1. What is Square in a Circle?

A square inscribed in a circle is a square drawn inside a circle such that all four vertices lie on the circumference of the circle. The diagonal of the square equals the diameter of the circle.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \text{diameter} \) — Diameter of the circumscribed circle
• \( \text{side} \) — Length of the square's side

Explanation: The relationship comes from the Pythagorean theorem, where the diagonal of the square (equal to the circle's diameter) forms the hypotenuse of a right triangle with two sides of the square.

3. Practical Applications

Details: This calculation is useful in engineering, architecture, and design when creating square elements that must fit perfectly within circular boundaries.

4. Using the Calculator

Tips: Simply enter the diameter of the circle in meters. The calculator will output the maximum side length of a square that can fit inside that circle.

5. Frequently Asked Questions (FAQ)

Q1: Can this formula be reversed to find diameter from side length?
A: Yes, diameter = side × √2

Q2: What's the area of the inscribed square?
A: Area = side² = (diameter²)/2

Q3: How does this relate to the circumradius?
A: The circle's radius is half the diameter, so side = radius × √2 × 2

Q4: What's the difference between inscribed and circumscribed squares?
A: Inscribed means square inside circle, circumscribed means circle inside square

Q5: Does this work for rectangles?
A: No, this specific formula only applies to perfect squares in circles