What Is The Arc Length Formula? How To Find The Length Of An Arc Using The Correct Equation

 

There is a very simple relation to calculate the length of an arc, but to understand the relation we have to first know where it comes from.

Arc is a portion of circumference or the curved path with a constant radius stretching from point A to point B. Arc length is the measure of the length of this arc. Arc have a central point around which it is curved, it is the center of the circle that would be formed if the arc is given a full 360o rotation. The other characteristic it has is the angle between the started and ending points if a line was stretched between the end points of arc and the center point, then the angle between these two lines will be the central angle.

All of these terminologies may be getting overwhelming but just take a breath, and look at the figure illustrated below, this will clear all the doubts and concepts about arcs.

Now that we know what an arc is we can move down to calculating the arc length. There is a simple relation the related the arc length, radius of the arc and the central angle. The relation is

s = r × ?

Here ‘s’ is the arc length

‘r’ is the radius of the arc

‘?’ is the central angle given in radians

Now we see that the arc length is simply the product of the central angle and radius of curvature.

To fully understand this formula, lets work out an example and see this relation is action

Lets say we are tasked to find the length of an arc which draws a central angle of 45o and has a radius of 50 cm.

First step is to write down all the data we are given

r = 50 cm

? = 45°

Remember! We are supposed to convert degree into radian before proceeding further

To convert into radian we multiply it with ?/180

? =45×?/180

? = ?/4 rad

Now to calculate the arc length we take the product of both these quantities

s=r×?

s=50×?/4

s=25?/2

Or

s=39.27 cm

Read more about Mathematics

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