Circular Sector Area Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/6/2026
The area of a circular sector is calculated with (angle ÷ 360) × π × radius². A quarter circle (90°) with a 5 cm radius has an area of about 19.63 cm².
Explanation
A circular sector is the portion of a disk bounded by two radii and the arc connecting them — visually, a "pie slice." Its area is calculated as a fraction of the full disk's area (π × radius²), the fraction simply being the ratio between the sector's angle and the full angle of the circle (360°). This formula offers a useful consistency check: applied to a 360° angle, it exactly returns the area of the full circle, since the sector then covers the whole disk. A circular sector shouldn't be confused with a circular segment, which is bounded by a chord and an arc rather than two radii — a different area, generally smaller, since it excludes the triangle formed by the two radii. This concept is used in applied geometry to calculate the surface of a rounded piece, the area swept by a windshield wiper, or the portion of land covered by an automatic sprinkler rotating over a given angle.
Example: a 90° sector, 5 cm radius
Inputs
Radius: 5 cm. Sector angle: 90°.
Calculation
Area = (90 ÷ 360) × π × 5² = 0.25 × π × 25 = 0.25 × 78.54 ≈ 19.63 cm².
Result
This 90° circular sector with a 5 cm radius has an area of about 19.63 cm².
Frequently asked questions
What is the difference between a sector and a circular segment?
A circular sector is bounded by two radii and an arc (a pie slice), while a circular segment is bounded by a chord (a straight line connecting two points on the circle) and the corresponding arc — the area left over after subtracting the triangle formed by the two radii from the sector's area. A segment therefore always has an area less than or equal to that of the sector with the same angle.
How do I calculate the arc length instead of the sector area?
Arc length follows similar logic but is proportional to the circumference rather than the area. This calculator focuses on area; for a circle's overall dimensions, see our circumscribed circle radius calculator, which uses a related geometric relationship for a triangle's circumscribed circle.
Does the formula work with an angle in radians?
This calculator expects an angle in degrees. With an angle in radians, the formula becomes simpler: area = (angle in radians ÷ 2) × radius², since a full circle corresponds to 2π radians rather than 360°.