Quick answer
The volume of a hollow cylinder (pipe) is V = πh(R² − r²). With outer radius 5, inner radius 3 and length 10 it is 502.6548.
Enter the outer radius, inner radius and length. The calculator returns the volume of the material.
Related tools: Cylinder Volume Calculator: Volume of a cylinder. Sphere Volume Calculator: Volume and surface area of a sphere. Volume of a Hemisphere Calculator: Volume and surface area of a hemisphere.
How to use the Hollow Cylinder Volume Calculator
- Enter outer radius (above 0).
- Enter inner radius (above 0).
- Enter length (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Outer radius | A number | > 0 |
| Inner radius | A number | > 0 |
| Length | A number | > 0 |
Formula and method
Formula
V = πh(R² − r²)
IEEE-754 double precision; shown to at most 6 decimal places.
Outer cylinder minus inner cylinder; inner radius must be smaller.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Outer radius = 5; Inner radius = 3; Length = 10.
| Result | Value |
|---|---|
| Volume | 502.654825 |
Example 2
Inputs: Outer radius = 2; Inner radius = 1; Length = 1.
| Result | Value |
|---|---|
| Volume | 9.424778 |
The first line is the headline result (volume). IEEE-754 double precision; shown to at most 6 decimal places.
The calculation
The ring area is π(25 − 9) = 50.27; times the length 10 gives 502.65. This is the volume of material, not the capacity of the hollow, which is π × 9 × 10 = 282.7.
Uses
Estimate the amount of metal in a tube or concrete in a pipe. Multiply by density for weight. The inner radius must be below the outer radius.
How the result changes with outer radius
Holding every other input at the first worked example, this table changes only outer radius. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Outer radius | Volume |
|---|---|
| 5 | 502.654825 |
| 10 | 2,858.849315 |
| 20 | 12,283.627276 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Inner radius: entering "5" shows "The inner radius must be smaller than the outer radius." beside that field and no result.
Choosing between the Hollow Cylinder Volume Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Cylinder Volume Calculator](/math/cylinder-volume-calculator/) | radius and height | Volume |
| [Sphere Volume Calculator](/math/sphere-volume-calculator/) | radius | Volume |
| [Volume of a Hemisphere Calculator](/math/volume-of-hemisphere/) | radius | Volume |
| [Cone Volume Calculator](/math/cone-volume-calculator/) | radius and height | Volume |
| [Pyramid Volume Calculator](/math/pyramid-volume-calculator/) | base length, base width and height | Volume |
Background: geometry measurements
Geometry results carry units that depend on the quantity: a perimeter or length is in linear units such as cm, an area or surface area is in square units (cm²) and a volume is in cubic units (cm³). Use one length unit for every input, because the calculator multiplies the numbers as given.
Flat (2D) shapes have an area and a perimeter; solids (3D) have a surface area and a volume. Two familiar checks: a circle of radius r has area πr² and circumference 2πr, and a sphere has volume (4/3)πr³ and surface area 4πr².
Assumptions and limitations
- Inner radius below outer radius
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for inner radius to confirm this.
Frequently asked questions
What is the capacity of the pipe's bore?
The bore's capacity is πr²h using the inner radius; for r = 3 and length 10 that is 282.7.
How do I find the weight?
Multiply volume by density.
What if I know diameters?
Halve each diameter to get the outer and inner radii before using the formula.
What does the Hollow Cylinder Volume Calculator calculate?
Volume of material in a pipe or tube. It returns Volume.
What formula does the Hollow Cylinder Volume Calculator use?
V = πh(R² − r²). Outer cylinder minus inner cylinder; inner radius must be smaller.
What do I need to enter in the hollow Cylinder Volume Calculator?
You enter Outer radius, Inner radius and Length.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Inner radius below outer radius.
What is an example of a hollow Cylinder Volume result?
With outer radius 5, inner radius 3 and length 10, the volume is 502.654825.
Related calculators
- Cylinder Volume Calculator — Volume of a cylinder.
- Sphere Volume Calculator — Volume and surface area of a sphere.
- Volume of a Hemisphere Calculator — Volume and surface area of a hemisphere.
- Cone Volume Calculator — Volume, slant height and surface area of a cone.
- Pyramid Volume Calculator — Volume of a pyramid from its base area and height (rectangular base).
- Cube Volume Calculator — Volume, surface area and diagonal of a cube.
Sources
- OpenStax, Prealgebra 2e (Rice University): perimeter, area, volume, circumference and the Pythagorean theorem
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.