If you ever need to work out the measurements and calculations of a square, you will find there are many options to do so. What’s more, they can be long-winded and time-consuming to complete by hand. If you want to know a square’s area, perimeter, or diagonal, then you can use this square calculator. Find out more about formulas for square calculations below.

What is a Square?

You can define a square as a quadrilateral which has four right 90-degree angles and four equal sides. It also has all the same properties as a rectangle, a parallelogram, a rhombus, or a trapezoid.

Square Calculator: Finding the Perimeter

The perimeter of the square is the same as the sum of all of its sides. A square’s sides are all equal, so the formula for finding the square’s perimeter looks like this: 

Perimeter = a + a + a + a = 4 x a

Square Calculator: Finding the Area

The length of the sides of your square dictates the area within it. The word “square” also happens to be a term associated with multiplying a value by itself to get an exponent to the second power. The formula for finding a square’s area looks like this: 

Area = a x a = a ²

Square Calculator: Find the Diagonal

A square’s diagonals are all of equal length. They are perpendicular bisectors of themselves and bisect angles. A square’s diagonal length is the side length times the square root of two. The formula, as a result, will be:

D = a√2

Here is an example where we find a square’s diagonal length: If the side of a square is four inches, the formula would be 4√2 to get the diagonal of 5.656 inches.

The Properties of a Square

When you are learning about squares and the measurements of them, you will come across a few unique terms, such as the ones below.

Bisection = when diagonals bisect square angles and each other
Perpendicular = the diagonals meet at 90 degrees and the square angles are equal to 90 degrees
Equality = all a square’s sides are equal, the diagonals are the same length, and all four angles are equal