How to Calculate and Solve for Distance Along Small circles | Latitude and Longitude

The image above represents distance along small circles. To calculate the distance along small circles, two essential parameters are needed, and these parameters are the value of r and angular difference (θ).

The formula for calculating the distance along small circles:

x = (^θ / ₃₆₀) x 2πr

Where;

x = Distance Along small circles
θ = Angular Difference
r = Radius of the small circle

Let’s solve an example;
Find the distance along small circles when the angular difference is 24 and the value of r is 6.

This implies that;

θ = Angular Difference = 24
r = Radius of the small circle = 6

x = (^θ / ₃₆₀) x 2πr
Then, x = (²⁴ / ₃₆₀) x 2π(6)
x = 0.066 x 37.69
x = 2.51

Therefore, the distance along small circle is 2.51 km.

Calculating the Angular Difference when the Distance Along Small Circle and the Value of r are Given

θ = ^x360 / _2πr

Where;

θ = Angular Difference
x = Distance Along small circles
r = Radius of the small circle

Let’s solve an example;
Find the angular difference when the distance along small circle is 15 and the value of r is 5.

This implies that;

x = Distance Along small circles = 15
r = Radius of the small circle = 5

θ = ^x360 / _2πr
θ = ^(15)360 / _2π(5)
So, θ = ⁵⁴⁰⁰ / _31.41
θ = 171.91

Therefore, the angular difference is 171.91°.

Read more: How to Calculate and Solve Distance Along Great Circles | Latitude and Longitude

Calculating the Value of r when the Distance Along Small Circle and the Angular Difference are Given

r = ^x360 / _{θ x 2π}

Where;

r = Radius of the small circle
x = Distance Along small circles
θ = Angular Difference

Let’s solve an example;
Given the distance along circles is 20 with an angular difference of 4. Find the value of r?

This implies that;

x = Distance Along small circles = 20
θ = Angular Difference = 4

r = ^x360 / _{θ x 2π}
r = ^(20)360 / _{4 x 2π}
So, r = ⁷²⁰⁰ / _{4 x 6.28}
r = ⁷²⁰⁰ / _25.13
r = 286.5

Therefore, the value of r is 286.5.

How to Calculate Distance Along Small circles Using Nickzom Calculator

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the distance along small circles.

To get the answer and workings of the distance along small circles 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 Latitude and Longitude under Mathematics.

Now, Click on Distance Along Small Circles under Latitude and Longitude

The screenshot below displays the page or activity to enter your values, to get the answer for the distance along small circles according to the respective parameters which are the angular difference (θ) and value of r.

Now, enter the values appropriately and accordingly for the parameters as required by the angular difference (θ) is 24 and value of r is 6.

Finally, Click on Calculate

As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the distance along small circles and presents the formula, workings and steps too.