Arc Length Calculator
Enter a radius and central angle (in degrees) below to instantly get arc length and sector area.
Arc Length & Sector Formulas
Arc length = r × θ (θ in radians). Sector area = (1/2) × r² × θ.
Worked example
A circle with radius 10 and a central angle of 60°.
60° in radians = 60 × π / 180 = π/3 ≈ 1.047
Arc length = 10 × 1.047 ≈ 10.47
Sector area = (1/2) × 10² × 1.047 ≈ 52.36
Frequently Asked Questions
What is the formula for arc length?
Arc length = r × θ, where r is the radius and θ is the central angle in radians. In degrees, that's r × (θ° × π / 180).
What is a sector, and how is its area different from arc length?
A sector is the pie-slice-shaped region bounded by an arc and the two radii on either side of it. Arc length is just the curved edge's length; sector area is the area of the whole pie-slice: (1/2) × r² × θ (θ in radians).
Why does the angle need to be in radians for the formula?
The formula r × θ only gives a length directly when θ is measured in radians, since a radian is defined so that an angle of 1 radian traces an arc exactly one radius long. Degrees need to be converted to radians first (multiply by π / 180).
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