Surface Area Calculator
Calculate the total and lateral surface area of 3D shapes.
This tool is for informational and educational purposes only. It is not a substitute for professional financial, medical, legal, or engineering advice. See Terms of Service.
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This calculator finds the total surface area of four common 3D shapes. For cylinders and cones, it also shows the lateral (side) surface area.
- Select a shape. Choose from sphere, cylinder, cone, or cube.
- Enter the dimensions. Spheres and cubes need one value. Cylinders and cones need a radius and height.
- Read the result. The total surface area displays with the formula. Cylinders and cones also show the lateral surface area separately.
Surface area is measured in square units. If your inputs are in inches, the surface area is in square inches. The lateral area excludes the base(s), which is useful for calculating material needed for the curved or slanted surface alone.
About Surface Area
Surface area is the total area of all faces and curved surfaces of a three-dimensional object. It determines how much material is needed to cover or wrap an object, how much paint is required, or how much heat transfers through a surface. A sphere has the minimum surface area for a given volume, which is why it minimizes heat loss. Cylinders and cones have two components: the lateral (side) surface and the base(s). The lateral area of a cylinder is a rectangle when unrolled (2*pi*r*h), while the lateral area of a cone is a sector of a circle (pi*r*l, where l is the slant height).
Frequently Asked Questions
What is the surface area of a sphere?
The surface area of a sphere is SA = 4 * pi * r^2. For a sphere with radius 5, the surface area is 4 * pi * 25 = approximately 314.1593 square units. A sphere's surface area is exactly 4 times the area of its great circle.
What is lateral surface area?
Lateral surface area is the area of only the side surface of a 3D shape, excluding the bases. For a cylinder, the lateral area is 2*pi*r*h. For a cone, it is pi*r*l where l is the slant height. This is useful when you only need to wrap the sides.
How is the slant height of a cone calculated?
The slant height l = sqrt(r^2 + h^2), where r is the radius and h is the vertical height. This uses the Pythagorean theorem. The calculator finds this automatically when you enter the radius and height.