# Square Calculator

## Square Shape

a = side length

q = diagonal length

P = perimeter

A = area

√ = square root

## Calculator Use

Use this square calculator to find the side length, diagonal length, perimeter or area of a geometric square. Given any 1 variable you can calculate the other 3 unknowns.

**Units:** Note that units of length are shown for convenience. They do not affect the calculations. The units are in place to give an indication of the order of the calculated results such as ft, ft^{2} or ft^{3}. Any other base unit can be substituted.

## Square Formulas:

A square is a convex quadrilateral with all sides equal length and positioned at right angles to each other. Or, a square is a regular polygon with four sides, a tetragon.

### Area of a square:

A = a^{2}

### Perimeter of a Square

P = 4a

### Polygon diagonals of a square

q = √(2a^{2}) = a√2

### Side of a Square

a = √A

a = P/4

a = q / √2

## Square Calculations

**Calculate q, P, A | Given a**

Given the length of a side calculate the diagonal, area and perimeter

- q = a√2
- A = a
^{2} - P = 4a

**Calculate a, P, A | Given q**

Given the diagonal length calculate the side length, perimeter and area- a = q / √2
- P = 4a
- A = a
^{2}

**Calculate a, q, A | Given P**

Given the perimeter calculate the side length, diagonal and area- a = P/4
- q = a√2
- A = a
^{2}

**Calculate a, q, P | Given A**

Given the area calculate the length of the sides, diagonal and the perimeter

- a = √A
- q = a√2
- P = 4a