Along-track distance calculator

What along-track distance means and what the response contains

Along-track distance is the arc length measured from the start of a great-circle path to the foot of the perpendicular from a query point onto that great circle. In aviation and marine navigation it answers questions such as how far along the planned track the closest approach to a weather cell or a navaid occurs, even when the aircraft or vessel is offset from the centreline. Cross-track distance is the complementary signed offset to the left or right of the track; both quantities come from the same spherical trigonometry and are returned together so consumers do not re-derive them. This calculator returns the normalised coordinates of the path start, path end, and query point, along_track_distance in the requested unit, the same value always echoed in metres as along_track_distance_m, cross_track_distance and its metres twin, the full great-circle track_length between the path ends, the haversine distance_to_point from start to the query location, fraction_along_track relative to the finite segment, path_bearing_deg and bearing_to_point_deg from true north, the unit tag, the radius used in metres, the method tag along_track_great_circle, the decimal precision applied, and a short formula string. There is no ellipsoid geodesic iteration here and no rhumb-line model: the engine either evaluates the closed spherical formulas inside the supported coordinate ranges or rejects the input with invalid_input. Rejected cases include missing coordinates, non-finite values, latitude outside negative ninety to ninety degrees, longitude outside negative one hundred eighty to one hundred eighty degrees, coincident path ends that leave the track direction undefined, and antipodal path ends that leave the great circle non-unique.

How coordinates, units, and radius are read so results stay reproducible

Latitude must lie between negative ninety and ninety degrees inclusive; longitude must lie between negative one hundred eighty and one hundred eighty inclusive. Optional leading plus signs and scientific notation on numeric strings are allowed when they parse as finite decimals; embedded spaces, hex prefixes, and non-numeric tokens are rejected with a clear message so a bad cell does not become a wrong track position. An optional radius field sets the sphere radius in metres when you need a textbook Earth radius other than the default six million three hundred seventy-one thousand and eight point eight metres. Internally the engine converts degrees to radians, computes the haversine central angle from start to the query point, obtains the initial great-circle bearings from start to end and from start to the point, forms the signed along-track angle with atan2 of sine delta thirteen times cosine of the bearing difference over cosine delta thirteen, multiplies by R for surface metres, and likewise forms the cross-track angle with asin of sine delta thirteen times sine of the bearing difference. The preferred fields are lat1 and lon1 for the path start, lat2 and lon2 for the path end, and lat and lon for the query point, all in decimal degrees, but aliases such as start_lat, end_lon, point_lat, lat3, and longitude are accepted so spreadsheets, query strings, and typed forms can reuse the same contract. An optional unit field chooses metres, kilometres (the default), statute miles, or nautical miles, with longer aliases such as kilometers and nautical_miles normalised to short tags. Optional precision, with aliases decimals and dp, chooses how many decimal places to expose for distances and bearings, defaulting to six and capped at fifteen so JSON goldens stay stable. Pair the free browser run on this page with the priced API when you need the identical mathematical result inside an automated pipeline without re-implementing along-track formulas yourself.

Where along-track projection fits in navigation study, ops, and software

On this page the work runs entirely in your browser; through the API each successful lookup costs $0.002, failed validation is not charged, and nothing is stored after the response returns. That split — free interactive exploration and a priced, identical API — matches the rest of the KIT tier-A catalog and lets you move from a classroom demo to an automated pipeline without changing the mathematical result. Pair it with rhumb-distance or coordinate conversion tools when you need related geo steps, and with other parse endpoints when you are building a small lab of free, deterministic navigation helpers.