Azimuth Calculator

This tool uses spherical trigonometry and the Haversine formula to compute both the forward azimuth and the great-circle distance between a starting coordinate (latitude and longitude) and a final coordinate. First, the algorithm computes intermediate directional arguments based on coordinate differences. The unconverted azimuth is found using the two-argument arctangent function: atan2(y, x), where y represents the longitudinal difference component and x accounts for the latitudinal interaction. Finally, the raw angle is normalized into a standard 0 to 360-degree compass range. Distance is derived concurrently using the angular separation of the two points multiplied by Earth's mean radius.

Imagine you want to calculate the azimuth and distance from a starting point at latitude 40.7128° N, longitude 74.0060° W (New York City) to a destination at latitude 51.5074° N, longitude 0.1278° W (London). First, convert all latitude and longitude values into radians. Next, compute the intermediate vector components using the sine and cosine differences of the coordinates. The longitudinal offset component (argument y) and the latitudinal vector parts (argument x) are evaluated via the atan2 function to yield the initial bearing angle of approximately 51.3 degrees. Simultaneously, the Haversine formula processes the angular separation to determine a great-circle distance of roughly 5,570 kilometers between the two cities.

Always double-check whether your input coordinates use decimal degrees or degrees-minutes-seconds, as mixing formats will result in severe directional errors. Ensure that southern latitudes and western longitudes are inputted as negative numbers to maintain the integrity of the trigonometric functions. Remember that the calculated azimuth represents the initial heading; on long-haul great-circle routes, the actual bearing continuously shifts as you travel along the curve.