The image represents road bank angle in circular motion.

To compute for the road bank angle, three essential parameters are needed and these parameters are **velocity (v), acceleration due to gravity (g) and radius (r).**

The formula for calculating the road bank angle;

θ = tan^{-1}(^{v²} / _{gr})

Where;

θ = Road Bank Angle

v = Velocity

g = Acceleration due to Gravity

r = Radius

Let’s solve an example;

Find the road bank angle where the acceleration due to gravity is 9.8, velocity is 35 and radius is 18.

This implies that;

v = Velocity = 35

g = Acceleration due to Gravity = 9.8

r = Radius = 18

θ = tan^{-1}(^{v²} / _{gr})

θ = tan^{-1}(^{35²} / _{(9.8)(18)})

θ = tan^{-1}(^{1225} / _{176.4})

θ = tan^{-1}(6.94)

θ = 81.81°

Therefore, the **road bank angle** is **81.81°.**

**Calculating the Velocity when Road Bank Angle, Acceleration due to Gravity and Radius is Given.**

v = √gr.tan θ

Where;

v = Velocity

θ = Road Bank Angle

g = Acceleration due to Gravity

r = Radius

Let’s solve an example;

Given that the road bank angle is 50, radius is 15 and acceleration due to gravity is 9.8. Find the velocity?

This implies that;

θ = Road Bank Angle = 50

g = Acceleration due to Gravity = 9.8

r = Radius = 15

v = √gr.tan θ

v = √(9.8 x 15)(tan 50)

v = √(147)(1.1917)

v = √175.1799

v = 13.235

Therefore, the **velocity** is **13.235.**

**Calculating the Radius when Road Bank Angle, Acceleration due to Gravity and Velocity is Given.**

r = ^{v2} / _{g.tanθ}

Where;

r = Radius

θ = Road Bank Angle

v = Velocity

g = Acceleration due to Gravity

Let’s solve an example;

Given that the road bank angle is 70, velocity is 30 and acceleration due to gravity is 9.8. Find the radius?

This implies that;

θ = Road Bank Angle = 70

g = Acceleration due to Gravity = 9.8

v = Velocity = 30

r = ^{v2} / _{g.tanθ}

r = ^{302} / _{9.8 x tan70}

r = ^{900} / _{9.8 x 2.74}

r = ^{900} / _{26.852}

r = 35.517

Therefore, the **radius** is **35.517.**

Nickzom Calculator – **The Calculator Encyclopedia** is capable of calculating the road bank angle.

To get the answer and workings of the road bank angle 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 **Mechanics **under **Engineering**

Now, Click on **Motion of Circular Path **under **Mechanics**

Click on **Road Bank Angle **under **Motion of Circular Path**

The screenshot below displays the page or activity to enter your value, to get the answer for the road bank angle according to the respective parameter which are the **velocity (v), acceleration due to gravity (g) and radius (r).**

Now, enter the value appropriately and accordingly for the parameter as required by the **velocity (v)** is **35**,** acceleration due to gravity (g)** is **9.8 **and** radius (r) **is **18.**

Finally, Click on Calculate

As you can see from the screenshot above, **Nickzom Calculator** – The Calculator Encyclopedia solves for the road bank angle and presents the formula, workings and steps too.