Great-Circle Distance & Bearing Calculator
Great-circle distance, initial and final bearing and midpoint of two latitude/longitude points in decimal or DMS, in km, miles, nautical miles and meters.
Point A
Point B
Type decimal degrees, or degrees, minutes and seconds with N, S, E or W.
Paste “latitude, longitude” or a map link with the coordinates in it (Google Maps, OpenStreetMap) into either box of a point to fill both.
Kilometers: 343.56 Miles: 213.48 Nautical miles: 185.51 Meters: 343556 On the WGS 84 ellipsoid (Vincenty): 343.92 km Initial bearing: 148.1° (SSE) Final bearing: 150° (SSE) Rhumb line, one heading: 343.57 km, 149.1° (SSE) Midpoint: 50.188595, 1.146618 Read as: Point A 51.5074, -0.1278 · Point B 48.8566, 2.3522
Initial bearing is the compass heading to set off on from point A. On a long route the heading keeps changing along the great circle, so it is the starting direction, not the whole way.
Final bearing is the heading on arrival at point B.
A rhumb line keeps one compass heading the whole way — what a ship steers without re-plotting its course — and is longer than the great circle except along a meridian or the equator.
The Earth is taken as a sphere of radius 6,371 km. The real Earth is slightly flattened, and against it that is off by at most 0.56% — on this route, at most 1.9 km.
Great-circle distance, not a straight line on a map
Enter the latitude and longitude of two points — in decimal degrees, or in degrees, minutes and seconds with N, S, E or W — and this tool returns the great-circle distance between them — the shortest path over the curved surface of the Earth. It is computed with the haversine formula on a sphere of mean radius 6371 km, and shown at once in kilometers, miles, nautical miles and meters. Beside them, the same distance is worked on the WGS 84 ellipsoid with Vincenty’s formula — the flattened Earth GPS uses — as a check on the sphere. London to Paris, for example, is about 343.6 km (213.5 mi). This is the as-the-crow-flies distance; a real road or flight route is longer because it follows roads, airways and detours. Paste a whole point — “latitude, longitude”, or a Google Maps or OpenStreetMap link with the coordinates in it — into either box of a point and both of its boxes fill.
Initial bearing and compass direction
Alongside the distance the tool shows the initial bearing: the heading in degrees from 0 to 360, measured clockwise from true north, that you set off on to follow the great circle from point A to point B. Because a great circle curves across the globe, this heading gradually changes along the way, which is why long routes drawn on a flat map look like arcs. The nearest point of the sixteen-point compass (N, NNE, NE, ENE, E and on round to NNW) appears next to the angle so you can read the direction at a glance — London to Paris reads SSE. The final bearing under it is the heading you arrive at point B on. The rhumb line comes after it: the one compass heading that gets you there without turning, and its length, which is longer than the great circle except along a meridian or the equator — the route a ship steers without re-plotting its course. The answer also gives the midpoint, the half-way point along the great circle, and shows each point as it was read. Everything is calculated locally in your browser, so your coordinates never leave your device.
Frequently asked questions
What is the difference between great-circle distance and driving distance?
Great-circle distance is the shortest path over the surface of the Earth, as the crow flies. Driving or flying distance is longer because it follows roads, airways and terrain rather than a straight arc.
Which Earth radius and formula does it use?
It uses the haversine formula on a sphere of mean radius 6371 km. Against the real, slightly flattened Earth that sphere is off by at most 0.56% — about half a percent — and the line under the answer says how many kilometers that comes to on your route; the ellipsoidal distance on WGS 84 (Vincenty), which the page gives as well, differs from the sphere’s by no more than that.
What does the initial bearing tell me?
It is the compass heading, 0 to 360 degrees clockwise from true north, to start out on toward the destination along the great circle. The heading changes as you travel, so it is the starting direction rather than a fixed one; the final bearing shown under it is the heading on arrival at point B.
Can I enter degrees, minutes and seconds, or get nautical miles?
Yes. Each box takes signed decimal degrees, or degrees, minutes and seconds with a hemisphere letter before or after — 51°30′26″N or N 51 30 26 — and the answer shows each point as it was read, so a slip is easy to spot; an entry it cannot read is quoted back in the error. Nautical miles get their own line beside kilometers, miles and meters, and the midpoint is the half-way point along the great circle, or none when the two points are exactly opposite each other on the globe.
Can I paste a whole coordinate pair or a map link, and which way am I heading on arrival?
Yes. Paste “latitude, longitude” — split by a comma, a semicolon or a space — a degrees-minutes-seconds pair, or a map link with the coordinates in it (a Google Maps pin or @ link, a ?q= link, an OpenStreetMap link, a geo: link) into either box of a point, and both boxes fill; a single coordinate goes into that box only. A short link with no coordinates in it cannot be read without asking the map service, so it is left alone. Under the initial bearing, the final bearing is the heading on arrival at point B.
Does it give a sixteen-point compass direction, and the rhumb line?
Yes. Each bearing is labelled with the nearest of the sixteen compass points, so London to Paris reads SSE rather than S. “On the WGS 84 ellipsoid (Vincenty)” works the distance on the flattened Earth GPS uses, a check on the sphere, and says “not settled” when the points are almost opposite each other. “Rhumb line, one heading” gives the single compass heading that gets you there without turning, and that route's length, which is longer than the great circle except along a meridian or the equator.