Area of a Sector Calculator
Measuring a Slice of a Circle
Finding the area of a sector means measuring one slice of a circle. Provide the radius and the central angle, and the calculator returns exactly how much surface that wedge covers. Students meet it in geometry and precalculus, while landscapers, designers, and machinists use it whenever a circular segment must be cut, paved, or priced.
A sector can be a sliver or nearly the whole disk. The formula scales smoothly between those extremes.
The Formula and a Worked Example
A full circle covers pi x r^2. A sector covers the same fraction of that area as its angle is of 360 degrees, which gives area = (angle / 360) x pi x r^2.
Worked example: radius 6 and angle 90 degrees. The sector area is (90 / 360) x pi x 6^2 = 0.25 x pi x 36 = 9 x pi, about 28.27 square units, rounded to two decimals. Since 90 degrees is one quarter of a turn, the wedge takes exactly one quarter of the circle’s area.
How to Use It
Type the distance from the center into the Radius box, then the central angle in degrees into the Angle box, and press Calculate area. For the wedge with radius 6 and angle 90 described above, the result is 28.27 square units. Nothing else is required.
Watch the angle range and the units. Angles from 0 to 360 are valid: 360 returns the full circle, pi x r^2, and 0 returns nothing. Values past 360, like 450, overcount because they wrap beyond one full turn. The answer inherits square units from the radius, so a radius in centimeters yields square centimeters.
Frequently Asked Questions
What is the sector area formula?
Sector area = (angle / 360) x pi x r^2, where r is the radius and the angle is in degrees. At angle 360 the bracket becomes 1, recovering the full circle area pi x r^2.
What is the area for angle 90 and radius 6?
(90 / 360) x pi x 6^2 = 0.25 x pi x 36 = 9 x pi, or about 28.27 square units. That is exactly one quarter of the full circle area, since 90 degrees is one quarter of 360.
Can the angle exceed 360 degrees?
It should not, because a sector is a slice of one circle and 360 degrees already completes it. An input of 450 would overcount, wrapping 90 degrees past the full circle and inflating the area.
What units does the answer use?
The answer comes out in square units of whatever the radius uses. A radius of 6 meters yields about 28.27 square meters for a 90 degree sector, while 6 inches would yield square inches instead.
How do I find a semicircle area?
Enter the radius with an angle of 180 degrees, which is half of a full turn. The formula then gives (180 / 360) x pi x r^2, exactly half of the circle’s area.