The area formula for a sector

Sector Area Calculator

A sector is a figure enclosed by a center of a circle, two points on the circumference, and an arc that does not coincide with these two points. Usually, the central angle of a sector is greater than 0° and less than 360°. Its area is equal to the product of the proportion of the arc corresponding to the central angle and the area of the circle.

1. Central Angle Calculation Method:
   The formula for calculating the area of a sector using the central angle calculation method is: S = (nπr²)/360, where n is the degree of the central angle corresponding to the arc, and r is the radius of the circle. For example, the area of a sector with a radius of 5 cm and a central angle of 60 degrees is: S = (60π × 5 × 5)/360 = 13.09 square centimeters.

2. Arc Length Calculation Method:
   The third formula for calculating the area of a sector using the arc length calculation method is S = (1/2)lr, where l is the radius of the sector and r is the arc length of the sector (arc length refers to the length of a segment of arc on the circumference). For example, the area of a sector with a radius of 8 cm and an arc length of 10 cm is: S = (1/2) × 8 × 10 = 40 square centimeters.

3. Central Angle Radian Calculation Method:
   The formula for calculating the area of a sector using the central angle radian calculation method is: S = (|α|r²)/2, where α is the radian of the central angle and r is the radius of the circle. For example, the area of a sector with a radius of 6 cm and a central angle of π/3 radians is: S = (|π/3| × 6 × 6)/2 = 18 square centimeters.