How to Calculate and Solve for Shortest Distance Between Two Points | Latitude and Longitude

The image above represents the shortest distance between two points. To calculate the shortest distance between two points, two essential parameters are needed, and these parameters are the Value of R and Angle Subtended at the Centre by the Chord (A(2β)).

The formula for calculating the shortest distance between two points:

y = (^A(2β) / ₃₆₀) x 2πR

Where;

y = Shortest Distance Between Two Points
A(2β) = Angle Subtended at the Centre by the Chord
R = Radius of the Earth

Let’s solve an example;
Find the shortest distance between two points with the angle subtended at the centre by the chord as 40 and radius of the earth as 6400.

This implies that;

A(2β) = Angle Subtended at the Centre by the Chord = 40°
R = Radius of the Earth = 6400

y = (^A(2β) / ₃₆₀) x 2πR
y = (⁴⁰ / ₃₆₀) x 2π x 6400
So, y = 0.111 x 2π x 6400
y = 0.111 x 40212.38
y = 4468.04

Therefore, the shortest distance between two points is 4468.04 km.

Calculating the Angle Subtended at the Centre by the Chord when the Shortest Distance Between Two Points and the Value of R are Given

A(2β) = ^{y x 360} / _2πR

 Where;

A(2β) = Angle Subtended at the Centre by the Chord
y = Shortest Distance Between Two Points
R = Radius of the Earth

Let’s solve an example;
Find the angle subtended at the centre by the chord when the shortest distance between two points is 36, and the value of R is 6400.

This implies that;

y = Shortest Distance Between Two Points = 36
R = Radius of the Earth = 6400

A(2β) = ^{y x 360} / _2πR
A(2β) = ^{36 x 360} / _{2π x 6400}
So, A(2β) = ¹²⁹⁶⁰ / _40212.38
A(2β) = 0.322

Therefore, the angle subtended at the centre by the chord is 0.322°.

Read more: How to Calculate and Solve for Same Meridian; Same Sides of the Equator | Latitude and Longitude

How to Calculate the Shortest Distance Between Two Points Using Nickzom Calculator

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the shortest distance between two points.

To get the answer and workings of the shortest distance between two points 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 Shortest Distance Between Two Points under Latitude and Longitude

The screenshot below displays the page or activity to enter your values, to get the answer for the shortest distance between two points according to the respective parameters which are the Value of R and Angle Subtended at the Centre by the Chord (A(2β)).

Now, enter the values appropriately and accordingly for the parameters as required by the Value of R is 6400 and Angle Subtended at the Centre by the Chord (A(2β)) is 40.

Finally, Click on Calculate

As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the shortest distance between two points and presents the formula, workings and steps too.