Rhumb line destination point

A rhumb-line destination calculator answers the direct problem of constant-bearing navigation: given where you start, the true course you hold without turning, and how far you sail or fly, where do you arrive? Unlike a great-circle path, a rhumb line—also called a loxodrome—crosses every meridian at the same angle, so the compass course stays fixed from departure to arrival. This tool takes a start latitude and longitude in decimal degrees, a constant bearing clockwise from true north, and a distance in meters, kilometers, statute miles, or nautical miles, then returns the spherical rhumb destination on mean Earth radius or any positive custom radius you supply.

How the rhumb-line destination formula works

Treat the Earth as a sphere of radius R—by default the conventional mean radius of six million three hundred seventy-one thousand meters—and convert the start latitude φ1 and longitude λ1 from degrees into radians. Convert the constant true bearing θ the same way, measuring clockwise from true north so that zero is due north, ninety is due east, one hundred eighty is due south, and two hundred seventy is due west.

Convert the travel distance into meters if needed, then form the angular distance δ equals d over R in radians. Advance latitude with Δφ equals δ times cos θ so that pure east–west courses leave latitude unchanged and pure north–south courses change only latitude. Form the isometric latitudes ψ1 and ψ2 as the natural logarithms of the tangents of π over four plus half of each geodetic latitude; their difference Δψ scales longitude change along the Mercator strip.

When |Δψ| is appreciable, set the scale factor q to Δφ over Δψ; when the course is essentially east–west and Δψ vanishes, fall back to q equals cos φ1 so longitude steps correctly on a parallel. Then Δλ equals δ times sin θ over q and λ2 equals λ1 plus Δλ. Convert φ2 and λ2 back to degrees, keep latitude inside the closed range from negative ninety through positive ninety, and fold longitude into the open–closed range around the antimeridian so GIS layers plot cleanly.

Paths that would drive latitude past a pole are rejected rather than wrapped, because a true rhumb cannot cross the pole while holding a fixed azimuth.

What you send and what you get back

Send four required finite numbers under the fields latitude, longitude, bearing, and distance. Latitude must lie in the closed interval from negative ninety to positive ninety degrees with north positive. Longitude must lie in the closed interval from negative one hundred eighty to positive one hundred eighty degrees with east positive.

Bearing is the constant rhumb true course in degrees; values outside zero to three hundred sixty are accepted when finite and then normalized into that half-open range for computation and reporting. Classic checks include leaving Greenwich near fifty-one point four seven seven eight north, zero point zero zero one five west, on a forty-five degree course for ten thousand meters, and verifying the destination sits northeast of the start on a track of constant azimuth.

Where rhumb-line destination calculators show up in real work

Maritime and aviation training constantly contrast rhumb-line sailing with great-circle flying, and students need a trusted oracle that returns destination lat/lon from a departure fix, constant true course, and distance without a chart protractor. Passage planners still plot many coastal and mid-latitude legs as rhumbs because the helm holds one compass heading, and logistics teams prototype ferry tracks, survey lines, and pipeline corridors the same way before committing to full ellipsoid libraries.

Orienteering curricula, hiking guides, and search-and-rescue grids often step waypoints by fixed distance on a fixed azimuth from a known trailhead. Game and simulation engines place entities on a spherical world with constant-heading motion so client and server stay aligned without shipping a heavy geodesic package.

If you later need the great-circle destination (shortest path with changing course), the inverse problem of distance and bearing between two fixed points, or full WGS84 Vincenty geodesics on the ellipsoid, treat those as separate search intents and landings—this page stays focused on the constant-bearing rhumb destination point.