# Face Diagonal of a Cube

## Method #1 – Face diagonal from the length of one side

### Formula – How to calculate the face diagonal of a cube from the length of one side

Face Diagonal = √(Side2 x 2)

##### Example

A cube has a side length of 10

Face Diagonal = √(102 x 2) = √(100 x 2) = √200 = 14.1421

## Method #2 – Face diagonal from the volume

### Formula – How to calculate the face diagonal of the cube from the volume

Step 1 – Find the length of one side from the volume

Side = 3√Volume

Step 2 – Find the face diagonal from the length of one side

Face Diagonal = √(Side2 x 2)

##### Example

A cube has a volume of 1,000

Side = 3√1000 = 10

Face Diagonal = √(102 x 2) = √(100 x 2) = √200 = 14.1421

## Method #3 – Face diagonal from the surface area

### Formula – How to calculate the face diagonal of a cube from the surface area

Step 1 – Find the length of one side from the surface area

Side = √(Surface Area ÷ 6)

Step 2 – Find the face diagonal from the length of one side

Face Diagonal = √(Side2 x 2)

##### Example

A cube has a surface area of 600

Side = √(600 ÷ 6) = √100 = 10

Face Diagonal = √(102 x 2) = √(100 x 2) = √200 = 14.1421

## Method #4 – Face diagonal from the perimeter

### Formula – How to calculate the face diagonal of the cube from the perimeter

Step 1 – Find the length of one side from the perimeter

Side = Perimeter ÷ 12

Step 2 – Find the face diagonal from the length of one side

Face Diagonal = √(Side2 x 2)

##### Example

A cube has a perimeter of 120

Side = 120 ÷ 12 = 10

Face Diagonal = √(102 x 2) = √(100 x 2) = √200 = 14.1421

## Method #5 – Face diagonal from the interior diagonal

### Formula – How to calculate the face diagonal of the cube from the interior diagonal

Step 1 – Find the length of one side from the interior diagonal

Side = Diagonal ÷ √3

Step 2 – Find the face diagonal from the length of one side

Face Diagonal = √(Side2 x 2)

##### Example

A cube has an interior diagonal of 14

Side = 14 ÷ √3 = 14 ÷ 1.4422 = 9.7074

Face Diagonal = √(9.70742 x 2) = √(94.2336 x 2) = √188.4672 = 13.7283