The image above represents the road bank angle in circular motion. To calculate 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;

Î¸ = tan^{-1}(^{vÂ²} / _{gr})

Where;

Î¸ = 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

Î¸ = tan^{-1}(^{vÂ²} / _{gr})

Î¸ = tan^{-1}(^{35Â²} / _{(9.8)(18)})

That is, Î¸ = tan^{-1}(^{1225} / _{176.4})

Î¸ = tan^{-1}(6.94)

Î¸ = 81.81Â°

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

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

v = âˆšgr.tan Î¸

Where;

v = Velocity

Î¸ = 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;

Î¸ = Road Bank Angle = 50

g = Acceleration due to Gravity = 9.8

r = Radius = 15

v = âˆšgr.tan Î¸

v = âˆš(9.8 x 15)(tan 50)

Then, v = âˆš(147)(1.1917)

v = âˆš175.1799

v = 13.235

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

### Master Every Calculation Instantly

Unlock solutions for every math, physics, engineering, and chemistry problem with step-by-step clarity. No internet required. Just knowledge at your fingertips, anytime, anywhere.

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

r = ^{v2} / _{g.tanÎ¸}

Where;

r = Radius

Î¸ = 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;

Î¸ = Road Bank Angle = 70

g = Acceleration due to Gravity = 9.8

v = Velocity = 30

r = ^{v2} / _{g.tanÎ¸}

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

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

r = ^{900} / _{26.852}

r = 35.517

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

**How to Calculate Road Bank Angle of a Body in Motion of Circular Path Using The Calculator Encyclopedia**

Nickzom Calculator â€“Â **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 â€“ The Calculator Encyclopedia.Â **First, you need to obtain the app.

You can get this app via any of these means:

**Web**Â â€“Â https://www.nickzom.org/calculator-plus

To get access to theÂ **professionalÂ **version via web, you need toÂ **register**Â andÂ **subscribeÂ **for**Â NGN 1,500Â **per**Â annum**Â to have utter access to all functionalities.

You can also try theÂ **demoÂ **version viaÂ https://www.nickzom.org/calculator

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

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

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

Once, you have obtained the calculator encyclopedia app, proceed to theÂ **Calculator Map,Â **then click onÂ **MechanicsÂ **underÂ **Engineering**

Now, Click onÂ **Motion of Circular PathÂ **underÂ **Mechanics**

Click onÂ **Road Bank Angle **underÂ **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)Â **isÂ **18.**

Finally, Click on Calculate

As you canÂ see from the screenshot above,Â **Nickzom Calculator** â€“ The Calculator Encyclopedia solves for the road bank angle and presents the formula, workings and steps too.