Arc Length, Radius or Central Angle Calculator

What is a Sector?

A sector is a portion of a circle enclosed by two radii and the corresponding arc. It resembles a slice of a pie or pizza.

Formulas for Sectors

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 sector 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 sector with the calculated dimensions and properties.