Hollow Cylinder Volume Calculator
Hollow cylinder volume uses the formula V = pi h times R squared minus r squared. For a pipe with outer radius 10 cm, inner radius 8 cm, and length 30 cm, pi times 30 times 36 gives 3,392.92 cm3 or 3.393 litres. This calculates the solid wall material of tubes and sleeves. Enter your dimensions below.
Calculator
Volume of a Hollow Cylinder
A hollow cylinder, also called a cylindrical shell, concentric cylinder, or annular cylinder, is a cylinder with a smaller cylinder removed from its center. Both cylinders share the same vertical axis. Drinking straws, water pipes, hollow tubes, hollow pipes, and toilet paper rolls are all examples of hollow cylinders: and they all use the same hollow cylinder formula.
The volume of a hollow cylinder formula is:
Where R is the external radius, r is the internal radius, and h is the cylinder's height.
The same formula can use the external diameter (D) and internal diameter (d): V = π × h × [(D² − d²) / 4].
For a toilet paper roll with an external diameter of 11 cm (5.5 cm external radius), an internal diameter of 4 cm (2 cm internal radius), and a height of 9 cm: V = π × 9 × (5.5² − 2²) = π × 9 × (30.25 − 4) = π × 9 × 26.25 = 742.2 cm³. This volume represents the space occupied by the paper and cardboard.
Adjust the slider to change the internal radius
Additional Worked Examples for Hollow Sections
Example 1 (Steel Pipe in Metric mm): Calculate the solid steel volume of a pipe with an outer diameter D = 114 mm (R = 57 mm), a wall thickness of 6 mm (inner radius r = 51 mm), and a length h = 1,000 mm (1 meter):
- R² − r² = 57² − 51² = 3,249 − 2,601 = 648 mm²
- V = π × 1,000 × 648 = 2,035,752 mm³ (2,035.75 cm³ or 2.036 liters of steel).
- Using steel density (7.85 g/cm³), the total pipe mass is 2,035.75 × 7.85 = 15.98 kg.
Example 2 (Concrete Culvert in Imperial Feet): A storm drain culvert has an outer radius of 2.5 ft, an inner radius of 2.0 ft, and a length of 20 ft:
- R² − r² = 2.5² − 2.0² = 6.25 − 4.00 = 2.25 sq ft
- V = π × 20 × 2.25 = 141.37 cubic feet (5.236 cubic yards of concrete).
Wall thickness and tube material volume
This tool computes the solid wall volume of tubes and pipes. It subtracts the empty inner cylinder from the outer cylinder.
For hands-on trade guidance on measuring plumbing pipes, schedules, and flow capacities, review our plumber's practical guide to measuring pipe volume.
Subtracting inner core from outer cylinder
The formula is V = pi times h times (R squared minus r squared). Here R is the outer radius and r is the inner radius. It gives the exact wall volume.
Frequently Asked Questions
What is the formula for a hollow cylinder?
The most simplified version of the formula is V = π × h × (R² − r²). In this equation, V is the volume of the material, h is the height, R is the larger external radius, and r is the smaller internal radius. Our hollow cylinder volume calculator runs this formula instantly.
What actually is a hollow cylinder?
In geometry, a hollow cylinder (also known as a cylindrical shell) is a solid object that is bounded by two concentric circular cylinders of the same height. Common real-world examples include wedding rings, PVC pipes, drinking straws, and heavy machinery sleeves.
How do I find the inner capacity of a pipe?
If you want to know how much liquid a pipe can hold, you don't actually need to find the volume of a hollow cylinder itself (the walls). Instead, you only need to calculate the standard volume of the empty space using just the internal radius: V = π × r² × h. Our tool displays both the shell volume and the inner cavity capacity for your convenience.
What happens if I use diameter instead of radius?
If you only have the outer diameter and inner diameter, simply divide both numbers by 2 to get your respective radii. Then, plug those two radius values into the cylinder volume calculator hollow tool.
Why does my answer come out negative?
A negative answer means you subtracted a larger number from a smaller number. Make sure the external (outer) radius is larger than the internal (inner) radius.
How do you calculate the volume of a paper cylinder?
To calculate the volume of a paper cylinder, measure the internal diameter and length of the tube, then apply V = π × r² × h. For a common 6-inch by 8-inch paper cylinder (6 inches in diameter, 8 inches tall): radius = 3 inches, so V = π × 3² × 8 = π × 9 × 8 = 226.19 cubic inches (about 3.70 litres). Paper cylinders include paper towel rolls, mailing tubes, poster tubes, and craft project tubes. For a paper towel roll (roughly 1.6 inches diameter × 11 inches long): V = π × 0.8² × 11 = 22.12 cubic inches. The volume tells you the internal capacity of the tube.