![Magnetic declination](https://upload.wikimedia.org/wikipedia/commons/c/c2/Magnetic_declination.svg)
Magnetic declination, or magnetic variation, is the
angle
In Euclidean geometry, an angle is the figure formed by two Ray (geometry), rays, called the ''Side (plane geometry), sides'' of the angle, sharing a common endpoint, called the ''vertex (geometry), vertex'' of the angle.
Angles formed by two ...
on the
horizontal plane
In astronomy, geography, and related sciences and contexts, a '' direction'' or ''plane'' passing by a given point is said to be vertical if it contains the local gravity direction at that point.
Conversely, a direction or plane is said to be hor ...
between
magnetic north
The north magnetic pole, also known as the magnetic north pole, is a point on the surface of Earth's Northern Hemisphere at which the planet's magnetic field points vertically downward (in other words, if a magnetic compass needle is allowed t ...
(the direction the north end of a magnetized
compass
A compass is a device that shows the cardinal directions used for navigation and geographic orientation. It commonly consists of a magnetized needle or other element, such as a compass card or compass rose, which can pivot to align itself with ...
needle points, corresponding to the direction of the
Earth's magnetic field
Earth's magnetic field, also known as the geomagnetic field, is the magnetic field that extends from Earth's interior out into space, where it interacts with the solar wind, a stream of charged particles emanating from the Sun. The magnetic f ...
lines) and
true north
True north (also called geodetic north or geographic north) is the direction along Earth's surface towards the geographic North Pole or True North Pole.
Geodetic north differs from ''magnetic'' north (the direction a compass points toward the ...
(the
direction along a
meridian
Meridian or a meridian line (from Latin ''meridies'' via Old French ''meridiane'', meaning “midday”) may refer to
Science
* Meridian (astronomy), imaginary circle in a plane perpendicular to the planes of the celestial equator and horizon
* ...
towards the geographic
North Pole
The North Pole, also known as the Geographic North Pole or Terrestrial North Pole, is the point in the Northern Hemisphere where the Earth's axis of rotation meets its surface. It is called the True North Pole to distinguish from the Mag ...
). This angle varies depending on position on the Earth's surface and
changes over time.
Somewhat more formally,
Bowditch defines variation as “the angle between the magnetic and geographic meridians at any place, expressed in degrees and minutes east or west to indicate the direction of magnetic north from true north. The angle between magnetic and grid meridians is called grid magnetic angle, grid variation, or grivation.”
By convention, declination is positive when magnetic north is east of true north, and negative when it is to the west. ''
Isogonic line
A contour line (also isoline, isopleth, or isarithm) of a function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value. It is a plane section of the three-dimensional grap ...
s'' are lines on the Earth's surface along which the declination has the same constant value, and lines along which the declination is zero are called ''agonic lines''. The lowercase Greek letter δ (delta) is frequently used as the symbol for magnetic declination.
The term ''
magnetic deviation
Magnetic deviation is the error induced in a compass by ''local'' magnetic fields, which must be allowed for, along with magnetic declination, if accurate bearings are to be calculated. (More loosely, "magnetic deviation" is used by some to mean ...
'' is sometimes used loosely to mean the same as magnetic declination, but more correctly it refers to the error in a compass reading induced by nearby metallic objects, such as iron on board a ship or aircraft.
Magnetic declination should not be confused with ''
magnetic inclination
Magnetic dip, dip angle, or magnetic inclination is the angle made with the horizontal by the Earth's magnetic field lines. This angle varies at different points on the Earth's surface. Positive values of inclination indicate that the magnetic fi ...
'', also known as magnetic dip, which is the angle that the Earth's magnetic field lines make with the downward side of the horizontal plane.
Declination change over time and location
Magnetic declination varies both from place to place and with the passage of time. As a traveller cruises the east coast of the United States, for example, the declination varies from 16 degrees west in Maine, to 6 in Florida, to 0 degrees in Louisiana, to 4 degrees east in Texas. The declination at London, UK was one degree west (2014), reducing to zero as of early 2020. Reports of measured magnetic declination for distant locations became commonplace in the 17th century, and
Edmund Halley
Edmond (or Edmund) Halley (; – ) was an English astronomer, mathematician and physicist. He was the second Astronomer Royal in Britain, succeeding John Flamsteed in 1720.
From an observatory he constructed on Saint Helena in 1676–77, Ha ...
made a map of declination for the Atlantic Ocean in 1700.
In most areas, the spatial variation reflects the irregularities of the flows deep in the Earth; in some areas, deposits of
iron
Iron () is a chemical element with symbol Fe (from la, ferrum) and atomic number 26. It is a metal that belongs to the first transition series and group 8 of the periodic table. It is, by mass, the most common element on Earth, right in f ...
ore
Ore is natural rock or sediment that contains one or more valuable minerals, typically containing metals, that can be mined, treated and sold at a profit.Encyclopædia Britannica. "Ore". Encyclopædia Britannica Online. Retrieved 7 April 2 ...
or
magnetite
Magnetite is a mineral and one of the main iron ores, with the chemical formula Fe2+Fe3+2O4. It is one of the oxides of iron, and is ferrimagnetic; it is attracted to a magnet and can be magnetized to become a permanent magnet itself. With the ...
in the Earth's crust may contribute strongly to the declination. Similarly,
secular
Secularity, also the secular or secularness (from Latin ''saeculum'', "worldly" or "of a generation"), is the state of being unrelated or neutral in regards to religion. Anything that does not have an explicit reference to religion, either negativ ...
changes to these flows result in slow changes to the field strength and direction at the same point on the Earth.
The magnetic declination in a given area may (most likely will) change slowly over time, possibly as little as 2–2.5 degrees every hundred years or so, depending upon how far from the
magnetic poles it is. For a location closer to the pole like
Ivujivik
Ivujivik ( iu, ᐃᕗᔨᕕᒃ , meaning "Place where ice accumulates because of strong currents", or "Sea-ice crash Area") is a Types of municipalities in Quebec, northern village (Inuit community) in Nunavik, Quebec, and the northernmost settlem ...
, the declination may change by 1 degree every three years. This may be insignificant to most travellers, but can be important if using magnetic bearings from old charts or
metes (directions) in old deeds for locating places with any precision.
As an example of how variation changes over time, see the two charts of the same area (western end of
Long Island Sound
Long Island Sound is a marine sound and tidal estuary of the Atlantic Ocean. It lies predominantly between the U.S. state of Connecticut to the north and Long Island in New York to the south. From west to east, the sound stretches from the Eas ...
), below, surveyed 124 years apart. The 1884 chart shows a variation of 8 degrees, 20 minutes West. The 2008 chart shows 13 degrees, 15 minutes West.
Determining declination
Direct measurement
The magnetic declination at any particular place can be measured directly by reference to the
celestial pole
The north and south celestial poles are the two points in the sky where Earth's rotation around a fixed axis, axis of rotation, indefinitely extended, intersects the celestial sphere. The north and south celestial poles appear permanently dire ...
s—the points in the heavens around which the stars appear to revolve, which mark the direction of true north and true south. The
instrument used to perform this measurement is known as a ''declinometer''.
The approximate position of the north celestial pole is indicated by
Polaris
Polaris is a star in the northern circumpolar constellation of Ursa Minor. It is designated α Ursae Minoris ( Latinized to ''Alpha Ursae Minoris'') and is commonly called the North Star or Pole Star. With an apparent magnitude that ...
(the North Star). In the northern hemisphere, declination can therefore be approximately determined as the difference between the magnetic bearing and a visual bearing on Polaris. Polaris currently traces a circle 0.73° in radius around the north celestial pole, so this technique is accurate to within a degree. At high latitudes a
plumb-bob
A plumb bob, plumb bob level, or plummet, is a weight, usually with a pointed tip on the bottom, suspended from a string and used as a vertical reference line, or plumb-line. It is a precursor to the spirit level and used to establish a vertic ...
is helpful to sight Polaris against a reference object close to the horizon, from which its bearing can be taken.
Determination from maps
A rough estimate of the local declination (within a few degrees) can be determined from a general isogonic chart of the world or a continent, such as those illustrated above. Isogonic lines are also shown on
aeronautical and
nautical chart
A nautical chart is a graphic representation of a sea area and adjacent coastal regions. Depending on the scale of the chart, it may show depths of water and heights of land (topographic map), natural features of the seabed, details of the coa ...
s.
Larger-scale local maps may indicate current local declination, often with the aid of a schematic diagram. Unless the area depicted is very small, declination may vary measurably over the extent of the map, so the data may be referred to a specific location on the map. The current rate and direction of change may also be shown, for example in
arcminute
A minute of arc, arcminute (arcmin), arc minute, or minute arc, denoted by the symbol , is a unit of angular measurement equal to of one degree. Since one degree is of a turn (or complete rotation), one minute of arc is of a turn. The na ...
s per year. The same diagram may show the angle of
grid north
A projected coordinate system, also known as a projected coordinate reference system, a planar coordinate system, or grid reference system, is a type of spatial reference system that represents locations on the Earth using cartesian coordina ...
(the direction of the map's north–south grid lines), which may differ from true north.
On the
topographic map
In modern mapping, a topographic map or topographic sheet is a type of map characterized by large- scale detail and quantitative representation of relief features, usually using contour lines (connecting points of equal elevation), but historic ...
s of the
U.S. Geological Survey
The United States Geological Survey (USGS), formerly simply known as the Geological Survey, is a scientific agency of the United States government. The scientists of the USGS study the landscape of the United States, its natural resources, and ...
(USGS), for example, a diagram shows the relationship between magnetic north in the area concerned (with an arrow marked "MN") and true north (a vertical line with a five-pointed star at its top), with a label near the angle between the MN arrow and the vertical line, stating the size of the declination and of that angle, in degrees,
mils, or both.
Models and software
Worldwide
empirical model
Empirical modelling refers to any kind of ( computer) modelling based on empirical observations rather than on mathematically describable relationships of the system modelled.
Empirical Modelling Empirical Modelling as a variety of empirical m ...
of the deep flows described above are available for describing and predicting features of the Earth's magnetic field, including the magnetic declination for any given location at any time in a given timespan. One such model is
World Magnetic Model
The World Magnetic Model (WMM) is a large spatial-scale representation of the Earth's magnetic field. It was developed jointly by the US National Geophysical Data Center and the British Geological Survey. The data and updates are issued by the ...
(WMM) of the US and UK. It is built with all the information available to the map-makers at the start of the five-year period it is prepared for. It reflects a highly predictable rate of change, and is usually more accurate than a map—which is likely months or years out of date. For historical data, the IGRF and GUFM models may be used. Tools for using such models include:
* Web apps hosted by the
National Geophysical Data Center
The United States National Geophysical Data Center (NGDC) provided scientific stewardship, products and services for geophysical data describing the solid earth, marine, and solar-terrestrial environment, as well as earth observations from spac ...
, a division of the
National Oceanic and Atmospheric Administration
The National Oceanic and Atmospheric Administration (abbreviated as NOAA ) is an United States scientific and regulatory agency within the United States Department of Commerce that forecasts weather, monitors oceanic and atmospheric conditio ...
of the United States.
* C demo program that for WMM by the
National Geospatial-Intelligence Agency
The National Geospatial-Intelligence Agency (NGA) is a combat support agency within the United States Department of Defense whose primary mission is collecting, analyzing, and distributing geospatial intelligence (GEOINT) in support of national ...
, along with various other third-party implementations.
The WMM, IGRF, and GUFM models only describe the magnetic field as emitted at the core-mantle boundary. In practice, the magnetic field is also distorted by the Earth crust, the distortion being
magnetic anomaly
In geophysics, a magnetic anomaly is a local variation in the Earth's magnetic field resulting from variations in the chemistry or magnetism of the rocks. Mapping of variation over an area is valuable in detecting structures obscured by overlying ...
. For more precise estimates, a larger crust-aware model such as the
Enhanced Magnetic Model
The World Magnetic Model (WMM) is a large spatial-scale representation of the Earth's magnetic field. It was developed jointly by the US National Geophysical Data Center and the British Geological Survey. The data and updates are issued by the ...
may be used. (See cited page for a comparison of declination contours.)
Using the declination
Adjustable compasses
A magnetic compass points to magnetic north, not geographic north. Compasses of the style commonly used for hiking include a declination adjustment in the form of a
bezel which swivels relative to the base plate. To establish a declination the bezel is rotated until the desired number of degrees plus or minus lie between the bezel's designation N (for North) and the direction indicated by the magnetic end of the needle (usually painted red). This allows the user to establish a true bearing for travel or orientation by aligning the embossed red indicator arrow on the base plate with a landmark or heading on a map. A compass thus adjusted can be said to be reading “true north” instead of magnetic north (as long as it remains within an area on the same isogonic line).
In the image to the left, the bezel's N has been aligned with the direction indicated by the magnetic end of the compass needle, reflecting a magnetic declination of 0 degrees. The arrow on the base plate indicates a bearing of 312 degrees.
Non-adjustable compasses
To work with both true and magnetic bearings, the user of a non-adjustable compass needs to make simple calculations that take into account the local magnetic declination. The example on the left shows how you would convert a magnetic bearing (one taken in the field using a non-adjustable compass) to a true bearing (one that you could plot on a map) by ''adding'' the magnetic declination. The declination in the example is 14°E (+14°). If, instead, the declination was 14°W (−14°), you would still “add” it to the magnetic bearing to obtain the true bearing: 40°+ (−14°) = 26°.
The opposite procedure is used in converting a true bearing to a magnetic bearing. With a local declination of 14°E, a true bearing (perhaps taken from a map) of 54° is converted to a magnetic bearing (for use in the field) by ''subtracting'' the declination: 54° – 14° = 40°. If, instead, the declination was 14°W (−14°), you would still “subtract” it from the true bearing to obtain the magnetic bearing: 54°- (−14°) = 68°.
Navigation
On aircraft or vessels there are three types of
bearing: true, magnetic, and compass bearing. Compass error is divided into two parts, namely magnetic variation and
magnetic deviation
Magnetic deviation is the error induced in a compass by ''local'' magnetic fields, which must be allowed for, along with magnetic declination, if accurate bearings are to be calculated. (More loosely, "magnetic deviation" is used by some to mean ...
, the latter originating from magnetic properties of the vessel or aircraft. Variation and deviation are signed quantities. As discussed above, positive (easterly) ''variation'' indicates that magnetic north is east of geographic north. Likewise, positive (easterly) ''deviation'' indicates that the compass needle is east of magnetic north.
Compass, magnetic and true bearings are related by:
The general equation relating compass and true bearings is
Where:
*
is Compass bearing
*
is Magnetic bearing
*
is True bearing
*
is magnetic Variation
*
is compass Deviation
*
for westerly Variation and Deviation
*
for easterly Variation and Deviation
For example, if the compass reads 32°, the local magnetic variation is −5.5° (i.e. West) and the deviation is 0.5° (i.e. East), the true bearing will be:
To calculate true bearing from compass bearing (and known deviation and variation):
*Compass bearing + deviation = magnetic bearing
*Magnetic bearing + variation = true bearing
To calculate compass bearing from true bearing (and known deviation and variation):
*True bearing - variation = Magnetic bearing
*Magnetic bearing - deviation = Compass bearing
These rules are often combined with the mnemonic "West is best, East is least"; that is to say, add W declinations when going from True bearings to Magnetic bearings, and subtract E ones.
Another simple way to remember which way to apply the correction for continental USA is:
* For locations east of the agonic line (zero declination), roughly east of the Mississippi: the magnetic bearing is always bigger.
* For locations west of the agonic line (zero declination), roughly west of the Mississippi: the magnetic bearing is always smaller.
Common abbreviations are:
*TC = true course;
*V = variation (of the Earth's magnetic field);
*MC = magnetic course (what the course would be in the absence of local deviation);
*D = deviation caused by magnetic material (mostly iron and steel) on the vessel;
*CC = compass course.
Deviation
Magnetic deviation
Magnetic deviation is the error induced in a compass by ''local'' magnetic fields, which must be allowed for, along with magnetic declination, if accurate bearings are to be calculated. (More loosely, "magnetic deviation" is used by some to mean ...
is the angle from a given magnetic bearing to the related bearing mark of the compass. Deviation is positive if a compass bearing mark (e.g., compass north) is right of the related magnetic bearing (e.g., magnetic north) and vice versa. For example, if the boat is aligned to magnetic north and the compass' north mark points 3° more east, deviation is +3°. Deviation varies for every compass in the same location and depends on such factors as the magnetic field of the vessel, wristwatches, etc. The value also varies depending on the orientation of the boat. Magnets and/or iron masses can correct for deviation, so that a particular compass accurately displays magnetic bearings. More commonly, however, a correction card lists errors for the compass, which can then be compensated for arithmetically. Deviation must be added to compass bearing to obtain magnetic bearing.
Air navigation
Air navigation is based on magnetic directions thus it is necessary to periodically revise navigational aids to reflect the drift in magnetic declination over time. This requirement applies to
VOR
VOR or vor may refer to:
Organizations
* Vale of Rheidol Railway in Wales
* Voice of Russia, a radio broadcaster
* Volvo Ocean Race, a yacht race
Science, technology and medicine
* VHF omnidirectional range, a radio navigation aid used in a ...
beacons,
runway
According to the International Civil Aviation Organization (ICAO), a runway is a "defined rectangular area on a land aerodrome prepared for the landing and takeoff of aircraft". Runways may be a man-made surface (often asphalt concrete, as ...
numbering,
airway
The respiratory tract is the subdivision of the respiratory system involved with the process of respiration in mammals. The respiratory tract is lined with respiratory epithelium as respiratory mucosa.
Air is breathed in through the nose to th ...
labeling, and
aircraft vectoring
Aircraft vectoring is a navigation service provided to aircraft by air traffic control. The controller decides on a particular airfield traffic pattern for the aircraft to fly, composed of specific legs or vectors. The aircraft then follows this p ...
directions given by
air traffic control
Air traffic control (ATC) is a service provided by ground-based air traffic controllers who direct aircraft on the ground and through a given section of controlled airspace, and can provide advisory services to aircraft in non-controlled airs ...
, all of which are based on magnetic direction.
Runway
According to the International Civil Aviation Organization (ICAO), a runway is a "defined rectangular area on a land aerodrome prepared for the landing and takeoff of aircraft". Runways may be a man-made surface (often asphalt concrete, as ...
s are designated by a number between 01 and 36, which is generally one tenth of the magnetic
azimuth
An azimuth (; from ar, اَلسُّمُوت, as-sumūt, the directions) is an angular measurement in a spherical coordinate system. More specifically, it is the horizontal angle from a cardinal direction, most commonly north.
Mathematicall ...
of the runway's
heading
Heading can refer to:
* Heading (metalworking), a process which incorporates the extruding and upsetting processes
* Headline, text at the top of a newspaper article
* Heading (navigation), the direction a person or vehicle is facing, usually s ...
: a runway numbered 09 points east (90°), runway 18 is south (180°), runway 27 points west (270°) and runway 36 points to the north (360° rather than 0°). However, due to magnetic declination, changes in runway designators have to occur at times to keep their designation in line with the runway's magnetic heading. An exception is made for runways within the
Northern Domestic Airspace of Canada; these are numbered relative to true north because proximity to the magnetic North Pole makes the magnetic declination large and changes in it happen at a high pace.
Radionavigation aids located on the ground, such as
VOR
VOR or vor may refer to:
Organizations
* Vale of Rheidol Railway in Wales
* Voice of Russia, a radio broadcaster
* Volvo Ocean Race, a yacht race
Science, technology and medicine
* VHF omnidirectional range, a radio navigation aid used in a ...
s, are also checked and updated to keep them aligned with magnetic north to allow pilots to use their magnetic compasses for accurate and reliable in-plane navigation.
For simplicity aviation sectional charts are drawn using true north so the entire chart need not be rotated as magnetic declination changes. Instead individual printed elements on the chart (such as VOR compass roses) are updated with each revision of the chart to reflect changes in magnetic declination. For an example refer to the sectional chart slightly west of
Winston-Salem, North Carolina
Winston-Salem is a city and the county seat of Forsyth County, North Carolina, United States. In the 2020 census, the population was 249,545, making it the second-largest municipality in the Piedmont Triad region, the 5th most populous city in N ...
in March 2021, magnetic north is 8 degrees west of true north
Note the dashed line marked 8°W.
/ref>
When plotting a course, some small aircraft pilots may plot a trip using true north on a sectional chart (map), then convert the true north bearings to magnetic north for in-plane navigation using the magnetic compass. These bearings are then converted on a pre-flight plan by adding or subtracting the local variation displayed on a sectional chart.
GPS
The Global Positioning System (GPS), originally Navstar GPS, is a Radionavigation-satellite service, satellite-based radionavigation system owned by the United States government and operated by the United States Space Force. It is one of t ...
systems used for aircraft navigation also display directions in terms of magnetic north even though their intrinsic coordinate system is based on true north. This is accomplished by means of lookup tables inside the GPS which account for magnetic declination. If flying under visual flight rules
In aviation, visual flight rules (VFR) are a set of regulations under which a pilot operates an aircraft in weather conditions generally clear enough to allow the pilot to see where the aircraft is going. Specifically, the weather must be better ...
it is acceptable to fly with an outdated GPS declination database however if flying IFR
In aviation, instrument flight rules (IFR) is one of two sets of regulations governing all aspects of civil aviation aircraft operations; the other is visual flight rules (VFR).
The U.S. Federal Aviation Administration's (FAA) ''Instrument Fly ...
the database must be updated every 28 days per FAA regulation.
As a fail-safe even the most advanced airliner will still have a magnetic compass in the cockpit. When onboard electronics fail, pilots can still rely on paper charts and the ancient and highly reliable device -- the magnetic compass.
References
External links
USGS Geomagnetism Program
Looks up your IP address location and tells you your declination.
Online declination calculator at the National Geophysical Data Center (NGDC)
Online declination and field strength calculator at the NGDC
Mobile web-app for magnetic declination at the NGDC
Historical magnetic declination viewer at the NGDC
Magnetic declination calculator at Natural Resources Canada
* ttp://www.ngdc.noaa.gov/geomag/WMM/soft.shtml World Magnetic Model source code download site
{{DEFAULTSORT:Magnetic Declination
Orientation (geometry)
Geomagnetism
Angle