What you need to learn about Arc length and circumference!

The circle is one of the most basic and interesting shapes when it comes to maths subject. A circle has a diameter of 360 degrees and similarly the half circle is of 180 degree length. Its studies and evaluation are one of the integral parts of any grade. From the starters, you are taught the very basic formulas like calculation of circumference and diameter. Without having its concept, the circumference is indeed very hard to understand but if you have basic and proper concepts, then these algebraic calculations are very easy. Students love to solve these problems when compared to calculus and integration. Facts and guidelines come very straight into these problems. Both terms are used in pre-algebra basics. Before looking into their formulas let’s take a look at these terms in a simple way:

What is circumference?

The circumference is a very famous term of geometry and has been derived from the Greek word circumference meaning ‘carrying around’ of the circle in a linear fashion. More simply and interestingly it is the distance of the circle. If we straighten up the circle it would be its length. In this scenario, we have just given it a new shape and that is a closed circular one. This is the special case of perimeter as circumference deals only with the edges.

How to calculate circumference?

Diameter is described as the line which divides the circle into two equal parts and starts from its surface. Now if we half this diameter this is known as the radius of the circle. It is not so difficult to calculate circumference manually, in case you are having problems doing it manually then use a circumference calculator to get the job done. Online calculators like these makes it very easy for the students to learn the concepts quickly and to live practice them with interest.


To find the circumference of a circle, following is the formula which is used:

C= 2πr or πd


Find the circumference of the following circle


C= π.18

C=56.6 in

What is an arc length?

Basically arc length is the derivation of the circle circumference. It is the same as the length of the string but in an arc, it’s just curved to form a circle. Between the endpoints the arc length is usually longer then the distance of a straight line. A portion of the circumference is just the length of the arc. As a full circle makes up to 360 degrees and arc length defines the portion of this whole figure.


We use the letter ‘s’ to represent the arc length.


Let’s see its formula and how it’s derived:

How to calculate arc length?

The length of the arc AB is equal to the circle’s circumference 2πr times equal to the fraction of the circle. The degree measure of the arc length is written as mAB

Length AB={mAB/360} (2π r)

Now see the calculations of the AB

Isn’t it pretty simple? If you find it difficult you can also use the online available arc length calculator.

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