Fractional Part of a Circle Calculator

How to Use This Calculator

1. Enter the radius (r) of the circle in any consistent units (meters, feet, etc.).
2. Enter the central angle (θ) in degrees. This is the angle at the center of the circle that subtends the sector.
3. The calculator will automatically compute:
• The fractional part of the circle (θ/360)
• The area of the sector (A = (θ/360) × πr²)
• The arc length (L = (θ/360) × 2πr)
4. If you already know the area of the sector, you can enter it instead of the radius and angle, and the calculator will solve for the radius and angle.

Mathematical Principles

The calculator uses the following formulas:

• Fraction of Circle: Fraction = θ/360, where θ is the central angle in degrees
• Sector Area: A = (θ/360) × πr²
• Arc Length: L = (θ/360) × 2πr

These calculations are based on the proportion of the central angle to the full circle (360 degrees).