1. What is the Diagonal of a Square?

The diagonal of a square is the line segment connecting two non-adjacent vertices. In any square, the diagonals are equal in length and bisect each other at 90 degrees. The length of the diagonal relates to the side length through a simple mathematical formula.

2. How Does the Calculator Work?

The calculator uses the diagonal formula:

Where:

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

Explanation: This formula derives 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 length is essential in construction, design, and geometry problems. It helps determine the maximum dimensions that can fit within square spaces and is used in various engineering applications.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: Why is the diagonal √2 times the side length?
A: This comes from the Pythagorean theorem: diagonal² = side² + side² → diagonal = √(2 × side²) = side × √2.

Q2: Does this formula work for rectangles?
A: No, for rectangles the formula is more complex: d = √(length² + width²). This calculator is specifically for squares where all sides are equal.

Q3: Can I use this for 3D cubes?
A: No, the space diagonal of a cube is different: d = s√3. This calculator only handles 2D squares.

Q4: How precise is this calculation?
A: The calculation is mathematically exact. The precision depends on your side length measurement accuracy.

Q5: What if my square is rotated?
A: The diagonal length remains the same regardless of rotation, as long as all sides are equal and angles are 90 degrees.