Magnetic Declination Calculator

A compass does one thing faithfully. A small magnetized needle turns on a pivot until it lines up with the horizontal part of the magnetic field where it rests. Nothing in that sentence mentions the North Pole.

That is the whole difficulty. Maps are drawn against true north, the direction along a line of longitude toward the axis the planet spins on. The needle answers to something else: a field made deep in the Earth’s fluid outer core, lopsided, tilted against the rotation axis, and never still. Over most of the planet the two directions roughly agree, which is why the compass became a navigation instrument at all. They rarely agree exactly, and the angle between them is called magnetic declination. Sailors and pilots call the same angle variation.

The needle follows a field, not a place

A common picture has the needle pointing at the north magnetic pole like a finger. It does not. It points along the horizontal trace of the field where you are standing, and a mile or two away that direction can be different. Follow the needle faithfully and you would reach the magnetic pole in the end, but by a curved route, not the shortest one.

The convention is simple and worth memorizing once. Declination is positive when magnetic north lies east of true north, negative when it lies west. Inclination, the angle the field makes with the horizontal, is positive when the field points down into the ground, as it does in the far north.

The angle has been a known nuisance for a long time. Natural Resources Canada dates the first known determination to China in about 720 AD, and the first precise European measurement to Georg Hartman in Rome in 1510. In 1700 Edmund Halley had the idea of drawing declination as contour lines on a chart of the Atlantic, and charts of that kind have been made ever since. The lines on a modern one bend and loop because the field itself is irregular.

One other word gets confused with it. Deviation is the error added by iron in the ship, aircraft or car around the compass. It belongs to the vehicle. Declination belongs to the planet.

A field written as 168 numbers

The modern answer to “what is the declination here, today” is a model, not a chart. The World Magnetic Model is produced by NOAA’s National Centers for Environmental Information and the British Geological Survey for the United States and United Kingdom defense mapping agencies, and it is the standard used for navigation by both militaries, by NATO and by the International Hydrographic Organization. The same model sits inside phones.

Its form is compact. The field outside the core can be written as the gradient of a potential, and that potential is expanded in spherical harmonics, functions long used in geodesy as well as geomagnetism. The standard model stops at degree and order 12, which takes 168 Gauss coefficients for the main field and a matching set for its rate of change. Each coefficient is given to a tenth of a nanotesla.

To use it you convert a latitude on the WGS 84 ellipsoid to a geocentric one and move every coefficient forward from the model’s base date by its yearly rate. Then you sum the series for the north, east and down components and rotate the result back to the local horizontal. Declination is then the angle whose tangent is the east component over the north component. The agencies publish a table of test values for checking the work, and software that agrees with the model equations to within a tenth of a nanotesla may carry the model’s name.

The measurements behind the coefficients come from the European Space Agency’s three Swarm satellites and from around 160 ground observatories. Signals from small-scale crustal rock and from currents in the upper atmosphere are noise for this purpose and are separated out during the fitting. What remains is the long-wavelength field of the core, with a resolution of roughly 3300 kilometers at the equator. The 2025 release came with a high-resolution companion that reaches about 300 kilometers, and the agencies encourage systems that can carry its much larger coefficient set to use it.

Why the model has a date on it

The core is a moving liquid, so the field drifts. The model captures the drift with one number per coefficient, a straight-line rate, and that is why it is good for only so long. The rate itself changes in ways nobody can forecast far ahead. NOAA puts it plainly: the model is very accurate on the day it is released and grows less so, and beyond five years the errors rise progressively. A new set of coefficients therefore appears every five years. The current one, WMM2025, was released on 17 December 2024 and runs from 2025.0 to 2030.0.

The drift is not uniform. Natural Resources Canada gives the example of Yellowknife, where declination changes by more than one degree every three years, against Ottawa, where the yearly change is almost zero. The north dip pole, which the 2025 model places at about 85.76 degrees north, is itself expected to travel roughly 35 kilometers a year, and near it declination changes sharply over short distances.

This is also why the declination printed in the margin of a paper map is a historical fact, not a current one. Topographic maps give the value for the year of printing and often an annual change beside it. You can multiply the change by the years elapsed, and for a recent map the result is fine. For an old one it is not, because the annual change does not stay constant.

Converting a bearing without losing the sign

Here the arithmetic is one line and the mistakes are all in the direction. With east declination counted as positive, a true bearing equals the magnetic bearing plus the declination. Going the other way, the magnetic bearing equals the true bearing minus the declination. East adds on the way to true and subtracts on the way back. West does the opposite.

Take Los Angeles, at 34.05 degrees north and 118.24 degrees west, on 4 October 2026. The 2025 model gives a declination of 11.34 degrees east, changing by about 0.08 degrees a year toward the west. A compass that reads 90 degrees there is pointing along a true bearing of 101.3 degrees. A line that the map says runs at 101.3 degrees true must be walked at 90 degrees on the compass.

Now New York, at 40.71 degrees north and 74.01 degrees west, on the same day. The declination is 12.46 degrees west, which is negative. The same compass reading of 90 degrees is a true bearing of 77.5 degrees. Apply the rule with the wrong sign in either city and you are wrong by twice the declination, more than 20 degrees, which over ten kilometers puts you about four kilometers off your line.

Maps add a third north. Grid north is the direction of the vertical lines of a plane grid such as Universal Transverse Mercator, and it differs from true north because a curved surface has been flattened. The angle between grid north and magnetic north, sometimes called grivation or the grid magnetic angle, is the declination with the grid’s convergence taken into account. A bearing measured against grid lines needs that angle, not the plain declination.

What a model of the core cannot know

The model’s own error estimate is modest in most places. For declination it is the square root of 0.26 degrees squared plus 5417 divided by the horizontal field in nanotesla, squared. At Los Angeles that comes to about 0.35 degrees. Where the horizontal field is weak the second term takes over.

That figure describes the field the model was built to describe. It does not cover the rock under your feet. NOAA notes that local anomalies of 3 or 4 degrees are not uncommon over small areas, and that anomalies exceeding 10 degrees are rare but real. One mapped area in Minnesota shows 16 degrees east with 12 degrees west a few miles away. No global model of degree 12 can see that.

Nor does it cover the sky. During a geomagnetic storm, currents in the ionosphere and magnetosphere disturb the field on the ground for hours. In southern Canada, Natural Resources Canada finds that a compass user will seldom see swings larger than 2 degrees, about the precision of an ordinary orienteering compass. In the Northwest Territories the same swing happens on more than one day in four.

Near the magnetic poles the instrument itself gives up. The field there is nearly vertical, so the horizontal part that steers a needle is feeble. The model marks a blackout zone wherever the horizontal intensity falls under 2000 nT, where its declination values are not accurate and a compass should not be relied on. Around that it marks a caution zone, up to 6000 nT.

So treat the number as what it is: a careful, dated estimate of the large-scale field. Correct your bearings with it. Check its date. Keep the compass away from steel, and where the ground or the sun is known to interfere, trust a second method.