Calculating distance between two points, using latitude longitude?

Question

Here's my try, it's just a snippet of my code:

final double RADIUS = 6371.01;
double temp = Math.cos(Math.toRadians(latA))
            * Math.cos(Math.toRadians(latB))
            * Math.cos(Math.toRadians((latB) - (latA)))
            + Math.sin(Math.toRadians(latA))
            * Math.sin(Math.toRadians(latB));
    return temp * RADIUS * Math.PI / 180;

I am using this formulae to get the latitude and longitude:

x = Deg + (Min + Sec / 60) / 60)

score 259 · Accepted Answer · edited Apr 20 '17 at 11:24

259

The Java code given by Dommer above gives slightly incorrect results but the small errors add up if you are processing say a GPS track. Here is an implementation of the Haversine method in Java which also takes into account height differences between two points.

/**
 * Calculate distance between two points in latitude and longitude taking
 * into account height difference. If you are not interested in height
 * difference pass 0.0. Uses Haversine method as its base.
 * 
 * lat1, lon1 Start point lat2, lon2 End point el1 Start altitude in meters
 * el2 End altitude in meters
 * @returns Distance in Meters
 */
public static double distance(double lat1, double lat2, double lon1,
        double lon2, double el1, double el2) {

    final int R = 6371; // Radius of the earth

    double latDistance = Math.toRadians(lat2 - lat1);
    double lonDistance = Math.toRadians(lon2 - lon1);
    double a = Math.sin(latDistance / 2) * Math.sin(latDistance / 2)
            + Math.cos(Math.toRadians(lat1)) * Math.cos(Math.toRadians(lat2))
            * Math.sin(lonDistance / 2) * Math.sin(lonDistance / 2);
    double c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1 - a));
    double distance = R * c * 1000; // convert to meters

    double height = el1 - el2;

    distance = Math.pow(distance, 2) + Math.pow(height, 2);

    return Math.sqrt(distance);
}

edited Apr 20 '17 at 11:24

Neeme Praks

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answered May 28 '13 at 14:30

David George

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Why not Math.toRadians() instead of deg2rad()? It would be really self-containing. – Aron Lorincz Feb 11 '15 at 13:29
2

@Bala - My bad, it is in the comment on the code on my computer but missing here. Distance in meters. – David George Jun 01 '15 at 15:45
4

@ÁronNemmondommegavezetéknevem I've updated the method to use your very good suggestion. – David George Jun 01 '15 at 15:52
2

Some comments here: http://stackoverflow.com/questions/28510115/java-math-toradiansangle-vs-hard-calculated?lq=1 – David George Jun 08 '15 at 10:11
Any particular relevance to variable names `a` and `c`? Are these the sides of a right-angled triangle with traditional labels `a`, `b` and `c`? – AlainD Jan 31 '17 at 15:30
I don't remember now, but it might well be that. – David George Feb 01 '17 at 20:21
1

the `a` may be negative – Guisong He Dec 21 '18 at 03:47
Can we use the above method as an alternative to Geofence? @DavidGeorge – sagar suri Mar 25 '20 at 09:14
Calculate the distance between saved location and the current location of the user? – sagar suri Mar 25 '20 at 09:14
CAUTION: this method is very bad in short distances, my test was 'System.out.println(distance(44.7866, 20.4489,44.8205, 20.2917, 0, 0));' and it displays 3521170.2534322045 while actual value is ~13000 (twose are coordinates of Belgrade city and Belgrade airport) – Mladen Adamovic Dec 21 '20 at 09:01
1

Your code is wrong which is why you get incorrect results. Read the API. Don't you think after 7 years and 235 upvotes someone may have spotted a problem? – David George Dec 22 '20 at 10:57
2

I made the same mistake as Mladen did, passed (lat1, lon1, lat2, lon2) instead of (lat1, lat2, lon1, lon2). Make sure you don't swap the values. – Andras Kloczl Sep 23 '21 at 23:54

score 87 · Answer 2 · edited Aug 06 '20 at 10:19

Here's a Java function that calculates the distance between two lat/long points, posted below, just in case it disappears again.

    private double distance(double lat1, double lon1, double lat2, double lon2, char unit) {
      double theta = lon1 - lon2;
      double dist = Math.sin(deg2rad(lat1)) * Math.sin(deg2rad(lat2)) + Math.cos(deg2rad(lat1)) * Math.cos(deg2rad(lat2)) * Math.cos(deg2rad(theta));
      dist = Math.acos(dist);
      dist = rad2deg(dist);
      dist = dist * 60 * 1.1515;
      if (unit == 'K') {
        dist = dist * 1.609344;
      } else if (unit == 'N') {
        dist = dist * 0.8684;
        }
      return (dist);
    }
    
    /*:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::*/
    /*::  This function converts decimal degrees to radians             :*/
    /*:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::*/
    private double deg2rad(double deg) {
      return (deg * Math.PI / 180.0);
    }
    
    /*:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::*/
    /*::  This function converts radians to decimal degrees             :*/
    /*:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::*/
    private double rad2deg(double rad) {
      return (rad * 180.0 / Math.PI);
    }
    
    System.out.println(distance(32.9697, -96.80322, 29.46786, -98.53506, 'M') + " Miles\n");
    System.out.println(distance(32.9697, -96.80322, 29.46786, -98.53506, 'K') + " Kilometers\n");
    System.out.println(distance(32.9697, -96.80322, 29.46786, -98.53506, 'N') + " Nautical Miles\n");

Google Map shows 200 Kms for 12.915700, 77.632046, 11.665154, 78.145657 where as the above code shows 149.82 Kms. Something is still incorrect. — Samy, Dec 30 '15 at 10:15
My kingdom for developers to label their variables *with the Units*. double dist => double distInMiles (or similar) (I'm not knocking the person who posted this answer, I'm upvoting.......but rather the original implementer of the code ) — granadaCoder, Aug 13 '19 at 13:51
this method works OK with small distances, I think it might be better than https://stackoverflow.com/a/20410612/1537394 as it uses sin/cos/acos which is logical as the Earth is kind of sphere. Upvoting. — Mladen Adamovic, Dec 21 '20 at 09:08
This function will return NaN instead of 0.0 for input 30.4570925, 74.1676477, 30.4570925, 74.1676477 because Math.acos() function does not accepts values greater than 1. — Saurabh Verma, Jul 13 '21 at 14:59

granadaCoder · Answer 3 · 2019-11-04T13:40:00.003

27

Future readers who stumble upon this SOF article.

Obviously, the question was asked in 2010 and its now 2019. But it comes up early in an internet search. The original question does not discount use of third-party-library (when I wrote this answer).

public double calculateDistanceInMeters(double lat1, double long1, double lat2,
                                     double long2) {


    double dist = org.apache.lucene.util.SloppyMath.haversinMeters(lat1, long1, lat2, long2);
    return dist;
}

and

<dependency>
  <groupId>org.apache.lucene</groupId>
  <artifactId>lucene-spatial</artifactId>
  <version>8.2.0</version>
</dependency>

https://mvnrepository.com/artifact/org.apache.lucene/lucene-spatial/8.2.0

Please read documentation about "SloppyMath" before diving in!

https://lucene.apache.org/core/8_2_0/core/org/apache/lucene/util/SloppyMath.html

edited Nov 04 '19 at 13:40

answered Aug 13 '19 at 17:00

granadaCoder

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Are you sure this is right? this jar file dont have ".util" i just checked it. – Adnan Ali Sep 29 '20 at 09:24
That's why I always publish the version with an answer. Make sure you are getting 8.2.0. 13 upvotes also suggests an answer is accurate. – granadaCoder Sep 29 '20 at 11:09
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I think it is a bad practice to add a dependency to something if you can replace it with 28 lines in your code, unless you are using more from that dependency – Mladen Adamovic Dec 21 '20 at 09:07
I need to convert these java script into java in Android Studio - any suggestions or steps to solution ? appreciate your help – bennyhardjono Oct 14 '21 at 05:50

score 15 · Answer 4 · edited Jun 14 '21 at 19:36

Note: this solution only works for short distances.

I tried to use dommer's posted formula for an application and found it did well for long distances but in my data I was using all very short distances, and dommer's post did very poorly. I needed speed, and the more complex geo calcs worked well but were too slow. So, in the case that you need speed and all the calculations you're making are short (maybe < 100m or so). I found this little approximation to work great. it assumes the world is flat mind you, so don't use it for long distances, it works by approximating the distance of a single Latitude and Longitude at the given Latitude and returning the Pythagorean distance in meters.

public class FlatEarthDist {
    //returns distance in meters
    public static double distance(double lat1, double lng1, 
                                      double lat2, double lng2){
     double a = (lat1-lat2)*FlatEarthDist.distPerLat(lat1);
     double b = (lng1-lng2)*FlatEarthDist.distPerLng(lat1);
     return Math.sqrt(a*a+b*b);
    }

    private static double distPerLng(double lat){
      return 0.0003121092*Math.pow(lat, 4)
             +0.0101182384*Math.pow(lat, 3)
                 -17.2385140059*lat*lat
             +5.5485277537*lat+111301.967182595;
    }

    private static double distPerLat(double lat){
            return -0.000000487305676*Math.pow(lat, 4)
                -0.0033668574*Math.pow(lat, 3)
                +0.4601181791*lat*lat
                -1.4558127346*lat+110579.25662316;
    }
}

could someone add details if this is working better for short distances than the accepted answer here: https://stackoverflow.com/a/16794680/1537394 ? — Mladen Adamovic, Dec 20 '20 at 12:17
No its not working fine for short distances. I walked for around 30 meters but it showed 88 meters. — Priyavrat Talyan, Nov 23 '22 at 06:52

Stan Sokolov · Answer 5 · 2020-12-01T22:55:24.823

was a lot of great answers provided however I found some performance shortcomings, so let me offer a version with performance in mind. Every constant is precalculated and x,y variables are introduced to avoid calculating the same value twice. Hope it helps

    private static final double r2d = 180.0D / 3.141592653589793D;
    private static final double d2r = 3.141592653589793D / 180.0D;
    private static final double d2km = 111189.57696D * r2d;
    public static double meters(double lt1, double ln1, double lt2, double ln2) {
        double x = lt1 * d2r;
        double y = lt2 * d2r;
        return Math.acos( Math.sin(x) * Math.sin(y) + Math.cos(x) * Math.cos(y) * Math.cos(d2r * (ln1 - ln2))) * d2km;
    }

score 5 · Answer 6 · answered Sep 12 '10 at 09:59

Here is a page with javascript examples for various spherical calculations. The very first one on the page should give you what you need.

http://www.movable-type.co.uk/scripts/latlong.html

Here is the Javascript code

var R = 6371; // km
var dLat = (lat2-lat1).toRad();
var dLon = (lon2-lon1).toRad(); 
var a = Math.sin(dLat/2) * Math.sin(dLat/2) + 
        Math.cos(lat1.toRad()) * Math.cos(lat2.toRad()) *
        Math.sin(dLon/2) * Math.sin(dLon/2); 
var c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a)); 
var d = R * c;

Where 'd' will hold the distance.

score 1 · Answer 7 · answered Dec 02 '14 at 12:17

package distanceAlgorithm;

public class CalDistance {
    public static void main(String[] args) {
        // TODO Auto-generated method stub
    CalDistance obj=new CalDistance();
    /*obj.distance(38.898556, -77.037852, 38.897147, -77.043934);*/
        System.out.println(obj.distance(38.898556, -77.037852, 38.897147, -77.043934, "M") + " Miles\n");
        System.out.println(obj.distance(38.898556, -77.037852, 38.897147, -77.043934, "K") + " Kilometers\n");
        System.out.println(obj.distance(32.9697, -96.80322, 29.46786, -98.53506, "N") + " Nautical Miles\n");       
    }   
    public double distance(double lat1, double lon1, double lat2, double lon2, String sr) {


          double theta = lon1 - lon2;
          double dist = Math.sin(deg2rad(lat1)) * Math.sin(deg2rad(lat2)) + Math.cos(deg2rad(lat1)) * Math.cos(deg2rad(lat2)) * Math.cos(deg2rad(theta));
          dist = Math.acos(dist);
          dist = rad2deg(dist);
          dist = dist * 60 * 1.1515;
          if (sr.equals("K")) {
            dist = dist * 1.609344;
          } else if (sr.equals("N")) {
            dist = dist * 0.8684;
            }
          return (dist);
        }
    public double deg2rad(double deg) {
          return (deg * Math.PI / 180.0);
        }
    public double rad2deg(double rad) {
          return (rad * 180.0 / Math.PI);
        }


    }

score 1 · Answer 8 · answered Jul 13 '20 at 10:58

Slightly upgraded answer from @David George:

public static double distance(double lat1, double lat2, double lon1,
                              double lon2, double el1, double el2) {

    final int R = 6371; // Radius of the earth

    double latDistance = Math.toRadians(lat2 - lat1);
    double lonDistance = Math.toRadians(lon2 - lon1);
    double a = Math.sin(latDistance / 2) * Math.sin(latDistance / 2)
            + Math.cos(Math.toRadians(lat1)) * Math.cos(Math.toRadians(lat2))
            * Math.sin(lonDistance / 2) * Math.sin(lonDistance / 2);
    double c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1 - a));
    double distance = R * c * 1000; // convert to meters

    double height = el1 - el2;

    distance = Math.pow(distance, 2) + Math.pow(height, 2);

    return Math.sqrt(distance);
}

public static double distanceBetweenLocations(Location l1, Location l2) {
    if(l1.hasAltitude() && l2.hasAltitude()) {
        return distance(l1.getLatitude(), l2.getLatitude(), l1.getLongitude(), l2.getLongitude(), l1.getAltitude(), l2.getAltitude());
    }
    return l1.distanceTo(l2);
}

distance function is the same, but I've created I small wrapper function, which takes 2 Location objects. Thanks to this, I only use distance function if both of locations actually have altitude, because sometimes they don't. And it can lead to strange results (if location doesn't know its altitude 0 will be returned). In this case, I fall back to classic distanceTo function.

Calculating distance between two points, using latitude longitude?

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