Area of a Sector

Learn how to find the area of a sector.

Area of a Sector Lesson

Sector Area Formula

There are two sector area formulas; one for a sector measured in radians, and another for a sector measured in degrees. They are given as:

  1. Radians: A = 12θr2
  2. Degrees: A = 1360θπr2

Where A is the area, θ is the sector angle, and r is the radius.

The Formulas for the Area of a Sector
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Area of a Sector Example Problems

Let's work through a couple of example problems together to practice finding the area of a sector.

Example Problem 1

Find the area of a sector with an angle of 90 degrees and a radius of 10.


  1. Plugging the given dimensions into the formula, we get:
    A = 1360θπr2
    A = 1360(90)π(102) = 25π
  2. The area is 25π.

Example Problem 2

The sector from problem 1 is changed so that the diameter is 10 instead of the radius being 10. What is the new area?


  1. First, let's convert diameter to radius.
    2r = d
    2r = 10
    r = 5
  2. Now let's plug the radius and angle into the formula.
    A = 1360θπr2
    A = 1360(90)π(52) = 6.25π
  3. The area is now 6.25π.
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