Square Formulas

The Square Formulas Calculator is a versatile and easy-to-use tool designed to find all fundamental properties of a square from a single known value.

Whether you know the side length, diagonal length, perimeter, or area, this calculator will instantly compute the remaining three properties using standard geometric formulas. It's perfect for students, engineers, architects, and anyone working on geometry problems or real-world construction projects.

The Geometry of a Square

A square is a regular quadrilateral, meaning it has four equal sides and four equal angles (all 90-degree right angles). Because of its symmetry, knowing just one of its core measurements allows you to determine all the others.

Core Formulas

Let $s$ represent the side length of the square:

1. Perimeter ($P$): The total distance around the outside of the square. $$P = 4 \times s$$

2. Area ($A$): The amount of 2D space enclosed within the square. $$A = s^2$$

3. Diagonal ($d$): The straight line distance connecting opposite corners. By the Pythagorean theorem ($s^2 + s^2 = d^2$), it is: $$d = s \times \sqrt{2}$$

Angles

• Internal Angle: The angle between any two adjacent sides is exactly 90°.
• Diagonal Angle: The angle at which the diagonals intersect each other is exactly 90°. The angle between a diagonal and a side is 45°.

How to Calculate from Other Properties

• If you know the Diagonal ($d$): $$s = \frac{d}{\sqrt{2}}$$
• If you know the Perimeter ($P$): $$s = \frac{P}{4}$$
• If you know the Area ($A$): $$s = \sqrt{A}$$