Destination point calculator

A destination-point calculator answers the spherical direct problem of navigation: given where you stand, the true course you leave on, and how far you travel, where do you arrive? This tool takes a start latitude and longitude in decimal degrees, an initial bearing clockwise from true north, and a distance in meters, kilometers, statute miles, or nautical miles, then returns the great-circle destination on a sphere of mean Earth radius—or any positive custom radius you supply. The formula uses only elementary trigonometry: convert degrees to radians, form the angular distance as path length over radius, evaluate the classic asin and atan2 destination identities, and normalize longitude into the open–closed range around the antimeridian.

How the great-circle 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 initial 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.

The destination latitude is the arcsine of sin φ1 times cos δ plus cos φ1 times sin δ times cos θ. The destination longitude is λ1 plus the two-argument arctangent of sin θ times sin δ times cos φ1 over cos δ minus sin φ1 times sin φ2, which preserves the correct quadrant when the course crosses meridians or poles.

After converting φ2 and λ2 back to degrees, clamp latitude naturally through arcsine into negative ninety through positive ninety and fold longitude into the range from negative one hundred eighty through positive one hundred eighty so map layers and GIS tools can plot the point without a second normalization pass. Zero distance returns the start point with a well-defined final bearing; distances that wrap the globe many times remain mathematically valid on the sphere though they may not match ellipsoid geodesics used by high-precision surveying.

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 initial great-circle azimuth 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 bearing for ten thousand meters, and verifying the destination sits northeast of the start.

Where destination-point calculators show up in real work

Aviation and maritime training constantly assign rhumb-line versus great-circle drills, and students need a trusted oracle that returns destination lat/lon from a departure fix, true course, and distance without a chart protractor. Search-and-rescue planning, hiking guides, and orienteering curricula build waypoints by projecting a bearing and distance from a known trailhead. Game and simulation engines place entities on a spherical world using the same closed form so client and server stay aligned without shipping a heavy geodesic package.

If you later need the inverse problem of distance and bearing between two fixed points, rhumb-line sailing, or full WGS84 Vincenty geodesics on the ellipsoid, treat those as separate search intents and landings rather than overloading this spherical destination-point page.