Segment of Circle Calculator

What is a Segment of a Circle?

A segment of a circle is a region bounded by a chord and the corresponding arc lying between the chord's endpoints.

Formulas for Circle Segments

Let $r$ be the radius, $\theta$ be the angle in degrees, and $L$ be the arc length. Then:

1. Arc Length: $L=\frac{\theta }{360}\times 2\pi r$

Step-by-Step Calculations

Let's calculate these properties for a segment with radius $r=5$ units and angle $\theta ={60}^{\circ }$:

1. Radius: $$r=5\text{ units}$$
2. Angle: $$\theta ={60}^{\circ }$$
3. Arc Length: $$L=\frac{60}{360}\times 2\pi \times 5=5.24\text{ units}$$

Visual Representation

This diagram illustrates the segment with the calculated dimensions and properties.