What Is a Sector?

How the slice is bounded

Sector geometry links area and arc length to the same central angle. Once the central angle is known, the sector's share of the whole circle can be read as a fraction of 360 degrees.

This page highlights the two radii and the curved boundary together so you can see why a sector depends on the center in a way that other circle regions do not.

A 90-degree sector takes one quarter of the full turn, so it takes one quarter of the circle's area and one quarter of its circumference for the matching arc. The straight sides are radii, while the curved side is an arc; naming each boundary makes the region much easier to recognise.

• A sector is the region bounded by two radii and the included arc.
• The center of the circle is always part of a sector because both bounding sides are radii.
• Sector area and arc length are both controlled by the same central-angle fraction of the full circle.
• A sector is a region, so it has area; an arc is only the curved boundary of that region.

Where sectors help

• Use sectors in area and arc-length problems based on central-angle measure.
• Use them in pie-chart style interpretations and other proportional circle regions.
• Use sector language when the center must be included as part of the geometry.

Sector mix-ups to avoid

• Do not confuse a sector with an arc; the sector is the filled region, not the curved edge alone.
• Do not replace one bounding radius with a chord, because that creates a segment region instead.
• Do not forget to use the central-angle fraction when moving from the whole circle to one sector.