1. What is the Diagonal of Square given Diameter of Incircle Formula?

The formula calculates the diagonal of a square when the diameter of its incircle is known. The incircle is the circle that fits perfectly inside the square, touching all four sides.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( d \) — Diagonal of the square
• \( D_i \) — Diameter of the incircle of the square
• \( \sqrt{2} \) — Mathematical constant (approximately 1.4142)

Explanation: The diameter of the incircle equals the side length of the square, and the diagonal of a square is \( \sqrt{2} \) times its side length.

3. Importance of Diagonal Calculation

Details: Calculating the diagonal of a square is important in geometry, construction, and various engineering applications where precise measurements are required.

4. Using the Calculator

Tips: Enter the diameter of the incircle in meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: Why is the diagonal \( \sqrt{2} \) times the diameter of the incircle?
A: Because the diameter of the incircle equals the side length of the square, and the diagonal is always \( \sqrt{2} \) times the side length.

Q2: What units should I use for the diameter?
A: You can use any consistent unit of length (meters, centimeters, inches, etc.), but the result will be in the same units.

Q3: Can this formula be used for rectangles?
A: No, this formula is specific to squares where all sides are equal and the incircle touches all four sides.

Q4: What if I know the radius instead of the diameter?
A: Simply multiply the radius by 2 to get the diameter, then use the formula.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact, though practical measurements may have some degree of error.