How to Calculate the Area of a Square
The area of a square measures the amount of two-dimensional space enclosed within its four equal sides. Since all sides of a square are equal, calculating the area requires only one measurement.
Area Formulas for a Square
From Side Length
The most direct method. Square the side length.
A = s²
From Diagonal
When you know the diagonal d, derive the side using d = s√2.
A = d² / 2
From Perimeter
Divide the perimeter by 4 to find the side, then square it.
A = (P / 4)²
Examples
Example 1: Side = 5 units
A = 5² = 25 square units.
Example 2: Diagonal = 10 units
A = 10² / 2 = 100 / 2 = 50 square units.
Example 3: Perimeter = 20 units
Side = 20 / 4 = 5, so A = 5² = 25 square units.
Why This Matters
Knowing how to calculate the area of a square is essential for flooring, painting, tiling, and many engineering and architectural applications. Whether you measure the side, diagonal, or perimeter, this calculator instantly derives the area for you.