Thread: Compute the distance between two points on the surface of earth

I wanted to know if my code for finding the distance between two points on the surface of Earth is correct. I had to research online and found the formula for the great circle distance formula for the shortest path between two points on a sphere (I didn't really go in depth, but I do understand the concept of great circle distance and I am familiar with some of the math concepts from Multivariable Calculus and Linear Algebra, though that doesn't matter that much here), which was

d = acos^-1[cos(x1)cos(x2)cos(y1 - y2) + sin(x1)sin(x2)]
where a is the radius of the Earth (here, in kilometers), (x1, y1) are the coordinates for distance 1 and (x2, y2) are the coordinates for distance 2.

I want to know if my code looks fine, because I looked at the solution for this problem and it was kind of different from mines. Also, how would go about this problem, out of curiosity?:

import java.lang.Math;
import java.util.Scanner;
 
class RicMain
{
	public static void main(String args[])
	{
		Scanner ip = new Scanner(System.in);
		double x1, x2, y1, y2, a, d;
 
		          //a is the radius of the sphere.
		a = 6371.01; //radius of Earth is 6371.01 km.
 
		System.out.print("Input the latitude of coordinate 1: ");
		x1 = ip.nextDouble();
		System.out.print("Input the longitude of coordinate 1: ");
		y1 = ip.nextDouble();
		System.out.print("Input the latitude of coordinate 2: ");
		x2 = ip.nextDouble();
		System.out.print("Input the longitude of coordinate 2: ");
		y2 = ip.nextDouble();
		//x1 and x2 are the latitude (x-axis).
		//y1 and y2 are the longitude (y-axis).
 
		//d is the great circle distance (distance between the two points (x1, y1) and (x2, y2).
		d = a * Math.atan((Math.cos(x1)*Math.cos(x2)*Math.cos(y1 - y2)) + (Math.sin(x1)*Math.sin(x2)));
		System.out.println("\nThe distance between points (x1, y1) and (x2, y2) is " + d);
	}
}

Also, I inputted the following:
Input the latitude of coordinate 1: 25
Input the longitude of coordinate 1: 35
Input the latitude of coordinate 2: 35.5
Input the longitude of coordinate 2: 25.5

The output is suppose to be: 1480.0848451069087 km

But my output was: 4157.795646651634

Not sure what's wrong. I think I have to convert it or something?

Originally Posted by Norm

One problem probably is the args for the trig methods:

You need to convert the degrees to radians.

Yes, that was what I was thinking. I was unsure at first if my output was in degrees or radians by default. So how would I do the conversions?

Originally Posted by Norm

Multiply the degrees by radians/degree
Check the Math class for a method

There was a mistake in the formula. It was suppose to be arccos, not arctan. I did that by accident. I made two new classes, the first one has the fixed formula with the degrees to radian conversion, and the other is using a nested class. They yield different outputs, but the nested class one is closer to the desired output when I input the following:

Input Data:
Input the latitude of coordinate 1: 25
Input the longitude of coordinate 1: 35
Input the latitude of coordinate 2: 35.5
Input the longitude of coordinate 2: 25.5


Expected Output

The distance between those points is: 1480.0848451069087 km

import java.lang.Math;  
 
import java.util.Scanner;  
 
 
 
class RicMain  
 
{  
 
    public static void main(String args[])  
 
    {  
 
        Scanner ip = new Scanner(System.in);  
 
        double x1, x2, y1, y2, a, d;  
 
 
 
        a = 6371.01;  //a is the radius of the sphere. 
 
                     //radius of Earth is 6371.01 km.  
 
 
 
        System.out.print("Input the latitude of coordinate 1: ");  
 
        x1 = ip.nextDouble();  
 
        System.out.print("Input the longitude of coordinate 1: ");  
 
        y1 = ip.nextDouble();  
 
        System.out.print("Input the latitude of coordinate 2: ");  
 
        x2 = ip.nextDouble();  
 
        System.out.print("Input the longitude of coordinate 2: ");  
 
        y2 = ip.nextDouble();  
 
        //x1 and x2 are the latitude (x-axis) in degrees.  
 
        //y1 and y2 are the longitude (y-axis) in degrees. 
 
 
 
        //d is the great circle distance (distance between the two points (x1, y1) and (x2, y2).  
 
        d = a * Math.acos((Math.cos(x1)*Math.cos(x2)*Math.cos(y1 - y2)) + (Math.sin(x1)*Math.sin(x2)));  
 
        System.out.println("\nThe distance between points (x1, y1) and (x2, y2) is " + Math.toRadians(d) + " km");  
 
    }  
 
}

import java.lang.Math;  
 
import java.util.Scanner;  
 
 
 
class RicMain  
 
{  
 
    public static void main(String args[])  
 
    {  
 
 
 
        Scanner ip = new Scanner(System.in); 
 
        double x1, y1, x2, y2; 
 
 
 
        System.out.print("Input the latitude of coordinate 1: "); 
 
        x1 = ip.nextDouble();  
 
        System.out.print("Input the longitude of coordinate 1: ");  
 
        y1 = ip.nextDouble();  
 
        System.out.print("Input the latitude of coordinate 2: ");  
 
        x2 = ip.nextDouble();  
 
        System.out.print("Input the longitude of coordinate 2: ");  
 
        y2 = ip.nextDouble();  
 
        //x1 and x2 are the latitude (x-axis) and measured in degrees.  
 
        //y1 and y2 are the longitude (y-axis) and measured in degrees.  
 
 
 
        System.out.println("\nThe distance between points (x1, y1) and (x2, y2) is " + d(x1, y1, x2, y2, y2) + "km");  
 
    }  
 
 
 
    //this inner class converts points to radians. 
 
    //Math.toRadians() converts degrees into radians. 
 
    public static double d(double x1, double x2, double y1, double y2, double a) 
 
    { 
 
        x1 = Math.toRadians(x1); 
 
        y1 = Math.toRadians(y1); 
 
        x2 = Math.toRadians(x2); 
 
        y2 = Math.toRadians(y2); 
 
 
 
        a = 6371.01; //radius of Earth is 6371.01 km. 
 
                     //a is the radius of the sphere. 
 
 
 
        return a * Math.acos((Math.cos(x1)*Math.cos(x2)*Math.cos(y1 - y2)) + (Math.sin(x1)*Math.sin(x2)));  
 
        //the great circle distance (distance between the two points (x1, y1) and (x2, y2). 
 
        //is given in degrees 
 
    } 
 
}