How it works

This calculator helps you find the total surface area of a cylinder. Just enter the radius of the base and the height of the cylinder, and we'll compute both the lateral surface area and the total surface area for you. Perfect for geometry homework and quick checks.

The Formula

Total Surface Area = 2πrh + 2πr²
Where:
r = radius of the base
h = height of the cylinder
π ≈ 3.14159

Worked Example

1. Example: A Soda Can

   Imagine a standard soda can with a radius of 3 cm and a height of 12 cm. To find its total surface area: Lateral Area = 2 × π × 3 cm × 12 cm = 72π cm² ≈ 226.19 cm² Base Area (one base) = π × (3 cm)² = 9π cm² ≈ 28.27 cm² Total Surface Area = 72π cm² + 2 × 9π cm² = 72π cm² + 18π cm² = 90π cm² ≈ 282.74 cm²

Tips, Assumptions & Limitations

• Ensure your radius and height are in the same units (e.g., both in cm or both in inches).
• The lateral surface area is the area of the curved side, while the total surface area includes the top and bottom circular bases.
• Remember that π (pi) is approximately 3.14159.