Surface Area Calculator
Calculate the total surface area, lateral surface area, and base area of common 3D shapes. Select a shape, enter its dimensions, and get instant results.
Surface area is the total area of the outer surfaces of a three-dimensional shape. It is measured in square units and is essential in applications like painting, packaging, heat transfer, and material estimation.
The formulas for common 3D shapes are: Cube: 6s² (where s is the side length). Rectangular prism: 2(lw + lh + wh). Sphere: 4πr². Cylinder: 2πr² + 2πrh (two circular bases plus the lateral rectangle). Cone: πr² + πrl (one circular base plus the lateral surface), where l is the slant height.
Lateral surface area excludes the bases and represents only the side surfaces. For a cylinder, it is the rectangle you would get if you unrolled the side. For a cone, it is the sector of a circle formed by the slant surface. Understanding the distinction between total and lateral surface area is important in applications where the base is not exposed, such as the sides of a paint can.