Calculate area, perimeter, and diagonal of a square.
The Square Area Calculator is a simple geometric utility designed to compute the area, perimeter, and diagonal of a square. A square is a regular quadrilateral, meaning it has four equal sides (s) and four equal right angles (90 degrees). It is a special case of a rectangle where the length and width are equal, exhibiting high symmetry.
The area (A) of a square is calculated by multiplying the side length by itself: A = s². The perimeter (P) is the sum of all four equal sides: P = 4s. The diagonal (d), which connects opposite corners, can be calculated using the Pythagorean theorem since the sides and diagonal form a right triangle: d = √(s² + s²) = s√2. If only the diagonal is known, the side length can be derived as s = d / √2, and the area as A = d² / 2.
Squares are widely used in architectural grids, floor tiling, layout planning, and chessboard patterns. In daily life, we use square area calculations to determine the size of square tables, patches of fabric, and crop plots. The square area calculator provides fast, exact computations, helping users calculate tiling requirements, estimate sizes, and check algebraic formulas instantly.
Properties of a Square
A square is a regular quadrilateral with four equal sides and four equal right angles (90°).
- Area (A):
A = s² - Perimeter (P):
P = 4 × s - Diagonal (d):
d = s × √2
How it Works & Formula
Determines the flat area, boundary perimeter, and diagonal of a square.
Practical Examples
A tile of 12 inches per side covers 12² = 144 square inches.
Frequently Asked Questions
What is the length of the diagonal?
The diagonal length is s × √2, which comes directly from the Pythagorean theorem.