Home > Math Topics > Trigonometry >

Arc Length and Radian Measure

HSG-C.B.5
Answer Keys Here

Aligned To Common Core Standard:

High School Geometry - HSG-C.B.5

How to Calculate the Length of an Arc - An arc is typically defined as the small segment present at the circumference of a circle. Or any fraction of circle's circumference lying between two points. Arc span is defined as the span along the arc. An arc measure is the angle made arc at the center of a circle. The angle is measured in radians or degrees. You can easily figure out the arc of the circle by taking less than full length around the circle within two radii. We use the following formula for calculating the length of an arc: arc measure= (arc length)/radius = s/r Let's understand it better with an example. If our arc length is 3cm and our radius is 4 cm. Write down the formula first: arc measure =s/r | arc measure = 3/4| This is written in radians; we can have it degrees by multiplying it with 180/ π = (3/4) (180/π) = 42.971 = 43 degrees. These worksheets and lessons teach students how to determine the length of the arc of a circle and the measure in radians.

Printable Worksheets And Lessons




Homework Sheets

A number of different conversion strategies are set for you over the course of this series.

  • Homework 1 - The length of an arc is simply the length of its "portion" of the circumference.
  • Homework 2 - A radian is the measure of an angle ø that, when drawn as a central angle, subtends an arc whose length equals the length of the radius of the circle.
  • Homework 3 - Convert 20° to radians.



Practice Worksheets

Many teachers write in and let us know that these were very helpful for them.

  • Practice 1 - Pi radians to degrees, what is that all about?
  • Practice 2 - Actually, the circumference itself can be considered an arc length.
  • Practice 3 - Arc lengths take a bit of time to comprehend.



Math Skill Quizzes

How would you go about using these as a daily warm up. It's a good idea!

  • Quiz 1 - What a huge advantage to look at it from that stance?
  • Quiz 2 - Don't just warm up take it all the way!
  • Quiz 3 - I never knew how important the circle was until now.