Calculate square area, perimeter, diagonal, and inscribed/circumscribed circle properties. Enter any measurement and get all values instantly.
Area
100.0000 cm^2
Showing inscribed circle (inside) and circumscribed circle (outside)
Side Length (a)
10.0000 cm
Area
100.0000 cm^2
A = a^2
Perimeter
40.0000 cm
P = 4a
Diagonal
14.1421 cm
d = a x sqrt(2)
Inscribed Circle Radius
5.0000 cm
r = a/2
Circumscribed Circle Radius
7.0711 cm
R = d/2 = (a x sqrt(2))/2
Inscribed Circle Area
78.5398 cm^2
78.5% of square
Circumscribed Circle Area
157.0796 cm^2
63.7% filled by square
| Side | Area | Perimeter | Diagonal |
|---|---|---|---|
| 1 | 1 | 4 | 1.414 |
| 2 | 4 | 8 | 2.828 |
| 5 | 25 | 20 | 7.071 |
| 10 | 100 | 40 | 14.142 |
| 20 | 400 | 80 | 28.284 |
| 50 | 2500 | 200 | 70.711 |
| 100 | 10000 | 400 | 141.421 |
Key relationship: The diagonal of a square is always sqrt(2) times (about 1.414x) the side length. This comes from the Pythagorean theorem: d^2 = a^2 + a^2 = 2a^2.
Area
100.0000 cm^2
Square formulas: Area = side x side = side squared. Perimeter = 4 x side. Diagonal = side x sqrt(2), approximately 1.414 x side. Inscribed circle radius = side / 2. Circumscribed circle radius = (side x sqrt(2)) / 2 = diagonal / 2.
A square is a regular quadrilateral with four equal sides and four right angles (90 degrees each). It is both a special rectangle (with equal sides) and a special rhombus (with right angles). The diagonals of a square are equal, bisect each other at right angles, and each diagonal divides the square into two congruent isosceles right triangles.
Square formulas: Area = side x side = side squared. Perimeter = 4 x side. Diagonal = side x sqrt(2), approximately 1.414 x side. Inscribed circle radius = side / 2. Circumscribed circle radius = (side x sqrt(2)) / 2 = diagonal / 2.
The area (A) of a square is calculated by squaring the side length: A = side x side = a^2. For example, a square with side 5 has area = 25 square units.
The diagonal (d) of a square equals the side multiplied by the square root of 2: d = a x sqrt(2) = a x 1.414... This comes from the Pythagorean theorem applied to the right triangle formed by two sides and the diagonal.
The inscribed circle (incircle) is the largest circle that fits inside the square, touching all four sides. Its radius equals half the side length: r = a/2. The circle's area is pi x (a/2)^2.
The circumscribed circle (circumcircle) is the smallest circle that completely contains the square, passing through all four corners. Its radius equals half the diagonal: R = (a x sqrt(2))/2 = d/2.
To find the side from the area, take the square root: side = sqrt(Area). For example, if area = 36, then side = sqrt(36) = 6.
A square's diagonals are equal in length, bisect each other at right angles (90 degrees), and divide the square into four congruent right isosceles triangles. Each diagonal = side x sqrt(2).
Last updated: 2025-01-15
Area
100.0000 cm^2