The Lateral Surface Area Calculator calculates the area of the sides of a 3D shape — everything except the top and bottom bases.
Lateral Surface Area Calculator
Lateral (side) area — the surface area without the bases — of a cylinder, cone, rectangular prism, any prism, square pyramid or triangular prism.
For prisms and cylinders, lateral area is the base perimeter multiplied by the height (2πrh for a cylinder). For cones and pyramids it uses the slant height (πrs for a cone). Choose a cylinder, cone, rectangular prism, triangular prism, any prism or square pyramid; the calculator also shows total surface area where it applies.
Formula
| Shape | Lateral surface area | Total surface area |
|---|---|---|
| Cylinder | L = 2πrh | A = L + 2πr² |
| Cone | L = πrs, s = √(r² + h²) | A = L + πr² |
| Rectangular prism | L = 2h(l + w) | A = L + 2lw |
| Any prism | L = P × h | A = L + 2B |
| Triangular prism | L = (a + b + c) × length | A = L + 2B |
| Square pyramid | L = 2as, s = √(h² + (a/2)²) | A = L + a² |
Where:
- L = lateral surface area; A = total surface area
- r = radius; h = vertical height; s = slant height
- l, w = base length and width; a = base side
- P = perimeter of the base; B = area of one base
How the Calculation Works
Step 1: Identify the side faces. For a prism or cylinder the sides wrap around the base; for a cone or pyramid they slope up to a point.
Step 2: For prisms and cylinders, multiply the distance around the base (perimeter or circumference) by the height. Unrolled, the sides form one long rectangle.
Step 3: For cones and pyramids, first find the slant height from the vertical height, then use πrs (cone) or 4 × ½ × a × s (square pyramid).
Variables Explained
| Variable | Meaning | Unit |
|---|---|---|
| P | Base perimeter (any prism mode) | cm, m, in, ft |
| h | Vertical height or prism length | cm, m, in, ft |
| s | Slant height along the face | cm, m, in, ft |
| L | Lateral surface area | cm², m², in², ft² |
Example Calculation
Cylinder
Given: radius = 3 cm, height = 10 cm
Calculation: L = 2 × 3.14159 × 3 × 10
Result: L ≈ 188.50 cm² (total surface area ≈ 245.04 cm²)
Cone
Given: radius = 3 cm, height = 4 cm
Slant height: s = √(3² + 4²) = 5 cm
Calculation: L = 3.14159 × 3 × 5
Result: L ≈ 47.12 cm²
Hexagonal prism (any prism mode)
Given: base perimeter = 18 cm (six 3 cm sides), height = 10 cm
Result: L = 18 × 10 = 180 cm²
Common Area Conversion Table
| Unit | Equivalent |
|---|---|
| 1 m² | 10,000 cm² |
| 1 ft² | 144 in² |
| 1 m² | 10.7639 ft² |
Shape Properties
Why lateral area matters
Lateral area is the right measure when the ends are open or not covered: a label around a can, insulation around a pipe, the walls of a round tank, or the paper of a cone. Add the bases only when they are part of the job.
Dimensions Explained
Vertical height vs slant height
Enter the vertical height for cones and pyramids; the calculator converts it to slant height. Using the slant height in place of the vertical height would overstate the height and give the wrong answer.
Spheres
A sphere has no bases, so its whole surface (4πr²) is curved area. Use the sphere or hemisphere calculator for those.
Frequently Asked Questions
What is lateral surface area?
It is the area of the side faces of a solid, excluding the base or bases.
What is the difference between lateral and total surface area?
Total surface area = lateral area + base area(s). For a cylinder, total = 2πrh + 2πr².
How do you find the lateral area of a prism?
Multiply the perimeter of the base by the height: L = P × h. This works for any right prism.
How do you find the lateral surface area of a cylinder?
Use L = 2πrh. A cylinder with a 3 cm radius and 10 cm height has a lateral area of about 188.5 cm².
How do you find the lateral area of a cone?
Use L = πrs, where s = √(r² + h²) is the slant height.
Is curved surface area the same as lateral surface area?
For a cylinder or cone, yes — the curved surface is the lateral surface.