Azimuth Calculator - GPS Bearing and Distance

Azimuth describes a horizontal direction as an angle measured clockwise from true north. North is 0 degrees, east is 90 degrees, south is 180 degrees, and west is 270 degrees. Navigators often use the word bearing for the same idea, although surveying conventions can also express bearings by quadrant. This calculator reports a full-circle initial azimuth, which is the direction a traveler should face when leaving the starting coordinate on the shortest route over a spherical Earth. The calculation uses latitude and longitude in decimal degrees. It converts both points to radians, evaluates the spherical initial-bearing equation with the two-argument arctangent, and normalizes the answer into the range from 0 through less than 360 degrees. The compass description divides that circle into sixteen sectors, so a value near 45 degrees is northeast while a value near 337.5 degrees is north-northwest. Because a great-circle route curves relative to lines on a flat map, the bearing changes during a long journey. The displayed number is specifically the initial bearing, not one unchanging heading for the entire trip. Distance is calculated with the Haversine formula and a mean Earth radius of 6,371.0088 kilometers. Haversine is stable for both nearby and widely separated points and gives the length of the shortest arc between them. It treats Earth as a sphere, so it is excellent for route estimates, geographic comparisons, radio-link planning, and general navigation. Professional land surveys over short baselines may instead require an ellipsoidal geodesic model and a specified datum because local precision can depend on Earth flattening, elevation, and coordinate reference systems. Use negative latitude for locations south of the equator and negative longitude for locations west of Greenwich. For example, New York is approximately 40.7128 latitude and -74.0060 longitude. London is about 51.5074 and -0.1278. Coordinate order matters: reversing the points changes the initial bearing and can produce a return bearing that is not exactly 180 degrees opposite on a long great-circle route. The distance remains the same in either direction. GPS readings include measurement uncertainty, and rounded coordinates can shift a computed heading significantly when two points are close together. Use enough decimal places for the scale of your task: four decimal places represent roughly eleven meters of latitude, while six represent about eleven centimeters. At identical coordinates, distance is zero and an azimuth has no practical direction, even though a numeric implementation may display zero. Always pair the result with appropriate maps, local conditions, magnetic-declination data, and safety procedures when using it for real navigation.