What is the formula for the total surface area of a cylinder?

The total surface area is S = 2πr² + 2πrh, where r is the base radius and h is the height. The term 2πr² covers both circular ends, and 2πrh covers the curved lateral surface.

What is the lateral surface area of a cylinder?

The lateral surface area (curved side only, excluding the two circular bases) is L = 2πrh. This is useful when calculating the surface of an open-ended cylinder such as a pipe or tube.

What units does the result use?

The result is in square units matching your input. If you enter the radius and height in centimeters, the surface area is in cm². The calculator labels the output unit automatically.

Can I enter the diameter instead of the radius?

This calculator uses the radius. If you know the diameter, divide it by 2 to get the radius before entering it.

How accurate is the calculation?

The tool uses JavaScript's built-in Math.PI (≈ 3.141592653589793) and displays results rounded to 6 significant figures, which is sufficient for virtually all engineering and classroom purposes.

What is the surface area of a cylinder with radius 3 and height 5?

Using the formula: 2π(3²) + 2π(3)(5) = 2π(9) + 2π(15) = 18π + 30π = 48π ≈ 150.796 square units. You can verify this instantly using the calculator above.

Surface Area of a Cylinder Calculator

Name: Surface Area of a Cylinder Calculator
Availability: InStock
Author: Nham Vu

Enter a cylinder radius and height to instantly get the total and lateral surface area, with unit selection and step-by-step breakdown.

Cylinder Dimensions

Radius (r)

Height (h)

Unit

Formulas

Total SA = 2πr² + 2πrh

Lateral SA = 2πrh

r = radius | h = height

Enter radius and height, then click Calculate

Summary

Enter a cylinder radius and height to instantly get the total and lateral surface area, with unit selection and step-by-step breakdown.

How it works

Enter the radius of the cylinder base in the input field.
Enter the height of the cylinder.
Select the unit of measurement (mm, cm, m, in, or ft).
Click Calculate to apply the formulas: Total SA = 2πr² + 2πrh and Lateral SA = 2πrh.
Review the step-by-step breakdown showing each component.
Use the Copy button to copy the total surface area result to your clipboard.

Use cases

Determine how much material is needed to manufacture a cylindrical container.
Calculate the paint or coating area for a pipe, tank, or column.
Solve geometry homework problems involving cylinder surface area.
Estimate label area for cans and cylindrical packaging.
Find the area of just the curved side (lateral surface) for open-top containers.
Verify engineering calculations for cylindrical pressure vessels.
Convert surface area between unit systems for international projects.
Teach the 2πr² + 2πrh formula with an interactive visual breakdown.

Frequently Asked Questions

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Last updated: 2026-05-23 · Reviewed by Nham Vu