# 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();
}
```

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.

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

or

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

but not both…

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);
```

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.

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