How to Calculate and Solve for the Radius of a Small Circle | Latitude and Longitude
Last Updated on March 17, 2024
The image above represents the radius of a small circle. To calculate the radius of a small circle, two essential parameters are needed, and these parameters are value of R and Value of the Latitude N or S of the Equator (α).
The formula for calculating radius of a small circle:
r = Rcosα
Where:
r = Radius of the small circle or Radius of Parallel of Latitude
R = Radius of the Earth
α = Value of the Latitude North or South of the Equator
Let’s solve an example;
Find the radius of a small circle when the value of R is 6400 and the value of the latitude north or south of the equator is 22.
This implies that;
R = Radius of the Earth = 6400
α = Value of the Latitude North or South of the Equator = 22
r = Rcosα
So, r = 6400 x cos22°
r = 6400 x 0.927
r = 5933.97
Therefore, the radius of a small circle is 5933.97 km.
Calculating the Value of the Latitude North or South of the Equator when the Radius of a Small Circle and Value of R are Given
α = r / Rcos
Where:
α = Value of the Latitude North or South of the Equator
R = Radius of the Earth
r = Radius of the small circle or Radius of Parallel of Latitude
Let’s solve an example;
Find the value of the latitude north or south of the equator with radius of the small circle as 20 and value of R as 6400.
This implies that;
R = Radius of the Earth = 6400
r = Radius of the small circle or Radius of Parallel of Latitude =20
α = r / Rcos
α = 20 / 6400cos
Then, α = 20 / 0.1736
α = 115.207
Therefore, the value of the latitude north or south of the equator is 115.207°.
How to Calculate the Radius of a Small Circle Using Nickzom Calculator
Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the radius of a small circle.
To get the answer and workings of the radius of a small 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 Latitude and Longitude under Mathematics.
Now, Click on Radius of a Small Circle under Latitude and Longitude
The screenshot below displays the page or activity to enter your values, to get the answer for the radius of a small circle according to the respective parameters which are the value of R and Value of the Latitude N or S of the Equator (α).
Now, enter the values appropriately and accordingly for the parameters as required by the value of R is 6400 and Value of the Latitude N or S of the Equator (α) is 22.
Finally, Click on Calculate
As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the radius of a small circle and presents the formula, workings and steps too.
