Cuboid Surface Area Calculator
A cuboid, or rectangular box, has six rectangular faces in three equal pairs. Its surface area is the total of all six faces: twice the sum of length times width, length times height, and width times height. Enter the three dimensions and this calculator returns the surface area, the volume (length times width times height), and the space diagonal that runs corner to corner through the interior. A cube is the special case where all three dimensions are equal. Use one consistent length unit throughout.
Cuboid formulas
Surface area = 2 x (l x w + l x h + w x h)
Volume = l x w x h
Space diagonal = square root of (l squared + w squared + h squared)
Total edge length = 4 x (l + w + h)
Opposite faces are equal in pairs, so each pair contributes twice its area to the surface. The space diagonal is the three-dimensional Pythagorean theorem, and a cuboid has 12 edges in three groups of four.
Cuboid geometry context
- A cuboid has six rectangular faces, twelve edges and eight vertices.
- Opposite faces are equal, so surface area pairs them.
- A cube is a cuboid with all three dimensions equal.
- The space diagonal is the longest straight line inside the box.
- Use one length unit; surface area is in that unit squared and volume in that unit cubed.
Cuboid surface area: frequently asked questions
What is the surface area of a cuboid?
The surface area of a cuboid is the total area of its six rectangular faces: SA = 2(lw + lh + wh), where l, w and h are the length, width and height. Opposite faces are equal in pairs, so each pair contributes twice its area. For a 4 by 3 by 2 box the surface area is 2(12 + 8 + 6) = 52 square units.
What is the difference between surface area and volume?
Surface area measures the total area of the outside faces, useful for wrapping, painting or material. Volume measures the space inside, useful for capacity. This calculator reports both: surface area in square units and volume in cubic units, from the same three dimensions.
How do you find the space diagonal of a cuboid?
The space diagonal runs from one corner to the opposite corner through the interior. It equals the square root of (length squared plus width squared plus height squared), a three-dimensional version of the Pythagorean theorem. It is the longest straight line that fits inside the box.
Is a cube a cuboid?
Yes. A cube is a cuboid in which all three dimensions are equal. Its surface area simplifies to 6 times the side squared and its volume to the side cubed. Enter equal length, width and height to treat a cube with this calculator.
What units does the result use?
Use the same length unit for length, width and height. The surface area is then in that unit squared (for example square inches), the volume in that unit cubed, and the diagonal in the same length unit. Convert any mismatched dimensions before entering them.
Official sources
- U.S. National Institute of Standards and Technology: Digital Library of Mathematical Functions.
- NASA: Volume and geometry reference.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.