Arc Length formula with Solved Examples

Arc Length 

Everything you need to know about the Arc length formula is provided below. Please proceed to read the whole document carefully to understand the topic completely.

The most accurate definition of arc length is the distance along the portion of the circumference that is contained inside any circle or curve (arc). The arc length may be thought of as any distance that runs along the curved line that constitutes the arc. The term “arc” refers to a segment of a curve or a portion of the circumference of a circle. Every single one of them has a gentle curvature to its outline. The length of an arc is more than the shortest distance that can be travelled in a straight line.

What is Arc Length?

The distance that separates two locations along a segment of a curve is known as the arc length, and it is measured in degrees. Any segment of the circumference may be considered an arc of a circle. The angle created between the two line segments that bind any given location to the endpoints of an arc is the angle that is referred to as the angle subtended by the arc at that point. As an example, the arc of the circle with the centre at Q is denoted by the letter OP in the diagram shown below. L is the value that denotes the length of this arc’s OP.

Arc Length Formula

Depending on the unit of the arc’s central angle, there are a few different formulae that may be used to compute the length of an arc. The values that are assigned to the degrees or radians used to describe the central angle are taken into account when determining the arc length of a circle. The formula for determining the length of an arc in a circle is multiplied by the circle’s radius.

Arc length = Θ x r

Arc length = Θ x (π/180) x r

 Here,

L= length of arc

Θ= central angle,

r = radius of circle.

Solved Examples

Q. Determine the length of an arc that is severed from a circle with a radius of 6 inches and also with a central angle that is 4 radians.

A.  Center angle, θ = 4 radians, 

radius, r = 6 inches . 

Using the formula, 

L = θ × r = 4 × 6 = 24 inches.

Therefore, Arc length (PQ) = 24 inches