to calculate it in Excel
Copy the whole table below and paste it into cell A1 in Excel. It works as is.
Table to find the volume of a pipe wall (from OD, ID and length)
| Outside diameter d1 (in) | 10 |
| Inside diameter d2 (in) | 8 |
| Length l (in) | 100 |
| Pipe volume (in³) | =PI()*(B1^2-B2^2)/4*B3 |
Table for the outer cylinder minus the hollow
| Outer radius r1 (in) | 5 |
| Inner radius r2 (in) | 4 |
| Length l (in) | 100 |
| Outer cylinder volume V1 (in³) | =PI()*B1^2*B3 |
| Hollow volume V2 (in³) | =PI()*B2^2*B3 |
| Pipe volume V (in³) | =B4-B5 |
Table to find the volume of a cylinder
| Base radius r (in) | 5 |
| Height h (in) | 100 |
| Cylinder volume (in³) | =PI()*B1^2*B2 |
Table to find the radius from the diameter
| Diameter d (in) | 10 |
| Radius r (in) | =B1/2 |
After pasting, column A holds the labels and column B holds the numbers. The upper rows are your inputs, and the formulas in the lower rows calculate from them automatically.
"PI()" is the Excel function that returns π (about 3.14159), "^" raises to a power (how many times to multiply), "*" is multiplication and "/" is division.
In the first table, for example, B4 shows about 2827.43 (in in³, because the inputs are in inches). In the second table, V1 is about 7853.98, V2 is about 5026.55 and V is about 2827.43, the same answer as the first table. Just replace the input numbers with the size of your own pipe.
"PI()" is the Excel function that returns π (about 3.14159), "^" raises to a power (how many times to multiply), "*" is multiplication and "/" is division.
In the first table, for example, B4 shows about 2827.43 (in in³, because the inputs are in inches). In the second table, V1 is about 7853.98, V2 is about 5026.55 and V is about 2827.43, the same answer as the first table. Just replace the input numbers with the size of your own pipe.
How to calculate it in Google Sheets
Copy the whole table below and paste it into cell A1 in Google Sheets. It works as is.
Table to find the volume of a pipe wall (from OD, ID and length)
| Outside diameter d1 (in) | 10 |
| Inside diameter d2 (in) | 8 |
| Length l (in) | 100 |
| Pipe volume (in³) | =PI()*(B1^2-B2^2)/4*B3 |
Table for the outer cylinder minus the hollow
| Outer radius r1 (in) | 5 |
| Inner radius r2 (in) | 4 |
| Length l (in) | 100 |
| Outer cylinder volume V1 (in³) | =PI()*B1^2*B3 |
| Hollow volume V2 (in³) | =PI()*B2^2*B3 |
| Pipe volume V (in³) | =B4-B5 |
Table to find the volume of a cylinder
| Base radius r (in) | 5 |
| Height h (in) | 100 |
| Cylinder volume (in³) | =PI()*B1^2*B2 |
Table to find the radius from the diameter
| Diameter d (in) | 10 |
| Radius r (in) | =B1/2 |
The same formulas as in Excel (including the PI() function) work as is. Copy the whole table, paste it into cell A1, and replace the input numbers with the size of your own pipe.
How to calculate it in Python
import math
outer_diameter = 10 # outside diameter (inches in this example)
inner_diameter = 8 # inside diameter (same unit as the outside diameter)
length = 100 # length
outer_radius = outer_diameter / 2 # outer radius
inner_radius = inner_diameter / 2 # inner radius
outer_volume = math.pi * outer_radius ** 2 * length # volume of the outer cylinder
inner_volume = math.pi * inner_radius ** 2 * length # volume of the hollow (inner cylinder)
pipe_volume = outer_volume - inner_volume # volume of the pipe (the wall)
print(f"Outer cylinder volume: {outer_volume} in3")
print(f"Hollow volume: {inner_volume} in3")
print(f"Pipe volume: {pipe_volume} in3")
Runs with just the standard math library. math.pi is π, "**" raises to a power (squared here) and "/" is division. Change the outside diameter, inside diameter and length at the top and run it. (If you use a unit other than inches, read the volume in the cube of that unit.)
How to write it in LaTeX and other math languages (copy and paste)
The idea behind the volume of a pipe (outside minus the hollow)
V = V₁ − V₂
V = V_{1} - V_{2}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>V</mi>
<mo>=</mo>
<msub><mi>V</mi><mn>1</mn></msub>
<mo>−</mo>
<msub><mi>V</mi><mn>2</mn></msub>
</mrow>
</math>
V = V_1 - V_2
v1 - v2
V := V1 - V2;
V = V1 - V2;
V = V_1 - V_2
Volume of a cylinder (the basic formula)
V = π × r² × h
V = \pi r^{2} h
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>V</mi>
<mo>=</mo>
<mi>π</mi>
<msup><mi>r</mi><mn>2</mn></msup>
<mi>h</mi>
</mrow>
</math>
V = pi r^2 h
Pi*r^2*h
V := Pi*r^2*h;
V = pi*r^2*h;
V = πr^2h
Formula for the volume of a pipe (the one this calculator uses)
V = π × (r₁² − r₂²) × l
V = \pi (r_1^{2} - r_2^{2}) l
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>V</mi>
<mo>=</mo>
<mi>π</mi>
<mo>(</mo>
<msup><msub><mi>r</mi><mn>1</mn></msub><mn>2</mn></msup>
<mo>−</mo>
<msup><msub><mi>r</mi><mn>2</mn></msub><mn>2</mn></msup>
<mo>)</mo>
<mi>l</mi>
</mrow>
</math>
V = pi (r_1^2 - r_2^2) l
Pi*(r1^2 - r2^2)*l
V := Pi*(r1^2 - r2^2)*l;
V = pi*(r1^2 - r2^2)*l;
V = π(r_1^2 - r_2^2)l
Diameter and radius
r = d ÷ 2
r = \frac{d}{2}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>r</mi>
<mo>=</mo>
<mfrac><mi>d</mi><mn>2</mn></mfrac>
</mrow>
</math>
r = d / 2
d/2
r := d/2;
r = d/2;
r = d/2
How to have ChatGPT do the calculation
You are a math calculation assistant. Do the following calculation by actually running Python code, and base your answer only on the numbers from the execution result (do not answer by mental math or guessing). A pipe (a hollow cylinder) has an outside diameter of 10 in, an inside diameter of 8 in and a length of 100 in. Find each of the following: 1. The volume of the outer cylinder in in³ 2. The volume of the hollow (inner cylinder) in in³ 3. The volume of the pipe (the wall) in in³ Show the formulas you used and the numbers from the execution result.
How to Use
-
1Enter your numbersType the numbers you want to calculate with into the input fields
-
2CalculatePress the "Calculate" button
-
3Check the resultThe result appears on the spot. The same page also explains the idea behind the calculation and the formula
DataChef Features
Easy and Free
Unlimited conversions for free.
No technical knowledge required.
Intuitive and user-friendly operation.
No technical knowledge required.
Intuitive and user-friendly operation.
No Registration Required
Available immediately after access.
Can be used without registering personal information.
Can be used without registering personal information.
Safe and Secure
Fully SSL encrypted communication.
Automatic file deletion by clicking "download".
Automatic file deletion by clicking "download".
Fast
High-speed site access
and rapid file conversion.
and rapid file conversion.
No Watermark
No watermark.
No attribution required.
No attribution required.
Commercial Use Available
Free for commercial use.
No need to contact us for commercial use permission.
No need to contact us for commercial use permission.
Related Features
Circle Calculator (Radius, Diameter, Circumference and Area)
Calculates the area, circumference and more of a circle, the cross section of a pipe, from the radius or the diameter
Area of a Rectangle Calculator (Length × Width)
Calculates the area of a rectangle and converts units. The starting point for understanding area
Exponent Calculator (Powers, a to the nth Power)
Calculates powers (a to the nth power), such as the radius squared
Ad 
