1. What is the Radius of Quarter Circle Formula?

The formula calculates the radius of a quarter circle when the perimeter is known. It's derived from the relationship between the perimeter and radius of a quarter circle.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r \) — Radius of Quarter Circle (meters)
• \( P \) — Perimeter of Quarter Circle (meters)
• \( \pi \) — Mathematical constant pi (approximately 3.14159)

Explanation: The formula is derived from the quarter circle perimeter formula \( P = r(\pi/2 + 2) \), solved for radius.

3. Importance of Radius Calculation

Details: Calculating the radius from perimeter is essential in geometry problems, architectural design, and various engineering applications where quarter circular shapes are involved.

4. Using the Calculator

Tips: Enter the perimeter value in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a quarter circle?
A: A quarter circle is one-fourth of a full circle, bounded by two radii at right angles and the connecting arc.

Q2: Why is pi used in the formula?
A: Pi (π) is the mathematical constant representing the ratio of a circle's circumference to its diameter, which is fundamental to all circular calculations.

Q3: Can this formula be used for any perimeter value?
A: Yes, as long as the perimeter value represents a valid quarter circle (positive value greater than zero).

Q4: What are the units of measurement?
A: The calculator uses meters, but the formula works with any consistent unit system (cm, mm, inches, etc.).

Q5: How accurate is the calculation?
A: The calculation uses double-precision floating point arithmetic with pi accurate to 15 decimal places, providing high precision results.