# Interior Diagonal of a Cube

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

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

Interior Diagonal = √3 x Side

##### Example

A cube has a side length of 10

Interior Diagonal = √3 x 10 = 1.73205 x 10 = 17.3205

## Method #2 – Interior diagonal from the volume

### Formula – How to calculate the interior 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 interior diagonal from the length of one side

Interior Diagonal = √3 x Side

##### Example

A cube has a volume of 1,000

Side = 3√1000 = 10

Interior Diagonal = √3 x 10 = 1.73205 x 10 = 17.3205

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

### Formula – How to calculate the interior 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 interior diagonal from the length of one side

Interior Diagonal = √3 x Side

##### Example

A cube has a surface area of 600

Side = √(600 ÷ 6) = √100 = 10

Interior Diagonal = √3 x 10 = 1.73205 x 10 = 17.3205

## Method #4 – Interior diagonal from the perimeter

### Formula – How to calculate the interior 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 interior diagonal from the length of one side

Interior Diagonal = √3 x Side

##### Example

A cube has a perimeter of 120

Side = 120 ÷ 12 = 10

Interior Diagonal = √3 x 10 = 1.73205 x 10 = 17.3205

## Method #5 – Interior diagonal from the face diagonal

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

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

Side = √(Diagonal2 ÷ 2)

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

Interior Diagonal = √3 x Side

##### Example

A cube has an face diagonal of 14

Side = √(142 ÷ 2) = √(196 ÷ 2) = √98 = 9.89949

Interior Diagonal = √3 x 9.89949 = 1.73205 x 9.89949 = 17.1464