Diagonal of a Cube Formula
The diagonal of a cube formula helps in calculating different diagonal of a cube, namely, face diagonal and the main diagonal. A cube is a threedimensional solid figure, also known as the square solid that has edges of all the same length, meaning that it has the length, width, and height equal, and each of its faces is a square. Let us understand the diagonal of a cube formula for both face and body diagonal using examples.
What is Diagonal of a Cube Formula?
Diagonal of a cube formula: Face diagonal
The formula to calculate the length of face diagonal of a cube is given as,
Length of each face diagonal of cube = √2 x units.
where x = Length of each side of a cube.
Diagonal of a cube formula: Body diagonal
The formula to calculate the length of body or main diagonal of a cube is given as,
Length of body diagonal of a cube = √3 x units.
where x = Length of each side of a cube.
Solved Examples Using Diagonal of a Cube Formula

Example 1:
Calculate the length of the diagonal of a cube whose each side measures 5 units?
Solution:
To find: Length of the diagonal of a given cube.
Using the diagonal of a cube formula,
Length of body diagonal of a cube = √3 x units.
= √3 × 5 units = 8.66 units
Answer: The length of the diagonal of a given cube = 8.66 units.

Example 2:
The length of the diagonal of a cube is 8√3 units. Find the length of each side.
Solution:
To find: Length of each side of the given cube.
Using the diagonal of a cube formula,
Length of diagonal of a cube = √3 x units = 8√3 units
x = 8√3/√3 = 8 units
Answer: Length of each side of the given cube = 8 units.