Square Calculator
Calculate area, perimeter, and diagonal of a square from any given parameter
Calculate Square Properties
Length of one side of the square
Square Properties
Formulas used:
- • Area: A = a²
- • Perimeter: P = 4a
- • Diagonal: d = a√2 ≈ 0 cm
Example Calculation
Square Table Example
Problem: Find the area, perimeter, and diagonal of a square table with side length 4 ft.
Given: Side length a = 4 ft
Solution
Area: A = a² = 4² = 16 ft²
Perimeter: P = 4a = 4 × 4 = 16 ft
Diagonal: d = a√2 = 4 × 1.414 = 5.657 ft
Square Properties
Equal Sides
All four sides are equal in length
Right Angles
All four angles are 90°
Equal Diagonals
Both diagonals are equal and bisect each other at 90°
Key Formulas
Area
A = a²
where a is side length
Perimeter
P = 4a
sum of all sides
Diagonal
d = a√2
diagonal across the square
Understanding Square Calculations
What is a Square?
A square is a regular quadrilateral with four equal sides and four equal angles (90°). It's a special case of a rectangle, rhombus, parallelogram, and trapezoid, inheriting properties from all these shapes.
Key Characteristics
- •All sides are equal in length
- •All angles are 90° (right angles)
- •Diagonals are equal and bisect each other at 90°
- •Has 4 lines of symmetry
Formula Derivations
Area Formula
Area is the space enclosed within the square's boundaries.
A = side × side = a²
Perimeter Formula
Perimeter is the total distance around the square.
P = a + a + a + a = 4a
Diagonal Formula
Using Pythagorean theorem: d² = a² + a²
d = √(2a²) = a√2 ≈ 1.414a