Cube Calculator
Enter the side length of a cube and instantly get its volume, surface area, face diagonal, and space diagonal. A cube with side length 5 has a volume of 125, surface area of 150, and a space diagonal of about 8.66.
Cube Formulas
A cube is a regular hexahedron with all six faces being identical squares. Given side length s:
- Volume: V = s³
- Surface Area: SA = 6s²
- Face Diagonal: d_f = s x sqrt(2) (the diagonal across one face)
- Space Diagonal: d_s = s x sqrt(3) (corner to opposite corner through the interior)
- Total Edge Length: 12s (a cube has 12 equal edges)
Worked Example: s = 4
- Volume = 4³ = 64 cubic units
- Surface Area = 6 x 16 = 96 square units
- Face Diagonal = 4 x 1.414 = 5.657 units
- Space Diagonal = 4 x 1.732 = 6.928 units
Why Two Diagonals?
The face diagonal lies flat on one face (like the diagonal of a square). The space diagonal cuts through the interior of the cube from one vertex to the farthest vertex. The space diagonal is always longer because it spans three dimensions instead of two.
Cubes in the Real World
Dice, ice cubes, Rubik's cubes, and storage boxes are everyday examples. Shipping companies use the cubic volume to calculate freight costs, and builders use surface area to estimate paint or material coverage.