Area of a Square
From Latin: area - "level ground, an open space,"
The number of square units it takes to completely fill a square.
Formula: Width × Height
Try this Drag the orange dots to move and resize the square. As the size of the square changes, the area is recalculated.

Area formula

The area of a square is given by the formula
area = width × height
But since the width and height are by definition the same, the formula is usually written as
area = s2
where s is the length of one side.

In strictly correct mathematical wording the formula above should be spoken as "s raised to the power of 2", meaning s is multiplied by itself. But we usually say it as "s squared". This wording actually comes from the square. The length of a line s multiplied by itself, creates the square of side s. Hence "s squared".

Calculator

ENTER ANY ONE VALUE
Side clear
Perimeter clear
Area clear
Diagonal clear
   
 

Use the calculator on the right to calculate the properties of a square.

Enter any one value and the other three will be calculated. For example, enter the side length and the area will be calculated.

Similarly, if you enter the area, the side length needed to get that area will be calculated.

The "diagonals" method

If you know the lengths of the diagonals, the area is half the product of the diagonals. Since both diagonals are congruent (same length), this simplifies to:


where
d is the length of either diagonal

Coordinate Geometry

If you know the coordinates of the vertices of a square, you can calculate all the other properties, including the area. For more on this, see Area and Perimeter of a square (Coordinate geometry)

Things to try

  1. In the figure above, click on "hide details"
  2. Drag the orange dots on the vertices to make a random-size square.
  3. Now try to estimate the area of the square just looking at the small unit squares inside it
When you done click "show details" to see how close you got.

Related polygon topics

General

Types of polygon

Area of various polygon types

Perimeter of various polygon types

Angles associated with polygons

Named polygons

COMMON CORE

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See which resources are available on this site for each element of the Common Core standards.

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