Arc Length Calculator
Enter a radius and a central angle to get the arc length along the curve — plus the area of the matching circular sector — for any slice of a circle.
Length and area at once
Enter the radius and central angle and the calculator returns the arc length (the curved edge) and the sector area (the enclosed pie slice) together.
Angle in degrees
The central angle runs from 0° to 360°. The radius is unit-agnostic — the arc length comes back in whatever length unit you enter.
What is an arc length calculator?
The curved distance along a circle
An arc length calculator finds the distance measured along the curved edge of a circle between two points, rather than the straight line between them. The full way around a circle is its circumference, 2πr; an arc is simply the slice of that circumference spanned by a given central angle. This tool turns two measurements — the radius and the central angle in degrees — into the arc length, alongside the area of the matching circular sector (the pie slice enclosed by the arc and two radii). It is the number behind the length of a curved fence, the run of a circular running track, the trim around an arched window, and the cut length of any curved part.
Enter a radius and a central angle in degrees to get the arc length and the matching sector area instantly.
The arc length is the fraction of the circle the angle covers (θ/360) multiplied by the full circumference, and the sector area scales the full circle area by the same fraction.
s = (θ/360) × 2 × π × rThe θ/360 fraction is the share of the full turn the arc spans, so a 90° arc is a quarter of the circumference and a 180° arc is half. Use the same fraction with the circle area πr² and you get the sector area. Take a radius of 10 and an angle of 90°: the arc length is (90/360) × 2 × π × 10 = 15.707963, and the sector area is (90/360) × π × 10² = 78.539816 square units.
The formula is exact, but a few practical points are worth keeping in mind.
Degrees, not radians, and consistent units
This calculator expects the central angle in degrees from 0° to 360°. If your angle is in radians, convert it first by multiplying by 180/π, or use the radian shortcut s = r × θ by hand. The radius is unit-agnostic, but keep it consistent: the arc length returns in the same length unit you enter, and the sector area returns in those units squared. The result describes a circular arc only — it does not apply to ellipses or other curves.