Area of a Square Calculator
Calculate the area, side length, diagonal, and perimeter of a square with multiple input methods
Calculate Square Properties
Length of one side of the square
Square Properties
Formulas Used:
Area: A = a² = 0.00²
Diagonal: d = a√2 = 0.00 × √2
Perimeter: P = 4a = 4 × 0.00
Side from area: a = √A = √0.00
Example Calculation
Square Garden Plot
Given: Side length = 8 meters
Find: Area, diagonal, and perimeter
Solution
Area: A = a² = 8² = 64 m²
Diagonal: d = a√2 = 8 × 1.414 ≈ 11.31 m
Perimeter: P = 4a = 4 × 8 = 32 m
Square Formulas
Area
A = a²
Where a is side length
Diagonal
d = a√2
Pythagorean theorem
Perimeter
P = 4a
Sum of all four sides
From Area
a = √A
Side from area
Square Properties
All sides are equal in length
All angles are 90 degrees
Diagonals are equal and bisect each other
Has 4 lines of symmetry
Is a special case of rectangle and rhombus
Understanding Square Area and Properties
What is the Area of a Square?
The area of a square is the amount of space enclosed within its four equal sides. It represents the number of square units that can fit inside the square. The most basic formula is A = a², where 'a' is the length of any side.
Alternative Formulas
- •From diagonal: A = d²/2
- •From perimeter: A = P²/16
- •From circumradius: A = 2R²
- •From inradius: A = 4r²
Real-World Applications
- •Calculating floor tile requirements
- •Determining land area for square plots
- •Computing fabric needed for square patterns
- •Designing square garden beds
- •Calculating paint coverage for square surfaces
Remember: Always ensure your measurements are in the same units before calculating. The area will be in square units (e.g., cm²).
Step-by-Step Calculation Guide
Method 1: From Side Length
- Measure one side of the square
- Square this measurement (multiply by itself)
- The result is the area in square units
Method 2: From Diagonal
- Measure the diagonal of the square
- Square the diagonal measurement
- Divide by 2 to get the area