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 of the square
• \( \sqrt{2} \) — Approximately 1.41421

Explanation: This formula comes from the Pythagorean theorem applied to the right triangle formed by two adjacent sides and the diagonal.

3. Importance of Diagonal Calculation

Details: Knowing the diagonal is important in geometry, construction, and design. It helps determine the maximum dimensions of objects fitting within squares and is used in various engineering applications.

4. Using the Calculator

Tips: Simply enter the side length of your square in any consistent units (meters, inches, feet, etc.). The calculator will output the diagonal in the same units.

5. Frequently Asked Questions (FAQ)

Q1: Why is the diagonal s√2?
A: By the Pythagorean theorem, diagonal² = side² + side² = 2×side², so diagonal = √(2×side²) = side×√2.

Q2: Are both diagonals of a square equal?
A: Yes, in a square both diagonals are exactly equal in length.

Q3: How is this different from a rectangle's diagonal?
A: For rectangles, the formula is √(length² + width²). The square formula is a special case where length = width.

Q4: Can I use this for 3D cubes?
A: No, this is for 2D squares. For cube diagonals, you'd need a different formula involving √3.

Q5: What if my side length is in fractions?
A: The calculator accepts decimal numbers, so you can enter fractions as decimals (e.g., 0.5 for 1/2).