Arc length

Definition

Arc length is the measure of the distance along a section of the circumference of a circle. It is calculated using the formula $s = r\theta$, where $r$ is the radius and $\theta$ is the central angle in radians.

5 Must Know Facts For Your Next Test

1. Arc length is directly proportional to both the radius and central angle.
2. The formula for arc length is $s = r\theta$, where $\theta$ must be in radians.
3. If the central angle is given in degrees, it must be converted to radians by multiplying by $\frac{\pi}{180}$.
4. Arc length can also be defined as a fraction of the circle's circumference: $s = \frac{\theta}{2\pi} \times 2\pi r = r\theta$.
5. The concept of arc length applies not only to circles but also to sectors and segments within circles.

Review Questions

• What is the formula for calculating arc length?
• How do you convert an angle from degrees to radians when calculating arc length?
• If a circle has a radius of 5 units and a central angle of $2$ radians, what is the arc length?

Related terms

Radius: The distance from the center of a circle to any point on its circumference.

Central Angle: An angle whose vertex is at the center of a circle and whose sides extend to intersect the circumference.

Radians: A unit of angular measure used in mathematics; one radian equals approximately $57.3$ degrees.