Calculate angle between two Latitude/Longitude points

Question

Is there a way to calculate angle between two Latitude/Longitude points?

What I am trying to achieve is to know where the user is heading. For example, user is head

Answer 1

With javascript, just use Turf:

var point1 = turf.point([-75.343, 39.984]);
var point2 = turf.point([-75.534, 39.123]);

var bearing = turf.bearing(point1, point2);

Answer 2

The general formula for calculating the angle(bearing) between two points is as follows:

θ = atan2(sin(Δlong)*cos(lat2), cos(lat1)*sin(lat2) − sin(lat1)*cos(lat2)*cos(Δlong))

Note that the angle(θ) should be converted to radians before using this formula and Δlong = long2 - long1.

atan2 is a common function found in almost all programming languages (mostly in the Math package/library). Usually there are also functions for conversion between degrees and radians(also in the Math package/library).

Remember that atan2 returns values in the range of -π ... +π, to convert the result to a compass bearing, you need to multiply θ by 180/π then use (θ+360) % 360, where % is modulus division operation returning the remainder of the division.

The following link is a good resource for formulas involving latitudes and longitudes. They also provide Javascript implementation of their formulas. In fact, this answer is based on the information from this page:

http://www.yourhomenow.com/house/haversine.html

Answer 3

In case someone need PHP code for this functionality:

/**
 * Calculate angle between 2 given latLng
 * @param  float $lat1
 * @param  float $lat2
 * @param  float $lng1
 * @param  float $lng2
 * @return integer
 */
function angle($lat1, $lat2, $lng1, $lng2) {
    $dLon = $lng2 - $lng1;
    $y = sin($dLon) * cos($lat2);
    $x = cos($lat1) * sin($lat2) - sin($lat1) * cos($lat2) * cos($dLon);
    return 360 - ((rad2deg(atan2($y, $x)) + 360) % 360);
}

Answer 4

Sample javascript code if the distance between points is less -

brng = Math.atan2(newLat - oldLat, newLong - oldLong);
brng = brng * (180 / Math.PI);
brng = (brng + 360) % 360;
brng = 360 - brng;

Answer 5

To provide heading you have to compute bearing.

To understand bearing read this article.

According to this article (section bearing) the formula is :

θ = atan2( sin Δλ ⋅ cos φ2 , cos φ1 ⋅ sin φ2 − sin φ1 ⋅ cos φ2 ⋅ cos Δλ )
where φ1, λ1 is the start point, 
      φ2, λ2 the end point,
      Δλ is the difference in longitude`

Here's a sample on how to compute the angle (in degrees) between two points expressed in Lat/Lon. (done in C#)

Let's say Point is a simple class with two double attributes X (for longitude) and Y (for latitude).

public double ComputeBearing(Point start,Point end)
{
     var φ1 = start.Y; //latitude 1
     var λ1 = start.X; //longitude 1
     var φ2 = end.Y; //latitude 2
     var λ2 = end.X; //longitude 2

     var y = Math.Sin(this.degreeToRadian(λ2 - λ1)) * Math.Cos(this.degreeToRadian(φ2));
     var x = Math.Cos(this.degreeToRadian(φ1)) * Math.Sin(this.degreeToRadian(φ2)) - Math.Sin(this.degreeToRadian(φ1)) * Math.Cos(this.degreeToRadian(φ2)) * Math.Cos(this.degreeToRadian(λ2 - λ1));

     var θ = Math.Atan2(y, x);
     θ = this.radianToDegree(θ);

     return θ;
}

Using the following methods :

public double degreeToRadian(double angle)
{
    return Math.PI * angle / 180.0;
}

public double radianToDegree(double angle)
{
    return angle * (180.0 / Math.PI);
}

By using ComputeBearing you will easily get an angle expressed in degrees easily usable as heading

Answer 6

Maybe this is what you want:

cos(say) = (cosd(90-lat(1))) * (cos(90-lat(2)))
         + (sin(90-lat(1))) * (sind(90-lat(2)) * (cosd(abs(Landa(2)-landa(1)))));