Cross-track distance calculator

What cross-track distance means and how to supply the three points

Imagine a great circle drawn through path start A and path end B on a spherical Earth model. From any third query point P you can drop a perpendicular along another great circle that meets the track at a right angle in the spherical sense. The length of that perpendicular, scaled by the sphere radius, is the cross-track distance. The signed form tells you which side of the directed path you are on: positive values mean left when travelling from A toward B, negative values mean right, and magnitudes near zero are reported as on track for numerical stability. Latitude must lie between minus ninety and ninety inclusive; longitude must lie between minus one hundred eighty and one hundred eighty inclusive. Send required fields lat and lon for the query point, start_lat and start_lon for A, and end_lat and end_lon for B, all in decimal degrees. Aliases such as latitude, longitude, lat1, lon1, lat2, and lon2 are accepted when your client already uses those names. Any coordinate outside those ranges raises invalid_input with a message that names the field and the bound, so callers never silently clamp bad GPS noise into a fake offset. Optional radius_m defaults to six million three hundred seventy-one thousand metres, the mean Earth radius used in many aviation examples; raise or lower it only when you intentionally model another sphere. If A and B coincide the path is undefined and the engine rejects the request. Identical inputs always produce identical JSON because the path is pure arithmetic with no wall clock and no external map service.

Reading signed metres, side labels, along-track distance, and bearings

Prefer metres for drone corridors and runway-scale monitoring; prefer kilometres for oceanic or long-haul air routes. On success the response echoes every coordinate and the radius used, then reports cross_track_m and cross_track_km as the signed perpendicular offset. absolute_m and absolute_km are the magnitude without sign, handy for threshold checks that only care how far you strayed. Validation failures never invent a distance: missing fields, non-finite numbers, out-of-range coordinates, and coincident endpoints all fail closed with invalid_input and are not charged under the prepaid API.

API usage, pricing, navigation workflows, and practical limits

The model is spherical, not ellipsoidal, so for sub-metre survey work you should apply a local ENU or full geodesic library instead; for navigation corridors, homework, and fleet alerts the mean-Earth sphere matches the formulas published in standard pilot and sailor references. Send a JSON body with the six required coordinates and optional radius_m, then call the free in-browser cross-track distance calculator for classroom demos, chart work, and quick mental checks without installing a geospatial library. Use the prepaid API when a flight-ops dashboard, vessel traffic system, last-mile delivery router, or simulation harness needs a stable contract under KIT balance at $0.002 per successful item; validation failures never consume balance after the engine rejects the request. Pair this endpoint with your own geocoder or AIS feed when you need place names or live tracks: this product only measures geometry on the sphere. Authors shipping SDKs can map cross_track_m and side directly into alert rules—fire when absolute_m exceeds a corridor half-width, and colour the map green, amber, or red from the same fields students see when they solve the spherical triangle by hand.