Bearing calculator – great circle and rhumb line

A bearing is the direction from one place to another, measured clockwise from north: 0° is north, 90° east, 180° south and 270° west. Over short distances one number is enough, but over long ones the answer depends on how you travel. The great circle, the shortest path, keeps changing direction: from New York's JFK airport the shortest route to London Heathrow sets off at 51.4°, towards north-east, and arrives heading 108.0°, a little south of east. A rhumb line keeps one compass bearing all the way, 78.0° for the same trip, but is 3.9 % longer. This calculator shows both on the map, the great circle as a solid line and the rhumb line dashed, and lists the initial and final bearing, the back bearing for the return trip, and both distances in kilometres, miles or nautical miles. It also works the other way round: give a start point, a bearing and a distance, and it places the end point, which is useful for plotting a course, a line of sight or a survey offset.

How to use it

1. Click on the map to set point A, or search a town; then set point B the same way.
2. Read the initial, final and back bearing, the great-circle distance and the rhumb line in the panel.
3. Or enter a bearing and a distance and press "Set point B" to find the point that far from A.
4. Drag A or B to adjust, switch units, copy the share link or download KML or GeoJSON.

How accurate is it?

Calculated on the ellipsoid

The great-circle values are really geodesic: the shortest path on the WGS84 ellipsoid, solved with GeographicLib, so bearings are correct to far better than a thousandth of a degree and distances to a millimetre. Many simple calculators use a sphere, which can put the bearing off by up to about 0.2° and the distance by up to 0.5 %. The rhumb line uses the isometric latitude of the ellipsoid and the exact meridian length, and is checked against a dense chain of short geodesic steps.

True north, not magnetic north

All bearings are measured from true (geographic) north, the direction to the North Pole. A magnetic compass points to magnetic north, which differs by the magnetic declination: a few degrees in most of Europe, up to 15–20° in parts of North America, and it changes over the years. Add or subtract the local declination from a current chart or a declination calculator before following a bearing with a compass.

Initial, final and back bearing

The initial bearing is the direction to leave A on the great circle; the final bearing is the direction of travel when arriving at B. The back bearing is the initial bearing from B back to A, which is always the final bearing turned by 180°. On a flat map it would also be the initial bearing turned by 180°, but on the Earth it differs from that more the longer the route and the further it is from the equator: 288.0° instead of 231.4° for the trip from London back to New York.

Good to know

The straight line on the map is neither

On a web map in Web Mercator projection, a straight line between two points is a rhumb line only in direction, and its length in pixels is not proportional to distance. Use the bearings and distances in the panel, not a ruler on the screen.

Rhumb lines near the poles

A rhumb line spirals towards the pole and becomes very long at high latitudes; between two points far north on opposite sides of the pole it can be several times longer than the great circle. For polar routes the great circle is the only sensible choice.

Antipodes

Two points exactly opposite each other on the Earth have many shortest paths, so their initial bearing is not defined. The tool shows one of them; move a point slightly to get a meaningful bearing.