Cube Calculator
Calculate the surface area, volume, face diagonal, and space diagonal of a cube from its side length.
About this Calculator
Calculate the surface area, volume, face diagonal, and space diagonal of a cube from its side length.
Formula & Calculations
Formula
Surface Area = 6s²; Volume = s³; Face Diagonal = s√2; Space Diagonal = s√3Where:
- s=Side length of the cube
- SA=Total surface area (sum of all 6 faces)
- V=Volume of the cube
- d_face=Face diagonal (diagonal across a single square face)
- d_space=Space diagonal (diagonal through the center of the cube)
Assumptions
- The cube is a regular hexahedron with all six faces being identical squares.
- All edges are equal in length.
- Face diagonals lie in a plane; space diagonals pass through the center of the cube.
Calculation Examples
Example 1
SA = 6 × 9 = 54. V = 27. d_face = 3 × √2 ≈ 4.2426. d_space = 3 × √3 ≈ 5.1962.
Example 2
SA = 6 × 25 = 150. V = 125.
Frequently Asked Questions
What is the difference between face diagonal and space diagonal?
A face diagonal connects two opposite corners on the same face of the cube, lying flat on one surface. A space diagonal connects two opposite corners through the interior of the cube, passing through the center. The space diagonal is always √(3/2) ≈ 1.225 times longer than the face diagonal.
How do you derive the space diagonal formula?
The space diagonal is the hypotenuse of a right triangle formed by an edge s and a face diagonal s√2. Applying the Pythagorean theorem: d_space = √(s² + (s√2)²) = √(s² + 2s²) = √(3s²) = s√3.