Sector Area Calculator
Calculate the area, arc length, chord length, and perimeter of a circle sector. Enter the radius and central angle in degrees to get instant results for all sector properties.
A sector is a pie-shaped region of a circle bounded by two radii and an arc. Think of it as a slice of pizza or a wedge of a pie chart. The central angle determines what fraction of the full circle the sector represents.
Sector Formulas (radius = r, central angle = theta in degrees):
- Sector Area: A = (theta/360) x pi x r^2
- Arc Length: L = (theta/360) x 2 x pi x r
- Chord Length: c = 2r x sin(theta/2)
- Sector Perimeter: P = arc length + 2r
A sector with theta = 180 degrees is a semicircle, theta = 90 degrees is a quarter circle (quadrant), and theta = 360 degrees is the full circle. The chord connects the two endpoints of the arc in a straight line and is always shorter than or equal to the arc length.
Sector calculations are used in pie charts, windshield wiper coverage, radar sweep areas, irrigation systems, and architectural design elements like arched windows and fan-shaped rooms.