# Square

A 4-sided regular polygon with all sides equal and all internal angles 90°
Try this Drag the orange dots on each vertex to reshape the square.

The square is probably the best known of the quadrilaterals. It is defined as having all sides equal, and its interior angles all right angles (90°). From this it follows that the opposite sides are also parallel.

A square is simply a specific case of a regular polygon, in this case with 4 sides. All the facts and properties described for regular polygons apply to a square. See Regular Polygons

## Attributes

 Vertex The vertex (plural: vertices) is a corner of the square. Every square has four vertices. Perimeter The distance around the square. All four sides are by definition the same length, so the perimeter is four times the length of one side, or: perimeter = 4s where s is the length of one side. See also Perimeter of a square. Area Like most quadrilaterals, the area is the length of one side times the perpendicular height. So in a square this is simply: area = s2 where s is the length of one side. See also Area of a square. Diagonals Each diagonal of a square is the perpendicular bisector of the other. That is, each cuts the other into two equal parts, and they cross and right angles (90°). The length of each diagonal is where s is the length of any one side. For more on this see Diagonals of a square

A square can be thought of as a special case of other quadrilaterals, for example

• a rectangle but with adjacent sides equal
• a parallelogram but with adjacent sides equal and the angles all 90°
• a rhombus but with angles all 90°

## Square inscribed in a circle

Like all regular polygons, a square can be inscribed in a circle, where each vertex is on the circle. For more see Inscribed square.

## Calculator

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

Use the calculator above 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.

## Constructing a square

A square can be constructed using a compass and straightedge. See Constructing a square with compass and straightedge for an animated demonstration.

## Coordinate Geometry

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