Add exact distance to GPS coordinates

I want to be able to add an exact distance to some GPS coordinates. I have a longitude and a latitude and I want to add a distance, let’s say 30 meters.

I found below formula but when I test it, it does not seem to be that accurate because the resulting long and lat are 37m away from the beginning coords.

public static Coordinates addDistanceToCoordinates(String lat, String lon, double distance) {
    Double latitude = Double.valueOf(lat);
    Double longitude = Double.valueOf(lon);

    double lat0 = cos(Math.PI / 180.0 * latitude);

    double x = longitude + (180/Math.PI)*(distance/6378137)/cos(lat0);
    double y = latitude + (180/Math.PI)*(distance/6378137);

    return Coordinates.builder().lon(x).lat(y).build();
}

Answer

If you have a center (x,y) and you move on the x axis by 30 meters and on the y axis by another 30 meters your distance from the center won’t be 30.

It will be Math.sqrt( Math.pow(x, 2) + Math.pow(y, 2) );.

Specifically, there are an infinite number of points that are 30 meters distant from the center (or your initial coordinates).

If you want to move in only one direction, then you can simply add/subtract 30 meters in either of your axis.

As you already did:

double x = longitude + (180/Math.PI)*(distance/6378137)/cos(lat0);

or

double y = latitude + (180/Math.PI)*(distance/6378137);

but not both…

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You are still better off by using angles in your calculations, which will turn handy when you move on both axis.

By knowing which direction you are headed to, for example 50° from the x axis,

double a = Math.toRadians(50);  // degrees

double x = longitude + (180/Math.PI) * (30 / 6378137)/cos(lat0) * Math.cos(a);
double y = latitude + (180/Math.PI) * (30 / 6378137) * Math.sin(a);

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Coming back to your question, if you want to move on the x axis and the y axis by the same distance and end up exactly 30 meters away from the center, then your angle will be double a = Math.toRadians(45); (if you head North-East) *

In fact you will obtain for both (30 / 6378137) * Math.cos(a) and (30 / 6378137) * Math.sin(a) a result of x1 = y1 = 3.325924707417923e-06.

If you then apply Pythagoras

double finalDistance = Math.sqrt(Math.pow(x1, 2) + Math.pow(y1, 2)) * 6378137; 

you will find finalDistance to be 30 meters from your initial coordinates.

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* The correct calculation would be Math.toRadians(45 * (2 * n - 1)); | where n = [1, 2, 3, 4]