GPS Coordinates and True Bearings, Demystified for Sign Makers
If you're making directional signs, you don't need to learn geodesy. You need just enough of it to put the right number on a plate. This article covers the minimum useful theory: what coordinates actually represent, what a bearing is, and why the same destination can have three different "directions" depending on how you measure it.
By the end you should be able to read any GPS coordinate, understand the angle on every plate Tervika produces, and know when a great-circle distance is honest and when it's misleading.
What latitude and longitude really are
The Earth is roughly a sphere. To name a point on it, you need two numbers. The convention we've used for centuries is latitude (how far north or south you are from the equator) and longitude (how far east or west you are from a reference meridian).
A few useful facts:
- Latitude runs from −90° (south pole) to +90° (north pole). The equator is 0°. Stockholm is around 59° N. Cape Town is around 34° S, written as a negative latitude.
- Longitude runs from −180° to +180°. The reference meridian — 0° longitude — runs through Greenwich in London, by historical accident more than physical necessity. Positive numbers are east of Greenwich, negative numbers are west.
- One degree of latitude is about 111 km, everywhere. This is roughly true because the Earth is approximately a sphere and meridians of longitude are great circles.
- One degree of longitude is 111 km only at the equator. It shrinks to zero at the poles. At 60° N — Stockholm, Oslo, southern Alaska — one degree of longitude is only about 56 km.
Tervika stores coordinates as decimal degrees, like 59.32938, 18.06871. This is the format GPS receivers and most map services use natively. The older sexagesimal notation — 59° 19' 45.77" N, 18° 04' 7.36" E — encodes the same point in degrees, minutes, and seconds. They're interchangeable; decimal degrees are easier to type and to do arithmetic with.
What "bearing" means
A bearing is the direction from one point to another, measured as a clockwise angle from a reference direction. Three things follow from this definition:
- A bearing is a direction, not a distance.
- A bearing is directional. The bearing from London to New York is not the same as the bearing from New York to London. (We'll come back to this — it's a surprise to most people.)
- A bearing depends on what you call "north."
That last point is where most signs go wrong. There are three plausible definitions of north, and they don't agree.
True north, magnetic north, and grid north
True north is the geographic north pole — the point where the Earth's rotation axis intersects the surface. A line of longitude is, by definition, a line that points at true north.
Magnetic north is a wandering point in northern Canada (currently drifting toward Siberia) where the Earth's magnetic field dips vertically into the ground. Compass needles point at magnetic north, not true north. The angle between the two — magnetic declination — depends on where you are. In central Europe it's a few degrees east. In western North America it can be more than 15° east. In eastern Greenland it's more than 30° west.
Grid north is the "up" direction on a map projection — typically slightly different from true north because most maps stretch the world onto a flat grid. Grid north is rarely relevant for sign making, but if you're working from a printed paper map and aligning your sign to the map's edge, you may be aligning to grid north without realising it.
For sign work, always use true bearings unless you have a specific reason not to. Tervika calculates true bearings from coordinates, which means a plate showing 247° is genuinely 247° from true north when you stand at the sign with your back to the post and look out along the arrow. If you align the sign using a phone's magnetic compass, you have to add or subtract the local declination. The compass and the plate are speaking different languages.
A specific reason you might not use true bearings: when you're embedding a sign in an existing wayfinding system that's already calibrated to magnetic. This is rare in private signs and common in some hiking trail networks.
The bearing from London to New York is not the bearing from New York to London
The shortest path between two points on a sphere is a piece of a great circle — a circle whose plane passes through the centre of the Earth. The equator is a great circle. Every meridian of longitude is a great circle. Lines of latitude (other than the equator) are not.
A great circle path looks straight on a globe but bends on a flat map. The classic example: the shortest line from London to New York passes north over Scotland, southern Greenland, and Newfoundland. On a Mercator projection it looks like an arc, but on the actual planet it's the straight line.
This means the bearing of New York from London is not 270° (due west). It's around 287° — slightly north of west — because the great-circle path heads north before bending south.
It also means the bearing in the other direction is asymmetric. From New York, the great-circle bearing back to London is around 51° — well north of east. If you fly from New York to London, you turn left to depart, and the destination is behind your right shoulder by the time you cross the mid-Atlantic.
For nearby destinations — within a few hundred kilometres — this asymmetry is small enough to ignore. For continental and intercontinental destinations, it's significant. Tervika calculates true initial great-circle bearings, which is the right number to put on a plate: it's the direction your finger would have to point at the moment you set off.
Great-circle vs. rhumb-line distance
Two destinations, two ways to measure the distance between them.
Great-circle distance is the shortest path along the Earth's surface — the arc of the great circle joining the two points. This is what aircraft fly and what ships try to follow.
Rhumb-line distance is the path you travel if you keep a constant compass heading. It's a longer path, but it's much easier to navigate by — which is why old ship's charts use rhumb-line ("loxodromic") sailing.
For neighbouring destinations the two distances are almost identical. Stockholm to Helsinki is about 393 km along the great circle and about 394 km along the rhumb line — the difference is rounding error. For long routes the gap widens. Stockholm to Tokyo is about 8,200 km along the great circle and around 9,800 km along the rhumb line. That's a 1,600 km difference between the two ways of asking "how far?"
For a fingerpost sign, the great-circle distance is the right one almost always. It's the honest answer: how far away is that place, in straight-line surface distance? The rhumb-line distance is an answer to a different question — how far would I travel to get there at a constant heading — which is rarely what someone reading a sign wants to know.
The minimum you need to remember
If you take only four things away:
- Decimal degrees are the friendliest format. They're what GPS uses, and they make arithmetic possible without converting back and forth from sexagesimal.
- Bearings are clockwise angles from a reference direction. Tervika's plates use true bearings, measured from geographic north.
- Magnetic and true are different by your local declination. Don't mix them. If you're aligning a sign with a magnetic compass, factor in the declination at your sign's location.
- Great-circle distance is the honest distance. It's what your sign should display, and it's what Tervika uses by default.
The geometry of the planet is fixed. The only choice you make as a sign maker is whether to be honest about it.