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.