Reference

Magnetic declination and true north

A magnetic compass points along the horizontal part of Earth’s magnetic field. That is not true north. The angle between them is called declination, it is different at every place on Earth, and it moves every year. Here is the correction, where the number comes from, a calculator that evaluates the current model for any place and date, and how large the error is if you skip it.

The correction

Declination is the horizontal angle between true north and the magnetic field vector, measured positive eastwards (British Geological Survey, An Overview of the Earth’s Magnetic Field). NOAA states the correction in one line: you compute the true bearing from a magnetic bearing by adding the magnetic declination to the magnetic bearing.

true bearing = magnetic bearing + declination

Declination is positive when magnetic north lies east of true north and negative when it lies west (NOAA NCEI, Magnetic Declination). Two worked examples, both computed from the World Magnetic Model 2025 through the BGS geomagnetic model web service for 21 September 2026:

Seattle, Washington (47.6062 N, 122.3321 W): declination +14.878°. A compass reading of 90.000° is a true bearing of 104.878°.
Eastport, Maine (44.9062 N, 66.9898 W): declination −15.605°. The same compass reading of 90.000° is a true bearing of 74.395°.

Those two places are 30.5° apart in declination. A compass that ignores declination is not slightly wrong in one place and right in another — it is wrong by a different amount everywhere.

Declination calculator (WMM2025)

This evaluates the World Magnetic Model 2025 in your browser from NOAA’s published coefficients — the same equations described further down this page. Nothing you enter leaves the page. Enter decimal degrees; a magnetic bearing is optional and is converted to true.

What it assumes. The main field only: WMM2025 to degree and order 12, valid 1 January 2025 to 31 December 2029, and nothing is given outside that window. It contains no crustal anomalies and no space weather, so local rock can move the real declination by degrees (see below). The date is taken at 00:00 UTC. The model wants height above the WGS 84 ellipsoid; using height above sea level instead changes the field by about 1 nT or less, according to the WMM2025 technical report. The ± figure is NCEI’s one-standard-deviation error model for declination, given further down. The code was checked against NCEI’s twelve official WMM2025 test values (declination, inclination, all five intensities and all their rates of change match to the printed precision) and against the technical report’s high-precision worked example (declination agrees to better than one millionth of a degree). For the places in the table below it agrees with the BGS figures to within 0.001° and 1 nT.

Declination is different everywhere, and it drifts

Every figure in this table is output from the World Magnetic Model 2025, evaluated at sea level for 21 September 2026 through the British Geological Survey’s geomagnetic model web service. H is the horizontal field intensity — the part of the field a compass actually uses — in nanotesla (nT, one billionth of a tesla). The last column is the rate at which declination is changing, in arcminutes per year (one arcminute is 1/60 of a degree).

Place	Declination	H (nT)	Drift (arcmin/yr)
Seattle, WA	+14.878°	19,064	−7.4
Casper, WY	+8.499°	19,593	−5.0
Houston, TX	+1.711°	24,135	−4.8
New Orleans, LA	−1.584°	23,987	−4.8
Miami, FL	−7.383°	25,278	−5.1
Eastport, ME	−15.605°	19,998	+6.9
London, UK	+1.200°	19,553	+10.2
Singapore	+0.234°	41,053	+1.9
Anchorage, AK	+13.999°	15,184	−16.9
Resolute, Canada	−14.889°	3,361	+37.0

The drift column is why a declination value printed in a book goes stale. At Anchorage the rate is 16.9 arcminutes a year; kept up for twenty years, that is 5.6°. At Resolute it is 37.0 arcminutes a year — 12.3° over twenty years at the same rate. (The rates themselves change unpredictably, which is why the model is replaced every five years.) Somewhere between Houston and New Orleans the declination passes through zero; that line, where magnetic and true north agree, is called the agonic line, and it moves too.

The field can also change faster than the five-year model cycle assumes. On 4 February 2019 NCEI released an out-of-cycle update to the World Magnetic Model, ahead of the scheduled WMM2020 release. The technical note NCEI and BGS published with it gives the reason: fast fluid flow in Earth’s outer core, especially in the north polar region, was about to push the model’s grid-variation error past the one-degree limit in its specification. NCEI’s announcement described the north magnetic pole as moving quickly away from the Canadian Arctic toward Siberia, and its FAQ gives the rate found by the most recent survey as approximately 55 km per year, north-northwest.

What the World Magnetic Model actually is

The World Magnetic Model (WMM) is a mathematical description of the large-scale part of Earth’s internal magnetic field, which is almost entirely the field generated in the core. WMM2025 was released on 17 December 2024 and expires on 31 December 2029. NCEI records it as produced by the United States’ National Geospatial-Intelligence Agency and the United Kingdom’s Defence Geographic Centre, and jointly developed by NCEI and the British Geological Survey.

It is a spherical harmonic model — the field is written as a sum of standard wave-like patterns over a sphere, in the same way a sound can be written as a sum of pure tones. The model states a magnetic scalar potential V, and the field is its gradient:

V(λ, φ′, r, t) = a Σ_n=1..12 Σ_m=0..n (a/r)ⁿ⁺¹ [ g_n^m(t) cos(mλ) + h_n^m(t) sin(mλ) ] P̄_n^m(sin φ′)

B = −∇V

Here a is the geomagnetic reference radius of 6371.2 km, r is distance from Earth’s centre, λ is longitude, φ′ is geocentric latitude, and P̄_n^m are the Schmidt semi-normalised associated Legendre functions. The whole model is 168 numbers — the Gauss coefficients g_n^m and h_n^m to degree and order 12 — plus 168 more giving how fast each one is changing, which makes the 336 coefficients the technical report counts. Time enters linearly:

g_n^m(t) = g_n^m(t₀) + (t − t₀) ġ_n^m(t₀)

That straight-line extrapolation is why the model has a five-year life: it drifts away from the real field as the epoch ages. The latitude you enter is geodetic (the one on a map), so the calculation first converts it to geocentric latitude and radius on the WGS 84 ellipsoid, and rotates the result back at the end. Evaluating it gives three components in the local frame — X north, Y east, Z down — and everything else follows from them:

H = √(X² + Y²) F = √(H² + Z²) D = arctan(Y / X) I = arctan(Z / H)

The arctangent for D is taken in the correct quadrant, so declination runs from −180° to +180°. Those four are worth checking rather than trusting. For Seattle the model returns X = 18,425 nT, Y = 4,895 nT, Z = 49,025 nT. Putting those through the formulae gives H = 19,064.1 nT, F = 52,601.3 nT, D = 14.8782° and I = 68.7506°, against the service’s own H = 19,064, F = 52,601, D = 14.878° and I = 68.751°. Agreement to the last digit the service prints.

How big the error is on the ground

An angular error turns into a distance error through the tangent. Cross-track offset after travelling a distance d on a bearing that is wrong by ε is d × tan(ε).

Bearing error	Offset at 1 km	Offset at 10 km
0.5°	8.7 m	87 m
1°	17.5 m	175 m
2°	34.9 m	349 m
8.5° (Casper declination)	149 m	1,495 m
15.6° (Eastport declination)	279 m	2,792 m

Uncorrected declination in the continental United States is a first-order error, not a refinement. At Eastport it puts you 279 m off line in the first kilometre.

How good the model is, and where it stops working

NCEI publishes an explicit error model. The one-standard-deviation uncertainty in declination is not a constant — it depends on how strong the horizontal field is where you are standing:

σ_D = √( 0.26² + (5417 / H)² ) degrees, with H in nT

For the same table of places: 0.385° at Seattle, 0.380° at Casper, 0.292° at Singapore, 1.633° at Resolute. The calculator above prints this figure beside every result. The companion figures are 0.20° for inclination and 138 nT for total intensity.

The 5417 / H term is the whole story about the poles. As the horizontal field collapses, the direction it points becomes meaningless. NCEI defines a blackout zone around each magnetic pole where H < 2000 nT and compasses should not be relied on for navigation, and a caution zone where 2000 ≤ H < 6000 nT. At the 6000 nT boundary the formula gives 0.94°; at 2000 nT it gives 2.72°. The calculator flags both zones.

Three things the WMM does not contain, in NCEI’s own words: the effects of Earth’s crust and upper mantle, the ionosphere, and the magnetosphere. The crustal part is the one that bites on land. NCEI reports local anomalies that can exceed 10°, and anomalies of three or four degrees that are not uncommon, though usually over small areas; its FAQ gives an example in Minnesota of a mapped area at 16° east declination with anomalies a few miles away at 12° west. No global model can predict those, because they are made by the rock under your feet.

The other two are covered on the magnetic interference page, along with the far larger errors produced by steel and wiring within a metre of the phone.

Doing this on a phone

Android hands an app a magnetic azimuth and leaves the declination correction to the app. A true bearing means evaluating a geomagnetic model at your position and date and adding the result, which is why a compass app that never asks for your location cannot give you true north for where you are standing.

Bearing does that on the phone, from your position and the current date, using Android’s built-in geomagnetic model (the GeomagneticField class), so true north works with no network connection. Which model that is depends on the phone’s Android version, and each is extrapolated past its end date: Android’s source carries WMM2020 from Android 12 on, WMM2015 in Android 9 to 11, and WMM2010 in Android 8. Computed from those coefficients for 21 September 2026, the Android 12 model differs from WMM2025 by 0.07° at Casper and 0.09° at Seattle — well inside the model’s own ±0.38° there — but by 1.2° at Resolute, where the field is changing fastest. On Android 9 to 11 the difference is 0.23° at Casper and 0.40° at Seattle, and on Android 8 it is 0.70° and 0.89°. The calculator on this page uses WMM2025. Bearing carries one banner ad, and removing the ad is a $2.99 one-time purchase with no subscription.