numvana

Circular Sector & Arc Length Calculator

Find the arc length, sector area, and chord length of a circle's slice from its radius and central angle.

Arc length
15.708
Sector area
78.5398
Chord length
14.1421
Percent of full circle
25%

How it works

A sector is the pie-slice-shaped region between two radii and the arc they cut off. Its arc length and area are the full circle's circumference and area scaled down by the fraction of a full turn the central angle covers: arc length = r·θ and sector area = ½·r²·θ, where θ is the angle in radians (this calculator takes degrees and converts internally).

The chord is the straight line connecting the two ends of the arc — the third side of the isosceles triangle formed by the two radii. It comes out to chord length = 2r·sin(θ/2), which is exactly the diameter when the angle is 180° (a semicircle) and shrinks to 0 as the angle approaches a full 360° turn, where the two arc ends meet back at the same point.

FAQ

What's the difference between a sector and a segment?

A sector is bounded by two radii and the arc between them — the whole pie slice. A segment is bounded by just the chord and the arc — the region cut off if you sliced straight across, ignoring the center. This calculator computes the sector's area (and the chord length, which you'd need to also find the segment's area by subtracting the triangle formed by the two radii and the chord).

Why does the calculator cap the angle at 360°?

A central angle beyond 360° would mean going around the circle more than once, which doesn't correspond to a distinct physical sector — 400°, for example, traces the same shape as 40°. Enter an angle between 0° and 360° to describe one slice of the circle.

Related calculators