Bearing from Coordinates

This formula gives the angle of a line measured from the north direction when you know how far it moves east and north between two points. It comes from right-triangle trigonometry: the east-west change is the opposite side and the north-south change is the adjacent side, so the tangent of the bearing angle is ΔE/ΔN. Because arctan only returns a principal angle, you must also consider the signs of ΔE and ΔN to place the bearing in the correct quadrant.

Use this when you have coordinates of two points and need the direction from one point to the other, such as in surveying, mapping, route setting, or checking traverses. It is especially useful when converting coordinate differences into a line bearing for field work or plan calculations.

• Using the northing change in the numerator and the easting change in the denominator
• Ignoring the signs of ΔE and ΔN, which can put the bearing in the wrong quadrant
• Forgetting that arctan gives an angle from the north axis here, not a compass bearing in degrees-minutes-seconds unless you convert it