geoprimsField-grade geospatial math

True north vs. magnetic north

What separates true, magnetic, and grid north, how the World Magnetic Model gives the angle between them, and how to convert a course without getting the sign backward.

For pilots · updated 2026-09-23

True north is the direction along a meridian to the geographic North Pole. Magnetic north is the direction a compass needle points, along the horizontal part of Earth’s magnetic field. The angle between them is magnetic declination, which pilots call variation. It is east when magnetic north lies east of true north and west when it lies west, and it changes with place and, slowly, with time.

Why it matters

Charts, METARs, TAFs, and winds aloft give directions in degrees true. Your compass, heading indicator, runway numbers, and the wind from the tower are magnetic. Every time a direction crosses from one world to the other, you add or subtract the variation. In Boulder, Colorado, it is 7.7° E, and at Boston’s Logan airport it is 14° W. Getting the sign wrong doubles the error instead of removing it.

How it is worked out

Earth’s main field is described by a model: a set of coefficients that give the field’s direction and strength anywhere, at any date the model covers. The standard one for navigation is the World Magnetic Model (WMM), made by the US National Geospatial-Intelligence Agency and the UK Defence Geographic Centre, with NOAA and the British Geological Survey. It is also built into Android and iOS phones. A new version comes out every five years, and the current one, WMM2025, was released in December 2024.

The field drifts, so the model carries a rate of change for each coefficient. This slow drift is called secular variation. For dates back to 1900, the International Geomagnetic Reference Field (IGRF), from the International Association of Geomagnetism and Aeronomy, does the same job. Its 14th generation was finalized in November 2024.

From the model at your place and date, the magnetic declination tool finds the north and east parts of the horizontal field. Declination is the angle between them: positive (east) when the field points east of true north.

A worked example

Boulder, Colorado, at 1,655 m, on September 18, 2026, with WMM2025:

Quantity Result
Declination (variation) 7.7° E (7.67°)
Change per year 0.081° toward the west
Model uncertainty about 0.37°
Inclination (dip) 66.02°

A true course of 090° there becomes 082.3° magnetic, from the true and magnetic bearing tool using the model value.

The same place over time, from IGRF-14:

Date Declination at Boulder
1950 14.1° E
2000 10.6° E
2026 7.7° E

In 76 years, magnetic north as seen from Boulder has swung more than 6° closer to true north. A chart printed a few years ago can be off by a few tenths of a degree, and a very old map by several degrees.

East is least, west is best

The memory aid is for going from true to magnetic. Subtract an easterly variation. Add a westerly one.

True course Variation Magnetic course
090° 7° E 083°
090° 12° W 102°

To go the other way, from magnetic to true, reverse it: add east, subtract west. NOAA puts it the same way from the other side: add the declination to a magnetic bearing to get a true bearing, with east counted positive. With 12° W, a magnetic 102° gives a true 090°.

Grid north and grivation

A third north comes from the map itself. On a UTM or UPS grid, grid north is the direction of the grid’s vertical lines. The angle from true north to grid north is the convergence of meridians, which the NGA also calls grid declination. It is small near a UTM zone’s center line and grows toward the zone edges and the poles.

Grid variation, or grivation, is the angle from grid north to magnetic north: declination minus convergence. It is what you apply when you navigate by a map grid with a compass. In Boulder, which is in UTM zone 13N, convergence is −0.1739°, and the grivation tool gives 7.8° E, barely different from the declination. Near the pole it is another story. At 86° N, 45° E on the polar grid (UPS north), declination is 45.32° and convergence 45°, so grivation is only 0.3° E. Declination alone would be off by 45°.

Near the magnetic poles the compass itself becomes unreliable. At that polar point the horizontal field is 3,230 nT, under the 6,000 nT limit the WMM uses to flag a caution zone, and the tool warns that compass readings may be degraded.

Common mistakes

Where the numbers come from

The models are WMM2025 and IGRF-14, both published through NOAA’s National Centers for Environmental Information. The declination sign convention follows NOAA, and the convergence definition follows the NGA’s standard for the universal grids. The magnetic declination tool gives declination, its yearly change, and the model’s uncertainty for any place and date. The true and magnetic bearing tool converts a bearing with a chart variation, the model, or both side by side. For navigation, use the variation printed on your current chart.

Try it: Magnetic declination

The calculator below is the real tool, running its worked example. Change any value; nothing leaves your device.

7.67°

Magnetic declination is 7.7° E, moving 0.081° west each year. The model is good to about 0.37°.

Declination
Declination uncertainty
Annual change
Inclination (dip)
Horizontal intensity H (nT)
North component X (nT)
Provenance
Computed by
geodesy.magnetic.declination 1.0.1, core 0.1.0
Model
WMM2025 main field, degree 12
Accuracy
Matches all 100 NCEI WMM2025 test values (declination and inclination to their printed 0.01°, intensities within 0.001 nT). The model itself is good to about 0.3° of declination away from the poles; local crustal anomalies of several degrees are not modeled.
Reference data
version WMM2025 (2024-11-13) of a reference dataset
Notes
None
Cites
NOAA National Centers for Environmental Information and British Geological Survey, The US/UK World Magnetic Model for 2025-2030: Technical Report; International Association of Geomagnetism and Aeronomy (IAGA), Working Group V-MOD, International Geomagnetic Reference Field: the fourteenth generation

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