1. What is the Diagonal of a Square?

The diagonal of a square is the line segment connecting two non-adjacent vertices. It divides the square into two congruent isosceles right triangles.

2. How Does the Calculator Work?

The calculator uses the diagonal formula:

Where:

• \( d \) — Diagonal length
• \( s \) — Side length of the square
• \( \sqrt{2} \) — Approximately 1.41421

Explanation: The formula derives from the Pythagorean theorem applied to the two sides of the square forming a right triangle with the diagonal.

3. Importance of Diagonal Calculation

Details: Knowing the diagonal is essential in geometry, construction, and design for determining distances between opposite corners and for creating precise square layouts.

4. Using the Calculator

Tips: Enter the side length in any consistent units (meters, inches, etc.). The result will be in the same units. Value must be positive.

5. Frequently Asked Questions (FAQ)

Q1: Why is the diagonal longer than the side?
A: The diagonal forms the hypotenuse of a right triangle with two sides, making it √2 (about 1.414) times longer than either side.

Q2: Can I calculate the side from the diagonal?
A: Yes, by rearranging the formula: \( s = \frac{d}{\sqrt{2}} \).

Q3: Does this work for rectangles?
A: No, rectangles use a different formula: \( d = \sqrt{length^2 + width^2} \).

Q4: How precise is this calculation?
A: Mathematically exact, though practical measurements may have precision limits.

Q5: Where is this used in real life?
A: Construction (framing square corners), graphic design (screen dimensions), and any field requiring precise square measurements.