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Calculate the surface area of a box or sphere

Find the total area of the faces of a closed box or the surface of a sphere. Enter the measurements and see the result with working.

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The length of the box.

The width of the box.

The height of the box.

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Worked example
  • Shape: Box
  • Length: 2 m
  • Width: 3 m
  • Height: 4 m

Result

Surface area

52 m²

Working

  1. S = 2 × (l×b + l×h + b×h)
    2 × (2 m × 3 m + 2 m × 4 m + 3 m × 4 m) = 52 m²

Which surface is calculated?

The surface area is the area of the outside of the shape. It can be used when you want to know the size of the surfaces to be covered with a material. The calculator covers a closed rectangular box and a sphere. An open box requires the missing face to be subtracted separately.

For the box, you enter length, width and height. For the sphere, you choose radius or diameter. The radius is measured from the center of the sphere to the surface, while the diameter runs through the center from one side to the other. The result can be shown in m² or cm².

Surface area formulas

A closed box has six faces that are equal in pairs. Therefore S = 2 × (l × b + l × h + b × h) is used. The three products give the area of one face from each pair, and the factor two adds the opposite face.

For a sphere the formula is S = 4 × π × r². The radius is used even when you choose diameter as the input in the calculator. The surface area describes the entire outside of the sphere.

Example with the six faces of a box

A box measures 2 m by 3 m by 4 m. The three different face areas are 2 × 3 = 6 m², 2 × 4 = 8 m² and 3 × 4 = 12 m². The sum is 6 + 8 + 12 = 26 m². The total surface is 2 × 26 = 52 m².