Given latitude and longitude in degrees find the distance between two points on the earth.
Image Source : Wikipedia
Examples:
Input : Latitude 1: 53.32055555555556
Latitude 2: 53.31861111111111
Longitude 1: -1.7297222222222221
Longitude 2: -1.6997222222222223
Output: Distance is: 2.0043678382716137 Kilometers
Problem can be solved using Haversine formula:
The great circle distance or the orthodromic distance is the shortest distance between two points on a sphere (or the surface of Earth). In order to use this method, we need to have the co-ordinates of point A and point B.The great circle method is chosen over other methods.
First, convert the latitude and longitude values from decimal degrees to radians. For this divide the values of longitude and latitude of both the points by 180/pi. The value of pi is 22/7. The value of 180/pi is approximately 57.29577951. If we want to calculate the distance between two places in miles, use the value 3, 963, which is the radius of Earth. If we want to calculate the distance between two places in kilometers, use the value 6, 378.8, which is the radius of Earth.
Find the value of the latitude in radians:
Value of Latitude in Radians, lat = Latitude / (180/pi) OR
Value of Latitude in Radians, lat = Latitude / 57.29577951
Find the value of longitude in radians:
Value of Longitude in Radians, long = Longitude / (180/pi) OR
Value of Longitude in Radians, long = Longitude / 57.29577951
Get the co-ordinates of point A in terms of latitude and longitude. Use the above conversion method to convert the values of latitude and longitude in radians. I will call it as lat1 and long1. Do the same for the co-ordinates of Point B and get lat2 and long2.
Now, to get the distance between point A and point B use the following formula:
Distance, d = 3963.0 * arccos[(sin(lat1) * sin(lat2)) + cos(lat1) * cos(lat2) * cos(long2 – long1)]
The obtained distance, d, is in miles. If you want your value to be in units of kilometers, multiple d by 1.609344.
d in kilometers = 1.609344 * d in miles
Thus you can have the shortest distance between two places on Earth using the great circle distance approach.
C++
// C++ program to calculate Distance // Between Two Points on Earth#include <bits/stdc++.h>using namespace std;// Utility function for // converting degrees to radianslong double toRadians(const long double & degree){ // cmath library in C++ // defines the constant // M_PI as the value of // pi accurate to 1e-30 long double one_deg = (M_PI) / 180; return (one_deg * degree);}long double distance(long double lat1, long double long1, long double lat2, long double long2){ // Convert the latitudes // and longitudes // from degree to radians. lat1 = toRadians(lat1); long1 = toRadians(long1); lat2 = toRadians(lat2); long2 = toRadians(long2); // Haversine Formula long double dlong = long2 - long1; long double dlat = lat2 - lat1; long double ans = pow(sin(dlat / 2), 2) + cos(lat1) * cos(lat2) * pow(sin(dlong / 2), 2); ans = 2 * asin(sqrt(ans)); // Radius of Earth in // Kilometers, R = 6371 // Use R = 3956 for miles long double R = 6371; // Calculate the result ans = ans * R; return ans;}// Driver Codeint main(){ long double lat1 = 53.32055555555556; long double long1 = -1.7297222222222221; long double lat2 = 53.31861111111111; long double long2 = -1.6997222222222223; // call the distance function cout << setprecision(15) << fixed; cout << distance(lat1, long1, lat2, long2) << " K.M"; return 0;}// This code is contributed// by Aayush Chaturvedi |
Java
// Java program to calculate Distance Between// Two Points on Earthimport java.util.*;import java.lang.*;class GFG { public static double distance(double lat1, double lat2, double lon1, double lon2) { // The math module contains a function // named toRadians which converts from // degrees to radians. lon1 = Math.toRadians(lon1); lon2 = Math.toRadians(lon2); lat1 = Math.toRadians(lat1); lat2 = Math.toRadians(lat2); // Haversine formula double dlon = lon2 - lon1; double dlat = lat2 - lat1; double a = Math.pow(Math.sin(dlat / 2), 2) + Math.cos(lat1) * Math.cos(lat2) * Math.pow(Math.sin(dlon / 2),2); double c = 2 * Math.asin(Math.sqrt(a)); // Radius of earth in kilometers. Use 3956 // for miles double r = 6371; // calculate the result return(c * r); } // driver code public static void main(String[] args) { double lat1 = 53.32055555555556; double lat2 = 53.31861111111111; double lon1 = -1.7297222222222221; double lon2 = -1.6997222222222223; System.out.println(distance(lat1, lat2, lon1, lon2) + " K.M"); }}// This code is contributed by Prasad Kshirsagar |
Python3
# Python 3 program to calculate Distance Between Two Points on Earthfrom math import radians, cos, sin, asin, sqrtdef distance(lat1, lat2, lon1, lon2): # The math module contains a function named # radians which converts from degrees to radians. lon1 = radians(lon1) lon2 = radians(lon2) lat1 = radians(lat1) lat2 = radians(lat2) # Haversine formula dlon = lon2 - lon1 dlat = lat2 - lat1 a = sin(dlat / 2)**2 + cos(lat1) * cos(lat2) * sin(dlon / 2)**2 c = 2 * asin(sqrt(a)) # Radius of earth in kilometers. Use 3956 for miles r = 6371 # calculate the result return(c * r) # driver code lat1 = 53.32055555555556lat2 = 53.31861111111111lon1 = -1.7297222222222221lon2 = -1.6997222222222223print(distance(lat1, lat2, lon1, lon2), "K.M") |
C#
// C# program to calculate // Distance Between Two// Points on Earthusing System;class GFG { static double toRadians( double angleIn10thofaDegree) { // Angle in 10th // of a degree return (angleIn10thofaDegree * Math.PI) / 180; } static double distance(double lat1, double lat2, double lon1, double lon2) { // The math module contains // a function named toRadians // which converts from degrees // to radians. lon1 = toRadians(lon1); lon2 = toRadians(lon2); lat1 = toRadians(lat1); lat2 = toRadians(lat2); // Haversine formula double dlon = lon2 - lon1; double dlat = lat2 - lat1; double a = Math.Pow(Math.Sin(dlat / 2), 2) + Math.Cos(lat1) * Math.Cos(lat2) * Math.Pow(Math.Sin(dlon / 2),2); double c = 2 * Math.Asin(Math.Sqrt(a)); // Radius of earth in // kilometers. Use 3956 // for miles double r = 6371; // calculate the result return (c * r); } // Driver code static void Main() { double lat1 = 53.32055555555556; double lat2 = 53.31861111111111; double lon1 = -1.7297222222222221; double lon2 = -1.6997222222222223; Console.WriteLine(distance(lat1, lat2, lon1, lon2) + " K.M"); }}// This code is contributed by // Manish Shaw(manishshaw1) |
PHP
<?php function twopoints_on_earth($latitudeFrom, $longitudeFrom, $latitudeTo, $longitudeTo) { $long1 = deg2rad($longitudeFrom); $long2 = deg2rad($longitudeTo); $lat1 = deg2rad($latitudeFrom); $lat2 = deg2rad($latitudeTo); //Haversine Formula $dlong = $long2 - $long1; $dlati = $lat2 - $lat1; $val = pow(sin($dlati/2),2)+cos($lat1)*cos($lat2)*pow(sin($dlong/2),2); $res = 2 * asin(sqrt($val)); $radius = 3958.756; return ($res*$radius); } // latitude and longitude of Two Points $latitudeFrom = 19.017656 ; $longitudeFrom = 72.856178; $latitudeTo = 40.7127; $longitudeTo = -74.0059; // Distance between Mumbai and New York print_r(twopoints_on_earth( $latitudeFrom, $longitudeFrom, $latitudeTo, $longitudeTo).' '.'miles');// This code is contributed by akash1295?> |
Javascript
<script>// JavaScript program to calculate Distance Between// Two Points on Earth function distance(lat1, lat2, lon1, lon2) { // The math module contains a function // named toRadians which converts from // degrees to radians. lon1 = lon1 * Math.PI / 180; lon2 = lon2 * Math.PI / 180; lat1 = lat1 * Math.PI / 180; lat2 = lat2 * Math.PI / 180; // Haversine formula let dlon = lon2 - lon1; let dlat = lat2 - lat1; let a = Math.pow(Math.sin(dlat / 2), 2) + Math.cos(lat1) * Math.cos(lat2) * Math.pow(Math.sin(dlon / 2),2); let c = 2 * Math.asin(Math.sqrt(a)); // Radius of earth in kilometers. Use 3956 // for miles let r = 6371; // calculate the result return(c * r); }// Driver code let lat1 = 53.32055555555556; let lat2 = 53.31861111111111; let lon1 = -1.7297222222222221; let lon2 = -1.6997222222222223; document.write(distance(lat1, lat2, lon1, lon2) + " K.M"); </script> |
2.004367838271690 K.M
Time Complexity: O(logn) as inbuilt sqrt function has been used
Auxiliary Space: O(1)
Please suggest if someone has a better solution which is more efficient in terms of space and time.
This article is contributed by Aarti_Rathi. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above
Reference: Wikipedia
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