Arc Length Calculator

How to Calculate Arc Length

Calculating the arc length is a fundamental skill in geometry and trigonometry. Here's a comprehensive guide on how to calculate the arc length of a sector:

Arc Length Formula

The formula for calculating arc length is:

$$L = \frac{\theta}{360°} \cdot 2\pi r$$

Where:

• $L$ is the arc length
• $\theta$ is the central angle in degrees
• $r$ is the radius of the circle

Calculation Steps

1. Identify the central angle ($\theta$) and radius ($r$) of the sector.
2. Convert the central angle to radians if necessary (the formula above uses degrees).
3. Substitute the values into the formula.
4. Perform the calculation to obtain the arc length.

Example Calculation

Let's calculate the arc length for a sector with a central angle of 45° and a radius of 10 units:

1. Central angle $\theta = 45°$
2. Radius $r = 10$ units
3. Substituting into the formula: $$L = \frac{45°}{360°} \cdot 2\pi \cdot 10$$
4. Simplifying: $$L = 0.125 \cdot 2\pi \cdot 10 \approx 7.85$$ units

Visual Representation

This pie chart visually represents a 45° arc, which is one-eighth of a full circle. The arc length calculated (approximately 7.85 units) corresponds to this portion of the circle's circumference.