1. What is the Diagonal of a Square?

The diagonal of a square is the line segment connecting two opposite corners. In a square, all diagonals are equal in length and bisect each other at right angles.

2. How Does the Calculator Work?

The calculator uses the diagonal formula:

Where:

• \( Side \) — Length of one side of the square (meters)
• \( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: This formula is derived 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: Calculating the diagonal is important in construction, engineering, design, and various mathematical applications where precise measurements of square shapes are required.

4. Using the Calculator

Tips: Enter the side length of the square in meters. The value must be positive and greater than zero. The calculator will automatically compute the diagonal length.

5. Frequently Asked Questions (FAQ)

Q1: Why is the diagonal longer than the side?
A: The diagonal cuts across the square, creating the hypotenuse of a right triangle, which is always longer than either of the other two sides.

Q2: Does this formula work for rectangles?
A: No, this specific formula only works for squares. For rectangles, use the formula: Diagonal = √(length² + width²).

Q3: What is the approximate value of √2?
A: The square root of 2 is approximately 1.41421356237, but it's an irrational number with infinite decimal places.

Q4: Can I use different units of measurement?
A: Yes, as long as you use the same unit for both input and output. The calculator defaults to meters but works with any unit of length.

Q5: How accurate is the calculation?
A: The calculation is mathematically precise. The result is rounded to 4 decimal places for practical use, but the underlying calculation uses the exact value of √2.