Circular Sector Area Calculator
Calculate the area of a circular sector from its radius and central angle in degrees. Formula: A = (π × r² × θ) / 360.
Formula
A = (π × r² × θ) / 360
Area of a circular sector
Picture a pizza slice: that is a circular sector, the piece of a disk closed off by two radii and the arc running between them. With radius r and central angle θ, the area is A = (θ/360°)·π·r² if you measure θ in degrees, or A = (1/2)·r²·θ if θ is in radians. Put r = 5 m and θ = 60° into the first one and you get (60/360)·π·25 ≈ 13.09 m².
For the arc length, use L = r·θ with θ in radians. A quadrant (θ = 90°) takes up π·r²/4, and once θ reaches 360° you are back to the whole disk, π·r². One thing to keep straight: a sector is two radii plus an arc, while a segment is a chord plus an arc. To get the segment, take the sector and subtract the triangle that the two radii make.
Applications
Sectors are everywhere once you look. Pie charts set each slice's angle in proportion to its value, so 25% of a budget turns into a 90° sector. They also drive gear and sprocket design, the layout of fan and ventilator blades, radar sweeps, analogue speedometers, sundials and irrigation rigs with rotating sprinklers. Architects reach for them when designing spiral staircases and circular amphitheatres.
FAQ
Sector vs segment, what's the difference? A sector sits between two radii and an arc, like a pizza slice. A segment sits between a chord and an arc, which is the shape you are left with after slicing straight across the circle.
How to convert degrees to radians? Multiply the degree figure by π/180. That turns 60° into π/3 rad ≈ 1.047 rad.
Sector perimeter? Add the two radii to the arc and you have it: P = 2r + r·θ (θ in radians).
What does a 360° sector mean? It is just the whole disk, which brings you right back to A = π·r², the usual area-of-a-circle formula.
Calculate the area of a circular sector
The circular sector is that "pizza slice" of the circle, the region between two radii and an arc. Its area is a fraction of the whole circle, proportional to the slice's angle. The tool calculates that from the radius and the central angle in degrees.
It works for geometry exercises, design projects (a pie-chart slice, a fan) and engineering and architecture math. You pass the radius and the angle, and the correct proportion gets applied to the circle's area. The rule of three is left to the tool.
Everything is processed in the browser, sending data nowhere. A practical reference for the area of a circle slice, already with the angle's proportion worked out.
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.