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Circle Sector Area Calculator

Calculate the area of a circle sector (pie-slice) from its radius and central angle in degrees.

Arc Length (L = rθ)
10.472
θ in radians = 1.0472
Sector Area (A = ½r²θ)
52.360
Semicircle Reference (θ = 180°, radius 10)
Area = ½πr²
157.080
Perimeter = πr + 2r
51.416
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Calculation Guide & Reference

Circle Sector Area Mathematics

Sector area calculator computes the area of a circle sector (pie-slice) from its radius and central angle in degrees.

Standardized Mathematical Formula
A = (1/2) × r² × θ (θ in radians)

A sector is the pie-slice-shaped region bounded by two radii and the arc between them. Its area is the same fraction of the whole circle's area (πr²) that the central angle is of a full rotation (2π radians).

Variables:
r:Radius of the circle
θ:Central angle, converted from degrees to radians
How It Works (Step-by-Step)
  • 1Enter the circle's radius (r).
  • 2Enter the central angle (θ) in degrees.
  • 3View the sector area, computed as half the radius squared times the angle in radians.
Real-World Numerical Example
Radius 10, Central Angle 60°

A pizza slice has a radius of 10 inches and a central angle of 60°.

•Convert angle to radians: 60 × π/180 ≈ 1.047 rad.
•Sector area: A = 0.5 × 10² × 1.047 ≈ 52.36 square inches.
Result: The sector (slice) covers approximately 52.36 square inches.
Calculation Best Practices & Tips
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In statistical analysis, always check both the mean and median to identify if data distribution is skewed by outliers.
When calculating percentage changes, ensure you divide by the original starting baseline value: ((New - Old) / Old) * 100.

Frequently Asked Questions (FAQ)

A sector is bounded by two radii and an arc (like a pie slice, including the center point); a segment is bounded by a chord and an arc (the region cut off by a straight line), which is a different, smaller shape for the same angle.

Since arc length L = rθ, you can solve for θ = L/r, then plug that into the sector area formula: A = (1/2) × r × L.

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