Calculating bounding box a certain distance away from a lat/long coordinate in Java

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Given a coordinate (lat, long), I am trying to calculate a square bounding box that is a given distance (e.g. 50km) away from the coordinate. So as input I have lat, long and distance and as output I would like two coordinates; one being the south-west (bottom-left) corner and one being the north-east (top-right) corner. I have seen a couple of answers on here that try to address this question in Python, but I am looking for a Java implementation in particular.

Just to be clear, I intend on using the algorithm on Earth only and so I don't need to accommodate a variable radius.

It doesn't have to be hugely accurate (+/-20% is fine) and it'll only be used to calculate bounding boxes over small distances (no more than 150km). So I'm happy to sacrifice some accuracy for an efficient algorithm. Any help is much appreciated.

Edit: I should have been clearer, I really am after a square, not a circle. I understand that the distance between the center of a square and various points along the square's perimeter is not a constant value like it is with a circle. I guess what I mean is a square where if you draw a line from the center to any one of the four points on the perimeter that results in a line perpendicular to a side of the perimeter, then those 4 lines have the same length.

bounding-box trigonometry geospatial latitude-longitude math
6 Answers

Based on IronMan response:

/**
 * Calculate the lat and len of a square around a point.
 * @return latMin, latMax, lngMin, lngMax
 */
public static double[] calculateSquareRadius(double lat, double lng, double radius) {
    double R = 6371;  // earth radius in km
    double latMin = lat - Math.toDegrees(radius/R);
    double latMax = lat + Math.toDegrees(radius/R);
    double lngMin = lng - Math.toDegrees(radius/R/Math.cos(Math.toRadians(lat)));
    double lngMax = lng + Math.toDegrees(radius/R/Math.cos(Math.toRadians(lat)));

    return new double[] {latMin, latMax, lngMin, lngMax};
}
user_97036210

Here is a simple solution that I used to generate bounding box coordinates that I use with GeoNames citieJSON API to get nearby big cities from a gps decimal coordinate.

This is a Java method from my GitHub repository: FusionTableModifyJava

I had a decimal GPS location and I needed to find the biggest city/state "near" that location. I needed a relatively accurate bounding box to pass to the citiesJSON GeoNames webservice to get back the biggest city in that bounding box. I pass the location and the "radius" I am interested in (in km) and it gives back the north, south, east, west decimal coordinates needed to pass to citiesJSON.

(I found these resources useful in doing my research:

Calculate distance, bearing and more between Latitude/Longitude points.

Longitude - Wikipedia)

It is not super accurate but accurate enough for what I was using it for:

    // Compute bounding Box coordinates for use with Geonames API.
    class BoundingBox
    {
        public double north, south, east, west;
        public BoundingBox(String location, float km)
        {
             //System.out.println(location + " : "+ km);
            String[] parts = location.replaceAll("\\s","").split(","); //remove spaces and split on ,

            double lat = Double.parseDouble(parts[0]);
            double lng = Double.parseDouble(parts[1]);

            double adjust = .008983112; // 1km in degrees at equator.
            //adjust = 0.008983152770714983; // 1km in degrees at equator.

            //System.out.println("deg: "+(1.0/40075.017)*360.0);


            north = lat + ( km * adjust);
            south = lat - ( km * adjust);

            double lngRatio = 1/Math.cos(Math.toRadians(lat)); //ratio for lng size
            //System.out.println("lngRatio: "+lngRatio);

            east = lng + (km * adjust) * lngRatio;
            west = lng - (km * adjust) * lngRatio;
        }

    }
user_91797640
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