Magnetic declination: converting between true and magnetic bearings

Magnetic declination is the angle between true north and magnetic north at one place. To turn a compass bearing into a true bearing, add the declination when it is east and subtract it when it is west. Declination changes with location and over time, so take the value for your place and date from a current model. The conversion is one addition, and the sections below show it with hypothetical values, the size of the error a wrong value causes, and where to find a current figure.

What declination is

A compass needle points to magnetic north, not to geographic (true) north. The angle between the two, measured at your position, is the declination. Wikipedia gives the convention: declination is positive when magnetic north is east of true north, and negative when it is west. NOAA’s model labels the same quantity “Geomagnetic Declination (Magnetic Variation)”, abbreviated D (DEC).

Converting a bearing from magnetic to true

The rule has one sign convention. East declination is added and west declination is subtracted, which gives the true bearing from the magnetic one. The reverse conversion uses the same numbers with the sign flipped.

true bearing     = magnetic bearing + declination   (east positive, west negative)
magnetic bearing = true bearing − declination

The sign follows from the picture. If magnetic north lies 10° east of true north, a direction 50° from magnetic north lies 60° from true north. A west value works the other way: with 4° west, a magnetic 50° becomes a true 46°.

The two declinations in the table are invented for arithmetic. They are not values for any real place, and the table should not be used as one.

How a small bearing error grows with distance

A bearing error does not stay small. If you walk a distance d on a heading that is off by an angle e, you finish d × sin(e) to one side of the line you meant to walk. The sideways error grows in proportion to the distance, so a small angle matters on a long leg.

sideways offset = distance × sin(error)
1 km at 1°:   1,000 × sin 1°  = 17.5 m
1 km at 5°:   1,000 × sin 5°  = 87.2 m
1 km at 10°:  1,000 × sin 10° = 173.6 m
3 km at 10°:  3,000 × sin 10° = 520.9 m

A 10° error over 3 km puts you more than half a kilometre from the intended line. That is enough to miss a path junction or a small lake that a plan depended on.

Finding a current declination value

NOAA’s National Centers for Environmental Information publish the World Magnetic Model. The NCEI product page says the model is updated every five years to address changes in Earth’s magnetic field. The current version, WMM2025, was released on 17 December 2024 and will remain valid until late 2029. NCEI’s magnetic field calculators include a declination calculator, which gives the value for a location you choose.

The model gives declination for a place and a date, so the same location needs a fresh reading for a different year. Use the value for the date of your trip rather than an old printed figure. A declination printed on a map or in an old note may no longer match the field, so check the date that goes with any value you use.

Grid north on a printed map

A map’s grid lines do not point to true north everywhere. A projected grid, such as UTM or a national grid, has its own north, and the angle between grid north and true north is called grid convergence. Many maps print a diagram in the margin that shows true, magnetic and grid north with the angles between them. Read the diagram on your own sheet, because these angles differ between maps and should not be carried from one sheet to another.

The slope from contour lines guide works from the same kind of sheet, and a bearing taken across its contours needs the same care about which north it refers to. When a bearing is taken from a map, state which north it refers to. A bearing on grid north needs a different correction from a bearing on true north, and mixing them is a common source of a large error.

Bearings for the sun and the solar tool

The NOAA solar position calculator measures azimuth clockwise from true north. The Sun & daylight tool takes its sight bearing in degrees true, so a compass reading in magnetic degrees must be converted before it goes into the tool. The link below uses a hypothetical 10° east declination to show the arithmetic. Bearings matter for the sun as well as for routes: the sun direction guide uses a true bearing to say where the morning light reaches an open end, and the sunset guide uses the same tool for the time of dusk.

true bearing = magnetic + declination = 50° + 10° = 60°

Phone compasses and paper backups

Compass apps on phones may show magnetic or true bearings, depending on their settings, and they need calibrating before use. Check which one the app is showing before you transfer a bearing to a map or to a tool. A paper compass and a written note of the declination and its date are a simple backup, because a phone can lose its battery or its calibration on a long trip. The ten essentials guide is the place to check the rest of the kit that goes with navigation.

Declination matters most when you set a bearing and walk it, for example to reach a ridge line in cloud. The offline trip planning checklist is the place to note the declination and its date, and the map scale guide explains how to measure the distance along that bearing on the map.