The Sector

A sector is a slice of a circle — the region between two radii and the arc. Its area is the circle's area scaled by the angle fraction: (θ ÷ 360) × πr² in degrees, or ½r²θ in radians, which is why radian formulas are so compact.

Three Lengths, One Slice

The sector has two straight radii, a curved arc, and a straight chord connecting the arc endpoints. Perimeter = 2r + arc length; chord = 2r·sin(θ/2). Together they describe the slice completely — useful in fabrication, gearing, and design.

Where Sectors Appear

Pizza and pie slices are sectors; gear teeth, fan blades, and pie charts are built from them. Radians make the math flow: arc = rθ and area = ½r²θ, so engineers prefer radians while everyday angles stay in degrees.