Magnetic Declination Inclination From Coordinates Calculator

Declination and inclination are the two angles that orient the geomagnetic field vector at a point. Declination is the horizontal angle between true north and magnetic north, counted positive east, and inclination is the angle the field lines make with the horizontal plane, positive downward in the northern hemisphere. The dipole approximation used here yields a compact relation for inclination: the tangent of the dip equals twice the cotangent of the angular distance from the geomagnetic pole, equivalently twice the tangent of magnetic latitude. Declination then follows from spherical trigonometry connecting the observation point, the geographic pole and the geomagnetic pole. Total intensity in the same approximation gives roughly 30,000 nT at the magnetic equator and about 60,000 nT at the poles, and falls off with the cube of distance from the Earth center, so altitude reduces it slightly. The dipole captures about 80 to 90 percent of the observed field, and the remainder is why this result should be treated as an estimate. Operational models such as the World Magnetic Model and the International Geomagnetic Reference Field carry spherical harmonic expansions to degree 13 or higher and typically achieve declination accuracy near 0.5 to 1 degree, whereas a dipole-only calculation can be off by several degrees, with the largest errors over the South Atlantic Anomaly and near the poles. Local crustal sources such as basalt flows and iron formations add further deviation that no global model resolves. The field is also non-stationary: the north magnetic dip pole has been migrating toward Siberia at roughly 50 to 60 km per year, so any declination value carries an epoch.

Chinese sources recognized that a magnetized needle does not point at true north well before Europe did; Shen Kuo described the deviation in the Dream Pool Essays around 1088. In Europe, Columbus recorded declination changing across the Atlantic during the 1492 voyage. Inclination was found separately: Georg Hartmann noted the downward tilt of a needle in 1544, and Robert Norman described and measured it in The Newe Attractive in 1581. William Gilbert brought these observations together in De Magnete in 1600, proposing that the Earth behaves as a great magnet, which explained why dip varies systematically with latitude. Henry Gellibrand discovered in 1634 that London declination had shifted measurably since earlier surveys, establishing secular variation as a real phenomenon. Edmond Halley produced the first published isogonic chart in 1701 from Atlantic voyages made expressly to map declination for navigation. Carl Friedrich Gauss, working with Wilhelm Weber and the Gottingen Magnetic Union, put the subject on a rigorous footing in the late 1830s by expressing the global field as a spherical harmonic series and demonstrating that its source is overwhelmingly internal. Modern practice descends directly from that method. The International Association of Geomagnetism and Aeronomy has issued the International Geomagnetic Reference Field since 1968, and NOAA together with the British Geological Survey produce the World Magnetic Model used by defense and consumer navigation systems, both revised on a five-year cycle. Satellite missions including Orsted, CHAMP and the Swarm constellation launched in 2013 now supply the bulk of the constraining data.