The Hollow Cylinder Surface Area Calculator calculates the surface area of a tube, sleeve or pipe section by adding its outer curved surface, inner curved surface and the two ring-shaped ends.
Hollow Cylinder (Tube) Surface Area Calculator
Inner, outer, end and total surface area of a hollow cylinder, round tube, rod sleeve or square tube.
The formula is A = 2π(R + r)L + 2π(R² − r²). You can enter the outer and inner radius, or the outer diameter and wall thickness, and there is a separate mode for square tubing. Each surface is shown separately so you can use just the outside or inside if you need to.
Formula
Round tube: A = 2π(R + r)L + 2π(R² − r²)
- Outer surface = 2πRL
- Inner surface = 2πrL
- Both ends (rings) = 2π(R² − r²)
Square tube: A = 4aL + 4(a − 2t)L + 2(a² − (a − 2t)²)
Where:
- R = outer radius; r = inner radius = R − wall thickness
- L = length of the tube
- a = outer side of a square tube; t = wall thickness
How the Calculation Works
Step 1: Find the outer curved surface: circumference 2πR times the length.
Step 2: Find the inner curved surface the same way using r.
Step 3: Find the area of one end ring, π(R² − r²), double it for both ends, and add all three parts.
Variables Explained
| Variable | Meaning | Unit |
|---|---|---|
| R | Outer radius (half the outside diameter) | mm, cm, in |
| r | Inner radius | mm, cm, in |
| t | Wall thickness | mm, cm, in |
| L | Length | mm, cm, m, in, ft |
| A | Surface area | mm², cm², m², in², ft² |
Example Calculation
Round tube
Given: outer radius = 5 cm, inner radius = 4 cm, length = 20 cm
Outer: 2 × π × 5 × 20 ≈ 628.32 cm²
Inner: 2 × π × 4 × 20 ≈ 502.65 cm²
Ends: 2 × π × (25 − 16) ≈ 56.55 cm²
Result: A ≈ 1,187.52 cm²
Square tube
Given: outer side = 5 cm, wall = 0.3 cm, length = 100 cm
Outer: 4 × 5 × 100 = 2,000 cm²; inner: 4 × 4.4 × 100 = 1,760 cm²; ends: 2 × (25 − 19.36) = 11.28 cm²
Result: A ≈ 3,771.28 cm²
Common Area Conversion Table
| Unit | Equivalent |
|---|---|
| 1 cm² | 100 mm² |
| 1 m² | 10,000 cm² |
| 1 in² | 6.4516 cm² |
| 1 ft² | 144 in² |
Shape Properties
A hollow cylinder is a solid cylinder with a smaller coaxial cylinder removed. Its cross-section is a ring (annulus). Wall thickness equals R − r.
Which surface to use
- Outer surface: painting, wrapping or insulating the outside.
- Inner surface: lining, coating or plating the bore.
- Total: plating or coating every face, such as galvanizing.
Dimensions Explained
Outer diameter and wall thickness
Tubing is usually sold by outer diameter (OD) and wall thickness. The calculator derives the inner radius as OD ÷ 2 − wall.
Related: Irregular Cylinder Surface Area Calculator.
Frequently Asked Questions
How do you find the surface area of a hollow cylinder?
Add outer, inner and end-ring areas: A = 2π(R + r)L + 2π(R² − r²).
What is the curved surface area of a hollow cylinder?
The outer plus inner curved surfaces: 2π(R + r)L. It excludes the ends.
How do you calculate the outer surface area of a tube?
Multiply the outer circumference by the length: 2πRL (or π × OD × L).
How do you find the inner radius of a tube?
Subtract the wall thickness from the outer radius: r = R − t.
What is the surface area of a square tube?
A = 4aL + 4(a − 2t)L + 2(a² − (a − 2t)²): outside faces, inside faces and the two square-ring ends.
