Arc Length Calculator

Find the arc length of a sector by entering the central angle and radius in the calculator below.

How to Calculate Arc Length

A sector is a portion of a circle shaped like a pie slice, composed of two radius edges and an outer arc of the circle. A semicircle and quadrant are examples of sectors.

diagram of a sector showing the radius, central angle, chord length, and arc length

The length of the arc in a sector can be found using an easy formula.

Arc Length Formula

The following formula defines the arc length of a sector.

arc length (s) = radius (r) × central angle (θ)

Thus, the arc length is equal to the radius r of the sector times the central angle θ in radians.

For example, find the arc length of a sector with a radius of 7 and a central angle of 2 radians.

arc length (s) = 7 × 2
arc length (s) = 14

Thus, the arc length s is equal to 14.

Calculate Arc Length using Sector Area and Central Angle

An alternative arc length formula defines how to find the length of the arc if the sector area and central angle are known.

arc length (s) = θ × 2A ÷ θ

The arc length s is equal to the central angle θ in radians, times the square root of 2 times the area A divided by θ.

How to Find Chord Length

A sector is divided into a triangle and outer segment by the chord. The chord, represented as line a in the sector image above, is the line that connects the points where the radii connect with the arc.

The chord can be found using the following formula:

chord (a) = 2r × sin(12θ)

Thus, the length of the chord a is equal to 2 times the radius r times the sine of 1/2 times the central angle θ.

How to Find Sector Area

The area of a sector can be found using the formula:

sector area = r² × θ2

The area of a sector is equal to the radius r squared times the central angle θ, divided by 2.

Try our area calculator to calculate the area of a sector and several other shapes.