Cylinder Surface Area Calculator
Total, lateral and base area of a cylinder from radius or diameter — closed, open at one end, or open at both ends.
A cylinder’s surface area covers a can, a tube, a duct, or a storage tank — any shape with two circular ends joined by a curved side. This calculator finds it from either the radius or the diameter, plus the height, and breaks the result into three parts: the combined area of the two circular ends (base area), the curved side wrapping between them (lateral area), and the total.
Enter your measurements in whichever form you have them — radius or diameter — and the calculator handles the conversion automatically.
Cylinder Surface Area Formula
Base Area (Both Circles)
Base Area = 2πr²
A cylinder has two identical circular ends, so this doubles the single-circle formula πr².
Lateral Area
Lateral Area = 2πrh
The lateral (side) area is the curved surface connecting the two circles. Unrolled flat, it’s a rectangle whose width is the circle’s circumference (2πr) and whose height is the cylinder’s height — which is exactly where this formula comes from.
Total Surface Area
Total Surface Area = 2πr² + 2πrh
By Radius vs. By Diameter
Since a lot of real-world measurements (pipe diameter, tank diameter) come as a diameter rather than a radius, this calculator offers both as direct inputs — the By Diameter mode simply divides by 2 first, then uses the exact same formulas.
Worked Example: By Radius
A cylindrical can with a 5-ft radius and a 10-ft height: Base Area = 2 × π × 5² ≈ 157.08 square feet, Lateral Area = 2 × π × 5 × 10 ≈ 314.16 square feet, Total SA = 157.08 + 314.16 ≈ 471.24 square feet.
Worked Example: By Diameter
A cylindrical tank with a 12-ft diameter and an 8-ft height: Radius = 12 ÷ 2 = 6 ft, Base Area = 2 × π × 6² ≈ 226.19 square feet, Lateral Area = 2 × π × 6 × 8 ≈ 301.59 square feet, Total SA = 226.19 + 301.59 ≈ 527.79 square feet.
When You Only Need Lateral Area
Not every project needs the full total surface area. If you’re painting only the outer wall of a cylindrical tank (not the top or bottom), wrapping a label around a can, or wallpapering the inside of a round room, the lateral area alone — without the two circular ends — is the number you actually need.
Frequently Asked Questions
How do I find a cylinder’s surface area from its diameter instead of radius?
Use the By Diameter mode: enter the diameter and height directly, and the calculator divides the diameter by 2 to get the radius before applying the standard formulas.
What’s the difference between lateral and total surface area?
Lateral area (2πrh) covers only the curved side of the cylinder. Total surface area adds the two circular ends on top of that: Total SA = Base Area (2πr²) + Lateral Area (2πrh).
How do I find a cylinder’s height if I know the total surface area?
Rearrange the total surface area formula to solve for height: Height = (Total SA − 2πr²) ÷ (2πr). This calculator doesn’t solve this reverse direction directly, but subtracting the base area from the total and dividing by the circle’s circumference (2πr) gets you there by hand.