# Diagonal of a Square

LAST UPDATE: February 2nd, 2022

## Method #1 – Diagonal from the length of one side

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

Length of the diagonal = √(L2 + L2)

Where “L” is the length of one side of the square.

##### Example

A square has a length of 10.

Length of the diagonal = √(102 + 102) = √(100 + 100) = √200 = 14.1421

## Method #2 – Diagonal from the Area

### Formula – How to calculate the diagonal of a square from the area

Length of the diagonal = √(a + a)

##### Example

A square has an area of 100 inches2

Length of the diagonal = √(100 + 100) = √200 = 14.1421

## Method #3 – Diagonal from the Perimeter

### Calculator

Length of the diagonal = √(a + a)

##### Example

A square has an area of 100 inches2

Length of the diagonal = √(100 + 100) = √200 = 14.1421

### … from the perimeter

Length of the diagonal = √((P ÷ 4)2 + (P ÷ 4)2)

##### Example

A square has a perimeter of 40.

Length of the diagonal = √((40 ÷ 4)2 + (40 ÷ 4)2)

Length of the diagonal = √(102 + 102)

Length of the diagonal = √(100 + 100)

Length of the diagonal = √200

Length of the diagonal = 14.1421