Sector Area (Degrees) Calculator
Find the area and arc length of a circular sector from its radius and central angle in degrees — the “pizza slice” of a circle.
How it works
Area = (θ/360) · π · r² · Arc = (θ/360) · 2πr · θ in degrees
A sector is the region between two radii and the arc they cut off — a slice of the circular pie. Its area is the same fraction of the whole circle’s area as the central angle is of a full 360° turn, and its arc length is that same fraction of the full circumference. A 360° “sector” is simply the entire circle.
Worked example
For a radius of 5 and a 60° angle, the fraction is 60/360 = 1/6, so the area is (1/6)·π·5² = 25π/6 ≈ 13.0900 square units and the arc is (1/6)·2π·5 = 5π/3 ≈ 5.2360 units.
Sources: Circular sector — Wikipedia
Frequently asked questions
How is a sector different from a segment?
A sector is bounded by two radii and an arc (a pie slice), while a segment is bounded by a chord and an arc. The segment is the sector minus the triangle formed by the two radii and the chord.
What if the angle is 360 degrees?
Then the sector is the whole circle: the area becomes π·r² and the arc length becomes the full circumference 2πr.
How do I convert the angle to radians?
Multiply degrees by π/180. In radians the sector area is simply ½·r²·θ, which is equivalent to the degree formula used here.
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This calculator is for educational purposes. Double-check important results before acting on them.