Azimuth and distance from coordinates calculator for survey stations

Enter the easting and northing for the occupied station, then the matching coordinates for the target station. The result includes clockwise azimuth from grid north, horizontal distance in the same unit as the coordinates, and both coordinate differences for a transparent survey check.

Set up the occupied and target stations correctly

Treat station 1 as the occupied, backsight-free starting point and station 2 as the target whose direction you need. Enter both coordinate pairs in one consistent projected or local grid. Easting measures displacement along the grid's east axis, while northing measures displacement along its north axis. Coordinate values may be positive or negative, but all four values must use the same origin, scale, datum, and linear unit. If your coordinates are in metres, the returned horizontal distance is in metres; if they are in feet, the distance is in feet. The calculator does not transform geographic latitude and longitude and does not apply a map projection. It also does not reconcile mixed grid zones, international feet, US survey feet, or site grids with different rotations. Preserve enough coordinate precision for the accuracy required by your work. Finally, remember that reversing the two stations changes the direction: the distance stays equal, but the reverse azimuth differs by 180 degrees after normalization.

Understand the azimuth and distance calculation

The calculator first subtracts station 1 from station 2. The resulting delta easting is positive when the target lies east of the occupied station, and delta northing is positive when it lies north. Horizontal distance is the planar hypotenuse formed by those two differences. Azimuth uses the survey convention of zero degrees at grid north, increasing clockwise: east is 90 degrees, south is 180 degrees, and west is 270 degrees. Internally, the direction comes from an atan2 calculation with delta easting as the first directional component and delta northing as the second. That ordering matters because the more familiar mathematical polar angle starts at the positive horizontal axis and grows counterclockwise. Negative raw directions are normalized into the interval from zero degrees inclusive to 360 degrees exclusive. Results are rounded consistently to ten decimal places. The returned deltas make it straightforward to reproduce the calculation independently, inspect signs, or carry the components into a traverse worksheet.

Use the result within its surveying limits

This is a plane-coordinate calculation, so its azimuth is a grid azimuth rather than automatically a true, magnetic, or geodetic azimuth. Apply an appropriate convergence or orientation correction separately when your project requires a different north reference. The calculation also returns a two-dimensional horizontal distance; it does not use elevations, slope distance, scale factor, sea-level reduction, combined factor, curvature, refraction, or instrument and target heights. Those corrections belong in the surrounding survey workflow and depend on the coordinate reference system and field method. A zero-distance pair is rejected because two coincident stations do not define a direction. For quality control, compare the delta signs with the expected quadrant, confirm the coordinate units, and check whether the target should lie generally northeast, southeast, southwest, or northwest. In production automation, retain the input coordinates and returned components beside the final azimuth and distance so reviewers can trace the result. The deterministic API performs the same arithmetic for identical inputs and costs $0.002 per request.