Arc Length Calculator
An arc is a slice of a circle’s circumference, cut by a central angle. Enter the radius and the angle in degrees to get the arc length, the area of the matching pie-slice sector, and the straight-line chord between the arc’s endpoints.
Results
Formula
How to use this calculator
- Enter the circle’s radius.
- Enter the central angle in degrees (0–360).
- Press Calculate for the arc, sector and chord.
Worked example
Radius 10, angle 60°.
- Radians: 60 × π/180 ≈ 1.0472.
- Arc: 10 × 1.0472 ≈ 10.472.
- Sector: ½ × 100 × 1.0472 ≈ 52.36; chord: 2 × 10 × sin 30° = 10.
Result: Arc length ≈ 10.472, sector area ≈ 52.360, chord = 10.
Frequently asked questions
Why convert degrees to radians at all?
The elegant arc formulas (arc = rθ) only work in radians, the natural unit of angle in mathematics. Degrees must be converted first — this calculator does it for you.
What is the difference between arc length and chord length?
Arc length follows the curve; chord length is the straight line between the same two endpoints. The chord is always shorter (equal only for a zero angle).
What is a sector?
The pie-slice region bounded by two radii and the arc between them. Its area is the same fraction of the circle’s area as the angle is of 360°.
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