Compass Bearing Calculator

True, magnetic and grid — three norths, and they disagree

A bearing is meaningless until you say which north it is measured from. True north is the pole, the top of the map, and what every calculation on this page produces. Magnetic north is where the needle actually points, which is somewhere in the Canadian Arctic and moving. Grid north is the top of the map's grid squares, a degree or so off true on most national grids and normally ignorable. The angle between true and magnetic at your position is the declination, sometimes called variation on a marine chart, and it runs from zero to more than twenty degrees depending on where you are standing. Twenty degrees is a kilometre off course over three kilometres walked.

• East is positive. If declination is 10° east, magnetic north sits 10° clockwise of true north, so the same direction reads 10° lower on your compass. This tool subtracts east declination and adds west declination, which is the direction that catches people out.
• It changes. Declination drifts by a fraction of a degree a year and the map legend that told you what it was may be twenty years old. Look it up fresh.
• Your phone lies about it quietly. A phone compass usually shows true north after applying a declination model, but it will read wrong next to a car, a laptop, a steel door frame or a magnetic phone mount, with no indication that anything is off.

Why the initial and final bearings differ

The shortest route between two points on a sphere is a great circle, and a great circle crosses each meridian at a different angle. So the heading you start on is not the heading you finish on. Yerevan to London starts around 305° and finishes around 273° — over thirty degrees of turn, spread across the whole flight. Walk two kilometres and the difference is a rounding error, which is exactly why nobody notices it on land and why it matters the moment you are crossing an ocean.

The practical consequence: a great circle is not a line you can steer. Hold one compass heading and you are following a rhumb line, which is longer — sometimes much longer at high latitudes. Aircraft and ships follow a great circle by breaking it into legs and re-checking the bearing at each waypoint, which is the same thing this tool does if you run it twice with the halfway point.

Back bearing is not the same as the bearing home

The back bearing is your initial bearing plus 180°, and on a short route it is the way home. On a long one it is not: the bearing home is the final bearing plus 180°, because that is the direction you are facing when you get there. Both numbers are shown above so the difference is visible instead of assumed.

What this does not account for

Terrain, obstacles, airspace, traffic separation, currents, wind and anything else real. The earth is modelled as a sphere here rather than the slightly squashed ellipsoid it is, which puts the distance within about half a percent — fine for planning, not enough for survey work. And a magnetic bearing assumes a compass that is level, away from metal and reading a normal magnetic field, which is not true near iron ore, power lines or the inside of a vehicle.