Surface Area Calculator
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How Surface Area Is Calculated for Each Shape
Surface area is the total area covering the outside of a three-dimensional solid, measured in square units. Each shape has its own well-established formula: a cube uses 6s², a rectangular prism uses 2(lw + lh + wh), a sphere uses 4πr², a right circular cylinder uses 2πr² + 2πrh (two circular bases plus the curved lateral surface), a right circular cone uses πr² + πr·s where the slant height s = √(r² + h²), and a triangular prism uses the two triangular ends plus three rectangular sides running the length of the prism. This calculator applies the exact formula for whichever shape you select.
Total Surface Area vs. Lateral Surface Area
"Total" surface area includes every face — top, bottom, and sides. "Lateral" surface area excludes the top and bottom (bases) and only counts the surface running around the shape, which matters for things like labeling a cylindrical can or painting the wall of a silo without its roof and floor. The breakdown above separates the lateral/side area from the base area so you can use whichever figure fits your project.
Related Geometry Tools
If you only need the enclosed capacity rather than the outer surface, use the volume calculator. For flat 2D shapes like rectangles, circles, and triangles, the area calculator covers those directly.
Frequently Asked Questions
What is the difference between total surface area and lateral surface area?
Total surface area adds up every face of a solid, including the top and bottom bases. Lateral surface area only counts the sides running around the shape and excludes the bases - useful when you only need to cover or paint the side of an object, like the wall of a cylindrical tank without its lid or floor.
How is the surface area of a cone calculated if I only know the radius and height?
You first need the slant height, found using the Pythagorean theorem: slant height s = sqrt(r^2 + h^2), where r is the base radius and h is the vertical height. The total surface area is then pi r squared (base) + pi r s (lateral surface). This calculator computes the slant height automatically from the radius and height you enter.