How it works
Surface area is the total area of every face or curved surface of a solid: the amount of material needed to wrap or paint it.
The lateral area excludes the base(s). For a cone and pyramid the sloped sides use the slant height, which is found from the vertical height with the Pythagorean theorem.
Formula
Cube 6s² · Box 2(lw+lh+wh) · Cylinder 2πr(r+h) · Sphere 4πr² · Cone πr(r+√(r²+h²)) · Capsule 2πrL + 4πr²
Questions people ask
What is the difference between surface area and volume?
Surface area measures the outside skin in square units; volume measures the space inside in cubic units.
How much paint do I need for a cylindrical tank?
Compute the lateral area (2πrh), add the top if you paint it, and divide by the coverage on the can: commonly about 350–400 sq ft per gallon.
What is slant height?
The distance from the tip of a cone or pyramid down its side to the edge of the base. For a cone it is √(r² + h²).