Geometry
Sector Area Calculator
Area and arc length of any circle sector. Compute the area of a sector and its arc length from radius and central angle in degrees or radians.
Live Vector System
Core Dimensions
Analytic Metrics
Surface Area
78.54
Perimeter
31.416
Mathematical Verification
Our engine utilizes double-precision floating-point arithmetic for geometric derivations. For triangles, we implement Heron's Theorem with strict validation to ensure the triangle inequality principle is maintained.
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Solution Methodology
01
Enter Radius & Angle
Provide radius r and central angle θ in degrees or radians.
02
Convert Angle Units
Internally normalise to radians for calculation: θ_rad = θ_deg × π/180.
03
Compute Area & Arc
Apply A = ½r²θ and s = rθ, then display chord length and sector perimeter.
Common Questions
How do you find the area of a sector?
In radians: A = ½r²θ. In degrees: A = (θ/360)πr². Both formulas express what fraction of the full circle the sector represents, then multiply by the full circle area πr².
What is the difference between sector area and segment area?
A sector is the pie-slice region bounded by two radii and the arc. A segment is the region between a chord and the arc. Segment area = Sector area − Triangle area of the triangle formed by the two radii and the chord.