How to Find the Radius of a Sector


The sector of a circle is a partition of that circle. A sector extends from the center, or origin, of the circle to its circumference and encompasses the area of any given angle that also originates from the center of the circle. A sector is best thought of as a piece of pie, and the bigger the angle of the sector, the bigger slice of pie. Each side of the segment is a radius of the circle. You can find the radius of both the sector and the circle by using the sector's angle and area.

  • Double the area of the segment. For example, if the segment area is 24 cm^2, then doubling it results in 48 cm^2.

  • Multiply the sector's angle by π, which is a numerical constant that begins 3.14, then divide that number by 180. For the example, the sector's angle is 60 degrees. Multiplying 60 by π results in 188.496, and dividing that number by 180 results in 1.0472.

  • Divide the area doubled by the number obtained in the previous step. For the example, 48 divided by 1.0472 results in 45.837.

  • Find the square root of that number. For the example, the square root of 45.837 is 6.77. The radius of this segment is 6.77 cm.

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