Sector Area & Arc Length Calculator

Area, arc length, chord and perimeter of a circular sector (pie slice) from its radius and central angle or arc length, plus the segment area.

Up to 360° (a full circle).
Sector area
52.36
Arc length
10.472
Central angle
60
Chord length
10
Sector perimeter (2r + arc)
30.472
Segment area (between chord and arc)
9.0586
Fraction of the full circle
16.67 %

Estimate generated with SortedSums: https://sortedsums.com/circular-sector-calculator/. For informational purposes only; verify before relying on it.

How it’s calculated

With the central angle θ in radians, the arc and the sector are simple proportions of the full circle.

θ (rad) = θ (deg) × π / 180 or θ = s / r Arc length s = r θ Sector area A = ½ r² θ Chord c = 2 r sin(θ/2) Segment area = ½ r² (θ − sin θ)

Example: r = 10 ft, θ = 60° = π/3 rad. Arc s = 10 × π/3 ≈ 10.47 ft; area = ½ × 100 × π/3 ≈ 52.36 ft²; chord = 2 × 10 × sin 30° = 10 ft; segment area = 50 × (1.0472 − 0.8660) ≈ 9.06 ft².

Frequently asked questions

What is the formula for the area of a sector?

A = ½r²θ with θ in radians, or A = (θ°/360) × πr² with θ in degrees.

How do I find the arc length?

Multiply the radius by the central angle in radians: s = rθ. In degrees, s = (θ°/360) × 2πr.

What is the difference between a sector and a segment?

A sector is the pie slice bounded by two radii and the arc. A segment is the smaller region between the chord and the arc; it equals the sector minus the triangle formed by the two radii.

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Sources

Formulas are taken from the free public references above. Results are provided “as is” for informational and educational purposes only. See our disclaimer.

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