Square Calculator (Geometry)
Find the area, perimeter, diagonal, or side length of any square. Enter one known value to solve for all others.
| Property | Value | Formula |
|---|
Square Geometry Formulas
Square geometry formulas let you find any property of a square when you know just one measurement.
| Find | Given | Formula |
|---|---|---|
| Area (A) | Side (a) | A = a² |
| Perimeter (P) | Side (a) | P = 4a |
| Diagonal (q) | Side (a) | q = a√2 |
| Side (a) | Area (A) | a = √A |
| Side (a) | Perimeter (P) | a = P / 4 |
| Side (a) | Diagonal (q) | a = q / √2 |
Properties of a Square
A square is a special quadrilateral with four equal sides and four right angles. Understanding its key properties helps solve geometry, construction, and design problems efficiently.
Area of a Square
Area measures the flat space inside the square. Area = a² means you multiply the side length by itself. A square with side 8 m has area 64 m².
Perimeter of a Square
Perimeter is the total length of all four sides. Since all sides are equal, P = 4a. A square with side 5 cm has perimeter 20 cm.
Diagonal of a Square
The diagonal of a square runs from one corner to the opposite corner. By the Pythagorean theorem, q = √(a² + a²) = a√2. A square with side 10 m has a diagonal of approximately 14.14 m.
Frequently Asked Questions
The area of a square is A = a², where a is the side length. For example, a square with side length 6 cm has area A = 6² = 36 cm².
The perimeter of a square is P = 4a, where a is the side length. For a square with side 5 m, perimeter = 4 × 5 = 20 m.
The diagonal of a square is q = a√2, derived from the Pythagorean theorem. For a square with side 4 cm, diagonal = 4 × √2 ≈ 5.657 cm.
To find side length from area, use a = √A. For area = 49 cm², side length = √49 = 7 cm.
To find side length from diagonal length, use a = q / √2. For diagonal = 10 cm, side = 10 / √2 ≈ 7.071 cm.