The image above represents the length of an arc of a circle.

To compute the length of an arc of a circle, two essential parameters are needed and this parameters are **radius of the circle (r)** and **angle of the circle (α).**

The formula for calculating the length of an arc of a circle:

L = ^{απr} / _{180}

Where;

L = Length of an arc of the circle

α = Angle of the circle

r = radius of the circle

Let’s solve an example:

Find the length of an arc of a circle when the angle of the circle is 90° and the radius of the circle is 20 cm.

This implies that;

α = Angle of the circle = 90°

r = Radius of the circle = 20 cm

L = ^{απr} / _{180}

L = ^{90 x 3.142 x 20} / _{180}

L = ^{5655.6} / _{180}

L = 31.42

Therefore, the **length of an arc of the circle** is **31.42 cm.**

**Calculating the Angle of a Circle using the Radius of the Circle and Length of an Arc of the Circle.**

α = ^{180L} / _{πr}

Where;

L = Length of an arc of the circle

r = Radius of the circle

Let’s solve an example;

Find the angle of the circle when the length of an arc of the circle is 60° and a radius of 140 cm.

This implies that;

L = Length of an arc of the circle = 60°

r = Radius of the circle = 140 cm

α = ^{180L} / _{πr}

α = ^{180 x 60} / _{3.142 x 140}

α = ^{10800} / _{439.88}

a = 24.55

Therefore, the **angle of the circle** is **24.55°.**

**Calculating the Radius of a Circle using the Length of an Arc of the Circle and the Angle of the Circle.**

r = ^{180L} / _{πα}

Where;

L = Length of an arc of the circle

α = Angle of the circle

Let’s solve an example;

Given that the angle of the circle is 100° with length of an arc of the circle 70 cm. Find the radius of the circle?

This implies that;

α = Angle of the circle = 100°

L = Length of an arc of the circle = 70 cm

r = ^{180L} / _{πα}

r = ^{180 x 70} / _{3.142 x 70}

r = ^{12600} / _{219.94}

r = 57.29

Therefore, the** radius of the circle** is **57.29 cm.**

Nickzom Calculator – **The Calculator Encyclopedia** is capable of calculating the length of an arc of a circle.

To get the answer and workings of the length of an arc of a circle using the **Nickzom Calculator – The Calculator Encyclopedia. **First, you need to obtain the app.

You can get this app via any of these means:

**Web** – https://www.nickzom.org/calculator-plus

To get access to the **professional **version via web, you need to **register** and **subscribe **for** NGN 1,500 **per** annum** to have utter access to all functionalities.

You can also try the **demo **version via https://www.nickzom.org/calculator

**Android (Paid)** – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator

**Android (Free)** – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator

**Apple (Paid)** – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8

Once, you have obtained the calculator encyclopedia app, proceed to the **Calculator Map, **then click on **Mensuration**** **under the **Mathematics** section

Now, click on** Length of an Arc of a Circle** under **Mensuration**

The screenshot below displays the page or activity to enter your values, to get the answer for the length of an arc of a circle according to the respective parameters which are the **radius of the circle (r)** and **angle of the circle (α).**

Now, enter the value appropriately and accordingly for the parameters as required by the **example** above where the **radius of the circle** is **20 cm** and **angle of the circle** is **90°.**

Finally, Click on **Calculate**

As you can see from the screenshot above, **Nickzom Calculator** – The Calculator Encyclopedia solves for the length of an arc of a circle and presents the formula, workings and steps too.