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Sector Area Calculator

A sector is a slice of a circle, bounded by two radii and the arc between them — a piece of pie. Enter the radius and the central angle to get its area, arc length and perimeter, plus the area of the segment cut off by the chord.

Quick examples
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Sector area18.85 in²
Arc length
6.28 in
Sector perimeter
18.28 in
Segment area
3.26 in²
Share of the full circle
16.67%

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      Formula

      Sector area = (angle ÷ 360) × π × radius²
      In radians: sector area = ½ × radius² × angle
      Arc length = radius × angle (in radians)
      Sector perimeter = arc length + 2 × radius
      Segment area = ½ × radius² × (angle − sin(angle)), angle in radians

      How to use it

      1. Enter the radius and its unit.
      2. Enter the central angle in degrees or radians.
      3. Read the sector area and, if you need them, the arc, perimeter and segment.

      Worked examples

      A 60° sector with a 6-inch radius: 18.85 in², which is 0.01216 m²

      Sector area
      18.85 in²
      Arc length
      6.28 in
      Sector perimeter
      18.28 in
      Segment area
      3.26 in²
      Share of the full circle
      16.67%

      A 120° sector with a 3 m radius

      Sector area
      9.42 m²
      Arc length
      6.28 m
      Sector perimeter
      12.28 m
      Segment area
      5.53 m²
      Share of the full circle
      33.33%

      Sector or segment

      A sector reaches the center of the circle, like a pizza slice. A segment is the part between a chord and the arc, like the piece cut off by a straight knife stroke. The segment equals the sector minus the triangle formed by the two radii and the chord.

      Questions people ask

      What is the area of a 60° sector with a radius of 6?

      One sixth of the circle: (60 ÷ 360) × π × 36 = 18.85 square units.

      What is the area of one slice of a 14-inch pizza cut into 8?

      Each slice is a 45° sector with a 7-inch radius: (45 ÷ 360) × π × 49 = 19.24 square inches.

      What share of a circle is a 120° sector?

      One third, or 33.33%, because 120 ÷ 360 = ⅓.

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