How beam headings work
Radio signals travel along great circles, the shortest route over the surface of a sphere. A great circle path is rarely what you'd expect from a flat map. From London, the short path to Tokyo heads north-north-east at about 32°, over Scandinavia and Siberia rather than east across Asia, and the beam heading to Los Angeles is about 312°, over Greenland and northern Canada.
The calculator works out the initial bearing of the great circle from your station to the other one, measured clockwise from true north. That's the direction to point a beam or set a rotator.
Distance = 2R × asin √( sin²(Δφ/2) + cos φ₁ × cos φ₂ × sin²(Δλ/2) )
Here φ is latitude, λ is longitude and R is the Earth's mean radius, 6,371 km.
Short path and long path
Every pair of stations is joined by two great circle routes: the short path, and the long path the other way round the world, pointing in the opposite direction. The long path is always 180° from the short path, and the two add up to about 40,000 km. Long path is worth trying when the short path is closed or crosses the polar regions during a geomagnetic storm. From the UK, VK and ZL are often worked by long path on 20m and 40m around sunrise and sunset, when much of the route is in darkness or along the grey line.
Reading the azimuthal map
The azimuthal equidistant map puts your station in the centre. Distances and directions from the centre are true, so the angle of a straight line from you to anywhere on the map is the beam heading, and its length is the distance. The price is that shapes far from the centre are badly stretched, and the outer edge is the single point on the opposite side of the world, your antipode. Radio amateurs have pinned these maps above their rotators for decades. Download yours as an image to print.
True north, magnetic north and your rotator
Headings are given from true north, which is what you want when your rotator is calibrated to true north from a known landmark or the sun. If you line up the beam with a compass, use the magnetic heading, which corrects for magnetic declination at your location using the World Magnetic Model 2025. In the UK the difference is currently small, under about 2°, but in much of North America it's 10° or more.
Callsigns and countries
When you type a callsign or prefix, the calculator finds its DXCC entity from the AD1C country file, the same data most logging programs use, and points to the centre of that country. For the US, Canada, Australia and Japan it uses the call area digit to pick a region, but US callsigns stay the same when people move, so treat those as approximate. For an exact heading, ask for the other station's locator. Most stations give it on request, and FT8 sends it in every CQ.
Questions
What is my beam heading to Australia from the UK?
From London the short path to Sydney is about 60°, roughly north-east, and the long path is about 240°. The distance is about 17,000 km by short path.
What's the difference between short path and long path?
The short path is the shortest great circle route. The long path goes the other way round the world, 180° from the short path. Long path signals sometimes beat the short path, especially when the long path is mostly in darkness or along the grey line.
Do I need to correct for magnetic declination?
Only if you align your antenna with a magnetic compass. Rotators set up to true north use the true headings. The calculator shows both.
Why does the map look distorted?
An azimuthal equidistant map keeps directions and distances from the centre correct, which is exactly what you need for beam headings. Everything else, especially shapes near the edge, is stretched.
Can it look up an individual callsign's address?
No. It identifies the country, and the call area for some large countries. Exact addresses need a paid callsign database, so ask the other station for their locator for a precise heading.