Lateral Surface Area Calculator

Lateral surface area is the area of all sides except the base. For a soup can it is the label area. For a cone it is the curved face only, not the circle at the bottom.

Cylinder

LSA = 2πrh

Unroll the curved surface and you get a rectangle: width is the circumference (2πr), height is h. Area = width × height.

Cone

LSA = πrl

Here l is the slant height, not the vertical height. l = √(r² + h²). The formula comes from unrolling the cone into a flat sector with radius l and arc length 2πr. Sector area = (2πr / 2πl) × πl² = πrl.

Most problems give r and h, not l. The calculator computes l for you.

Square pyramid

LSA = 2bl

Here b is the base side length and l is the slant height of a triangular face: l = √((b/2)² + h²). The pyramid has 4 triangular faces each with area (b·l)/2. Total LSA = 4 × (bl/2) = 2bl.

Practical uses

Painting a grain silo or cylindrical tank: you need the lateral area of the barrel. The top and bottom are separate items.

Sheet metal: forming a cone from flat stock requires a sector of radius l and arc 2πr. LSA tells you exactly how much material to cut.

Roof sheathing for a hip roof approximates a square pyramid. Each triangular face is a separate raftered plane, and LSA gives the total sheathing area before waste.

The total surface area adds the base back. Cylinder: total SA = LSA + 2πr². Cone: total SA = LSA + πr². Square pyramid: total SA = LSA + b².

The lateral area is always less than the total surface area. For a very flat cylinder (large r, small h) the two lids dominate. For a tall thin cylinder the lateral area dominates.