How to Calculate Surface Areas

Understanding and calculating surface area is crucial in many fields, from construction and manufacturing to art and packaging. It represents the total area that the surface of a three-dimensional object occupies. Whether you're trying to determine how much paint you need for a room, the amount of material required to wrap a gift, or the heat transfer properties of an object, knowing its surface area is essential.

This calculator helps you determine the surface area for several common 3D shapes: Cubes, Rectangular Prisms, Cylinders, and Spheres. Simply select the shape, input the required dimensions, and get your result in square units.

How to Calculate Surface Area for Different Shapes

1. Cube

A cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. All sides are of equal length.

Formula: Surface Area (SA) = 6 × side²

Example: If a cube has a side length of 5 units, its surface area would be 6 × 5² = 6 × 25 = 150 square units.

Cube Surface Area

2. Rectangular Prism

A rectangular prism (also known as a cuboid) is a three-dimensional solid shape with six rectangular faces. It has a length, width, and height.

Formula: Surface Area (SA) = 2 × (length × width + length × height + width × height)

Example: For a rectangular prism with length = 10 units, width = 4 units, and height = 3 units, the surface area would be 2 × (10×4 + 10×3 + 4×3) = 2 × (40 + 30 + 12) = 2 × 82 = 164 square units.

Rectangular Prism Surface Area

3. Cylinder

A cylinder is a three-dimensional solid that holds two parallel bases, usually circular, connected by a curved surface. Its surface area includes the area of the two circular bases and the area of the curved side.

Formula: Surface Area (SA) = 2 × π × radius × height + 2 × π × radius²

Example: If a cylinder has a radius of 3 units and a height of 7 units, its surface area would be 2 × π × 3 × 7 + 2 × π × 3² = 42π + 18π = 60π ≈ 188.5 square units.

Cylinder Surface Area

4. Sphere

A sphere is a perfectly round three-dimensional object in which every point on its surface is equidistant from its center. It has no edges or vertices.

Formula: Surface Area (SA) = 4 × π × radius²

Example: For a sphere with a radius of 6 units, the surface area would be 4 × π × 6² = 4 × π × 36 = 144π ≈ 452.39 square units.

Sphere Surface Area

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