This calculator calculates the area, perimeter, circumradius, inradius and diagonal length of a square. You can select to how many decimal places the calculation should be rounded. The calculator always uses the rounded values for further calculations.
Formulas
| Area | A = a² | ||||
| Perimeter | P = 4 ∙ a | ||||
| Diagonal length | d = a ∙ 2 = R ∙ 2 | ||||
| Circumradius | R =
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| Inradius | r =
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What is a square?
A rectangle is a quadrilateral where all 4 interior angles are right angles. Opposite sides have the same side lengths and are parallel to each other.
A square is a rectangle where all 4 sides are of the same length.
Area of a square
The area A of a square, where all sides have the side length a, can be easily calculated using the following formula:
Example:
A square has side lengths of 3 cm. The area therefore is:
A=a²=(3 cm)²=9 cm²
If you know the area A of the square and want to calculate the side length a, you have to extract the root of the area:
Example:
A square has an area of 25 cm². To calculate the side lengths you have to calculate:
a=A=25 cm²=5 cm
Perimeter of a square
To calculate the perimeter, all side lengths must be summed up. Since all 4 sides of a square have the same side length, the length of one side can be multiplied by 4 to calculate the perimeter.
Example:
The sides of a square have a length of 3 cm each. The perimeter is calculated as follows:
P=4∙a=4∙3 cm=12 cm
If the perimeter is known and the length of the sides is to be calculated from it, the perimeter must be divided by 4.
| P |
| 4 |
Example:
A square has a perimeter of 20 cm. The side length a is to be calculated:
a=| P |
| 4 |
| 20 cm |
| 4 |
Diagonal length
In a square, you draw a diagonal by drawing a line from one angle of the square to the opposite angle. The length of this line is the diagonal length. If the length of the diagonal is called d and the length of one side of the square is called a, then the following applies:
Example:
The sides of a square have a length of 3 cm each. To calculate the length of the diagonal you have to calculate:
d=2∙a=2∙3 cm≈4.242641 cmIf the diagonal length is known and you want to calculate the side length a, then divide the diagonal length by 2.
| d |
| 2 |
Example:
The diagonal length in a square is 10 cm. So the following applies to the side length a:
a=| d |
| 2 |
| 10 cm |
| 2 |
Circumradius
A circumcircle of a square is a circle where all 4 corners of the square lie on this circle. The diameter of this circle is the diagonal length of the square. Thus, the radius of the circumcircle is half of the diagonal length of the square.
| d |
| 2 |
If you want to calculate the circumradius with the help of the side length a, then you can also calculate as follows:
| a |
| 2 |
If the radius R is known and you want to calculate the side length a or the diagonal length d, then you calculate:
Inradius
The incircle of a square is a circle that lies inside the square and touches each side of the square at exactly one point (exactly in the middle). The center of the incircle is exactly in the center of the square. The diameter of the incircle is exactly as long as the side lengths of the square. Thus applies:
| a |
| 2 |
If the inradius r is known and the side length a is to be calculated, then one calculates: