1. What is the Diagonal of a Square?

The diagonal of a square is the line segment connecting two non-adjacent vertices. In a square, both diagonals are equal in length and bisect each other at 90 degrees.

2. How Does the Calculator Work?

The calculator uses the diagonal formula:

Where:

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

Explanation: This formula comes from the Pythagorean theorem, where the diagonal forms the hypotenuse of a right triangle with two sides of the square.

3. Importance of Diagonal Calculation

Details: Knowing the diagonal length is important in construction, design, and various engineering applications where square shapes are used.

4. Using the Calculator

Tips: Simply enter the length of one side of the square. The value must be positive. The calculator will compute the diagonal length using the formula above.

5. Frequently Asked Questions (FAQ)

Q1: Why is the diagonal longer than the sides?
A: The diagonal cuts across the square, making it the hypotenuse of a right triangle formed by two sides, so it's naturally longer.

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

Q3: Does this formula work for rectangles?
A: No, for rectangles the diagonal formula is \( d = \sqrt{l^2 + w^2} \), where l is length and w is width.

Q4: What's the ratio of diagonal to side length?
A: The ratio is exactly \( \sqrt{2} \), approximately 1.41421:1.

Q5: How precise is this calculation?
A: The calculation is mathematically exact. Any imprecision comes only from rounding the result.