The distance calculator uses the Haversine formula:

         a = sin²(Δφ/2) + cos φ1 * cos φ2 * sin²(Δλ/2)
         c = 2 * atan2( √a, √(1−a) )
         d = R * c
         Where φ is the latitude in radians, λ is the longitude in radians and R is the earth’s radius in km.
                            

The bearing calculator uses the formula:

         θ = atan2( cos φ2 * sin Δλ , cos φ1 * sin φ2 − sin φ1 * cos φ2 * cos Δλ )
         Where φ1,λ1 are the start coordinates in radians, φ2,λ2 are the end coordinates in radians,
         Δλ is the difference in longitude and θ is the bearing in radians.
                            

The code then converts radians back to degrees (multiply by pi/180).

Note that since atan2 returns values of -π..+π (-180°..+180°) we have to normalise the result and return 0°..360° for a compass heading by converting negative values to 180°..360°. We do this by adding 360 then taking the floating point modulus of 360, i.e. (θ + 360) % 360