Nearest point on a great-circle segment

It projects the query location onto the segment's great circle, checks whether that projection lies between the two endpoints, and clamps the answer to the nearer endpoint when it does not. The response includes the nearest coordinates, the position classification, the fraction along the segment, and the spherical separation as both an angle and a distance.

Describe the query location and the segment

Enter the query location as lat and lon, then identify the segment with start_lat, start_lon, end_lat, and end_lon. Every coordinate uses decimal degrees: latitude runs from south to north between -90 and 90, while longitude runs west to east between -180 and 180. The segment is the shorter great-circle arc joining its endpoints, not a straight line on a flat map and not a constant-bearing rhumb line. This distinction matters on long routes and at high latitudes, where common planar projection formulas can place the nearest point noticeably incorrectly. The default sphere radius is the IUGG mean Earth radius. You may supply a different positive radius when modeling another sphere or matching an established calculation, without changing the returned nearest latitude and longitude. The optional precision setting controls rounding of all numeric response fields; it does not reduce the internal precision used to select the point.

Understand projection and endpoint clamping

The calculator converts all three locations into three-dimensional unit vectors. The cross product of the endpoint vectors defines the plane of the great circle, and removing the query vector's component normal to that plane gives its perpendicular spherical projection. A projection on the infinite great circle is not automatically on the finite segment. The algorithm therefore compares angular arc lengths to determine whether the projected vector lies on the shorter arc from start to end. If it does, the response reports location as segment and supplies its fractional progress from zero at the start to one at the end. If it falls outside, the result is clamped to whichever endpoint has the smaller angular separation, and location becomes start or end. Coincident endpoints form a valid zero-length segment. Exactly antipodal endpoints are rejected because infinitely many great circles connect them, so the intended segment cannot be inferred from those two coordinates alone.

Use the result in geographic workflows

The nearest object is the coordinate to store, display, or feed into a later geographic calculation. The fraction is useful for locating an event along a route or interpolating metadata such as planned time, provided that metadata follows the same great-circle segment. The angular distance is independent of the chosen sphere radius, while distance_m is that angle multiplied by earth_radius_m. This is a spherical model, so it is appropriate for navigation estimates, global visualizations, route matching, and other tasks where a stable great-circle answer is desired. It is not an ellipsoidal geodesic solver and should not replace a surveyed terrestrial boundary calculation that requires a named datum and centimeter-level accuracy. For polylines, call the capability once for each segment and retain the result with the smallest distance. If two endpoint distances are exactly tied in an otherwise ambiguous case, the deterministic result favors the start, which keeps repeated runs stable.