New SAT Math: Circle Arc Length

The fourth category of New SAT Math problems – Additional Topics in Math – doesn’t sound too frightening, but don’t let the generic name fool you. Many of the problems that show up on the test combine skills you may have learned from multiple math classes throughout middle and high school. Circle arc length, for example, combines geometry along with some basic trigonometry skills.
New SAT Math Circle Arc Length -magoosh

New SAT Math: Basic Circle Skills Review

If you’re a little shaky or foggy on your knowledge of circle concepts, check this section out. It’s a great refresher on what you’ve probably already learned before during one of your math classes.

If you already have a strong grasp on this, go ahead and skip to the next section!

Value of Pi

The value of pi is about 3.14. You may already have a pi button on your calculator, but you should have this value memorized anyway.

Circumference of a Circle

The circumference of a circle is diameter*pi. The circumference tells you the length of the perimeter of a circle.

It takes about 3.14 diameters to equal the circumference of a circle.

Degrees in a Circle

A circle consists of 360 degrees. Half of the circle is 180 degrees, and a quarter of a circle is 90 degrees.


Radians are an angle measure equivalent to an arc length of one radius of a circle. It is a relative measurement. 1 radian equals about 57.3 degrees.

Remember to check your calculator settings carefully to make sure it is set properly for either degrees or radians. You can bet that test makers will throw in a trap answer here or there for unsuspecting students.

New SAT Math: Arc Length of a Circle

Now that you’ve thoroughly brushed up on the basics of circles, let’s get right into figuring out how to calculate the arc length of a circle. The new SAT contains problems that really dig deep into seeing how well you understand basic concepts, so take extra care to know the fundamentals forwards and backwards.

Circle Arc Length

The total circle arc length is the circumference, or the perimeter of a circle. When we want to find out the length of a small part of that circumference, we need to multiply it by a fraction between 0 and 1.

We can use either degrees or radians in order to represent this fraction. An entire circle equals 360 degrees or 2pi radians, so our formula looks like this:

Circle Arc Length = circumference * (x degrees / 360)
Circle Arc Length = circumference * (x radians / 2pi)
Looking for more help with circles on the SAT? Check out our videos about unit circle basics and tangents to a circle.


  • Minh Nguyen

    Minh's passion for helping students succeed grew during his time as a career counselor at the University of California, Irvine. Now, he's helping students all over the world by spilling SAT/ACT secrets through blog posts on Magoosh. When he's not busy tutoring or writing, he enjoys playing guitar, traveling, and talking about himself in third-person.

By the way, Magoosh can help you study for both the SAT and ACT exams. Click here to learn more!

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