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.