Rhumb line bearing calculator

Coordinates outside the valid latitude range of minus ninety to plus ninety or the longitude range of minus one hundred eighty to plus one hundred eighty produce a clear invalid_input error and are never charged.

What a rhumb-line bearing is and how it differs from great-circle course

When start and end coincide, the geometric bearing is undefined; this API conventionally reports zero degrees and states that fact in the message field so automated tests stay deterministic.

How to call the API and what comes back

Latitudes at the geographic poles are also rejected because the isometric-latitude formula is not finite there. Send a JSON body with four required finite numbers: lat1 (aliases start_lat, latitude1, from_lat), lon1 (aliases start_lon, longitude1, from_lon, lng1), lat2 (aliases end_lat, latitude2, to_lat), and lon2 (aliases end_lon, longitude2, to_lon, lng2). Latitude must lie in the closed interval from minus ninety to plus ninety degrees and longitude in the closed interval from minus one hundred eighty to plus one hundred eighty degrees; any value outside those ranges returns invalid_input with an explicit outside-its-valid-range message. On success the response echoes rounded lat1, lon1, lat2, and lon2; sets bearing_deg to the constant course in degrees on zero inclusive through three hundred sixty exclusive; sets bearing_rad to the same angle in radians; sets compass to a sixteen-point label such as N, NE, or WSW; sets formula to the atan2 and delta-psi expression; sets units for degrees and radians; sets message to a short English summary; and sets steps to an ordered array of substitution lines you can assert in tests. Failed validation—missing fields, non-finite numbers, out-of-range coordinates, or polar latitudes—returns invalid_input and is never charged. Pricing is a flat $0.002 per successful request with unit item and zero marginal unit price.

Practical tips, limits, and related searches

Prefer this capability when you already have two points and only need the constant heading; if your source is a great-circle flight plan, convert or re-sample with an orthodromic tool instead. Keep both latitudes strictly inside the open polar band if you plan long north–south legs near the high latitudes; the API already rejects true poles, but values within a few microdegrees of ninety can still stress tan of pi over four plus phi over two in floating point on other systems. Prefer sending numeric JSON rather than pre-formatted strings when you control the client; string numbers are accepted only when they match a strict finite numeric pattern. When teaching, pair examples: a classic Dover-area leg around fifty-one point one two seven north, one point three three eight east to fifty point nine six four north, one point eight five three east yields a southeast-ish constant course; a pure east leg along a parallel yields ninety degrees; a pure south leg along a meridian yields one hundred eighty degrees; and latitude ninety-one or longitude two hundred demonstrates the hard invalid_input path. This landing targets people searching for a rhumb line bearing calculator, loxodrome constant course, or constant compass heading between two coordinates; it is not a rhumb-distance calculator, not a destination-from-course tool, and not an ellipsoidal geodesic solver. Failed tasks that return invalid_input do not consume prepaid balance, which keeps exploratory scripts cheap when learners deliberately send out-of-range longitudes. Round-trip checks are easy: recompute delta-psi and atan2 by hand for a short east–west or north–south leg and confirm that bearing_deg matches within the same six-decimal rounding, and confirm that swapping start and end rotates the course by approximately one hundred eighty degrees on a simple meridional segment.