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Cube Volume and Surface Area Calculator

Volume, surface area and diagonals of a cube

How it is calculated

The only input is the edge length a, which must be above zero. From it the tool computes Volume = a³, Surface area = 6 × a², Face diagonal = a × √2 and Space diagonal = a × √3. The face diagonal crosses one square face from corner to corner. The space diagonal runs through the inside of the cube from one corner to the opposite corner. The result carries no unit: if the edge is in centimetres, the volume is in cm³, the surface area is in cm² and the two diagonals are in cm. Everything is rounded to two decimals, so for small edges the volume can show as 0.00 even though it is not exactly zero. Only a perfect cube with equal edges is supported; for a box with three different sides a cuboid calculator is needed.

Worked example

A cube has an edge of 2.5. Volume = 2.5³ = 2.5 × 2.5 × 2.5 = 15.625, shown as 15.63. Surface area = 6 × 2.5² = 6 × 6.25 = 37.50. Face diagonal = 2.5 × 1.4142 ≈ 3.54. Space diagonal = 2.5 × 1.7321 ≈ 4.33. If the edge is in metres, the volume is about 15.63 m³ and the surface area 37.50 m².

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Common mistakes

  • Mixing up volume and surface area units. Volume is in cubic units (m³) while surface area is in square units (m²), so they cannot be compared.
  • Entering the face diagonal or space diagonal as the edge. If you know the space diagonal d, the edge is d ÷ √3.
  • Doubling the edge and expecting double the volume. Doubling the edge multiplies the surface area by 4 and the volume by 8.
  • Entering the edge in one unit and expecting the volume in another. 100 cm entered as the edge gives a volume of 1,000,000 cm³, not 1 m³ as a number.
  • Using the tool for a box with unequal sides. All edges here are assumed equal.

About this calculator

Given only the edge length a of a cube, this calculator returns all four core measurements: volume = a³, total surface area = 6a² (six identical square faces), the face diagonal = a√2 (the diagonal across one square face, from the Pythagorean theorem), and the space diagonal = a√3 (the diagonal running corner-to-corner through the solid's interior).

Students use it to check geometry homework on 3D solids, and it comes up in practical contexts too — packaging designers computing how much material covers a cube-shaped box, and woodworkers or machinists checking whether a diagonal brace or dowel will fit through a cubic frame corner-to-corner.

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Comments (1)

  • Editorial team

    The space diagonal tells you the longest straight object a cubic box can hold. For a 10-unit edge it is 17.32, so a rod of that length just touches opposite corners, while the face diagonal of 14.14 is the longest flat piece that fits on one side. Volume is in cubic units and area in square units of whatever you entered. Which packaging or construction problem led you here?

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