How this calculator works
A cube has twelve equal edges, so one edge length defines the whole solid. Volume is the edge cubed and surface area is six identical faces, each with area a². The face diagonal cuts across one square face and is a√2 long. The space diagonal runs from one corner to the opposite corner through the interior and is a√3 long. To work the other way, undo each formula by division or a cube root.
Formula
V = a³; surface area = 6a²; face diagonal = a√2; space diagonal = a√3.
Worked example
A cube with a 3 m edge has a volume of 27 m³, a surface area of 54 m², a face diagonal of 3√2 ≈ 4.243 m and a space diagonal of 3√3 ≈ 5.196 m. Enter a volume of 8 m³ instead and the edge comes back as 2 m.
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Frequently asked questions
Is the space diagonal the same as the face diagonal?
No. The face diagonal lies on the surface of one square face and equals a√2. The space diagonal passes through the inside of the cube and equals a√3, which is always longer.
Why does the surface area use six faces?
A cube has a top, a bottom and four sides. Every face is the same square, so the total is six times the area of one face.
Can I mix units for different outputs?
Yes. Enter the known measurement in millimetres, centimetres, metres, kilometres, inches, feet or yards, then pick the unit beside any result. The calculation itself always uses consistent metric base units.