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The **Ordnance Survey National Grid reference system** (also known as **British National Grid** (**BNG**)^{ [1] }^{ [2] }) is a system of geographic grid references used in Great Britain, distinct from latitude and longitude.

- Grid letters
- Grid digits
- All-numeric grid references
- Compatibility with related systems
- Datum shift between OSGB 36 and WGS 84
- Datum shift between OSGB 36 and ED 50
- Summary parameters of the coordinate system
- See also
- Notes
- References
- External links

The Ordnance Survey (OS) devised the national grid reference system, and it is heavily used in their survey data, and in maps based on those surveys, whether published by the Ordnance Survey or by commercial map producers. Grid references are also commonly quoted in other publications and data sources, such as guide books and government planning documents.

A number of different systems exist that can provide grid references for locations within the British Isles: this article describes the system created solely for Great Britain and its outlying islands (including the Isle of Man); the Irish grid reference system was a similar system created by the Ordnance Survey of Ireland and the Ordnance Survey of Northern Ireland for the island of Ireland. The Universal Transverse Mercator coordinate system (UTM) is used to provide grid references for worldwide locations, and this is the system commonly used for the Channel Islands and Ireland (since 2001). European-wide agencies also use UTM when mapping locations, or may use the Military Grid Reference System (MGRS) system, or variants of it.

For the first letter, the grid is divided into squares of size 500 km by 500 km, outlined in dark grey on the map to the right. There are four of these which contain significant land area within Great Britain: S, T, N and H. The O square contains a tiny area of North Yorkshire, Beast Cliff at OV 0000 , almost all of which lies below mean high tide.^{ [3] }

For the second letter, each 500 km square is subdivided into 25 squares of size 100 km by 100 km, each with a letter code from A to Z (omitting I) starting with A in the north-west corner to Z in the south-east corner. These squares are outlined in light grey on the map, with those containing land lettered. The central (2° W) meridian is shown in red.

Within each square, *eastings* and *northings* from the south west corner of the square are given numerically. For example, NH0325 means a 1 km square whose south-west corner is 3 km east and 25 km north from the south-west corner of square NH. A location can be indicated to varying resolutions numerically, usually from two digits in each coordinate (for a 1 km square) through to five (for a 1 m square); in each case the first half of the digits is for the first coordinate and the second half for the other. The most common usage is the *six figure grid reference*, employing three digits in each coordinate to determine a 100 m square. For example, the grid reference of the 100 m square containing the summit of Ben Nevis is ** NN 166 712 **. (Grid references may be written with or without spaces; e.g., also NN166712.) NN has an easting of 200 km and northing of 700 km, so the OSGB36 National Grid location for Ben Nevis is at 216600, 771200.

Grid references may also be quoted as a pair of numbers: eastings then northings in metres, measured from the southwest corner of the SV square. Note that 14 digits may be required for locations in Orkney and further north. For example, the grid reference for Sullom Voe oil terminal in the Shetland Islands may be given as HU396753 or 439668,1175316.

Another, distinct, form of all-numeric grid reference is an abbreviated alphanumeric reference where the letters are simply omitted, e.g. 166712 for the summit of Ben Nevis. Unlike the numeric references described above, this abbreviated grid reference is incomplete; it gives the location relative to an OS 100×100 km square, but does not specify which square. It is often used informally when the context identifies the OS 2-letter square. For example, within the context of a location known to be on OS Landranger sheet 41 (which extends from NN000500 in the south-west to NN400900 in the north-east) the abbreviated grid reference 166712 is equivalent to NN166712. If working with more than one Landranger sheet, this may also be given as 41/166712.

Alternatively, sometimes numbers instead of the two-letter combinations are used for the 100×100 km squares. The numbering follows a grid index where the tens denote the progress from West to East and the units from South to North. In the north of Scotland, the numbering is modified: the 100 km square to the north of 39 is numbered N30; the square to the north of 49 is N40, etc.

The grid is based on the *OSGB36* datum (Ordnance Survey Great Britain 1936, based on the Airy 1830 ellipsoid), and was introduced after the retriangulation of 1936–1962.^{[ citation needed ]} It replaced the previously used Cassini Grid which, up to the end of World War II, had been issued only to the military.^{[ citation needed ]}

The Airy ellipsoid is a regional best fit for Britain; more modern mapping tends to use the GRS80 ellipsoid used by the Global Positioning System (the Airy ellipsoid assumes the Earth to be about 1 km smaller in diameter than the GRS80 ellipsoid, and to be slightly less flattened). The British maps adopt a transverse Mercator projection with an origin (the "true" origin) at 49° N, 2° W (an offshore point in the English Channel which lies between the island of Jersey and the French port of St. Malo).^{ [4] } Over the Airy ellipsoid a straight line grid, the National Grid, is placed with a new false origin to eliminate negative numbers, creating a 700 km by 1300 km grid. This false origin is located south-west of the Isles of Scilly.

In order to minimize the overall scale error, a factor of 2499/2500 is applied. This creates two lines of longitude about 180 km east and west of the central meridian along which the local scale factor equals 1, i.e. map scale is correct. Inside these lines the local scale factor is less than 1, with a minimum of 0.04% too small at the central meridian.^{ [5] } Outside these lines the local scale factor is greater than 1, and is about 0.04% too large near the east and west coasts. Grid north and true north are only aligned on the central meridian (400 km easting) of the grid which is 2° W (OSGB36) and approx. 2° 0′ 5″ W (WGS 84).

OSGB 36 was also used by Admiralty nautical charts until 2000^{[ citation needed ]} after which WGS 84 has been used.

A geodetic transformation between OSGB 36 and other terrestrial reference systems (like ITRF2000, ETRS89, or WGS 84) can become quite tedious if attempted manually. The most common transformation is called the Helmert datum transformation, which results in a typical 7 m error from true. The definitive transformation from ETRS89 that is published by the OSGB is called the National Grid Transformation OSTN15.^{ [6] } This models the detailed distortions in the 1936–1962 retriangulation, and achieves backwards compatibility in grid coordinates to sub-metre accuracy.

The difference between the coordinates on different datums varies from place to place. The longitude and latitude positions on OSGB 36 are the same as for WGS 84 at a point in the Atlantic Ocean well to the west of Great Britain. In Cornwall, the WGS 84 longitude *lines* are about 70 metres east of their OSGB 36 equivalents, this value rising gradually to about 120 m east on the east coast of East Anglia. The WGS 84 latitude *lines* are about 70 m south of the OSGB 36 lines in South Cornwall, the difference diminishing to zero in the Scottish Borders, and then increasing to about 50 m north on the north coast of Scotland. (If the *lines* are further *east*, then the longitude *value* of any given point is further *west*. Similarly, if the lines are further south, the values will give the point a more northerly latitude.) The smallest datum shift is on the west coast of Scotland and the greatest in Kent.

These two datums are not both in general use in any one place, but for a point in the English Channel halfway between Dover and Calais, the ED50 longitude lines are about 20 m east of the OSGB36 equivalents, and the ED50 latitude lines are about 150 m south of the OSGB36 ones.^{[ citation needed ]}

- Datum: OSGB36
- Map projection: Transverse Mercator projection using Redfearn series
- True Origin: 49°N, 2°W
- False Origin: 400 km west, 100 km north of True Origin
- Scale Factor: 0.9996012717+
^{ [7] } - EPSG Code: EPSG:27700

- Ellipsoid: Airy 1830
^{ [8] } - Semi-major axis a: 6377563.396 m
- Semi-minor axis b: 6356256.909 m
- Flattening (derived constant): 1/299.3249646

- ↑ "OSGB 1936 / British National Grid: EPSG Projection -- Spatial Reference".
*spatialreference.org*. - ↑ "Coordinate systems and projections for beginners".
- ↑ Standing, 2006
- ↑ OS Net, The true origin
- ↑ Ordnance Survey (1946) p. 4
- ↑ "Surveying guidelines". Ordnance Survey. Archived from the original on 18 July 2017.
- ↑ Scale factor is defined by its base-10 logarithm of (0.9998268 − 1) exactly.
- ↑ The defining Airy dimensions are a = 20923713 "feet", b = 20853810 "feet". In the Retriangulation the base-10 logarithm of the number of metres in a "foot" was set at (0.48401603 − 1) exactly and the Airy metric dimensions are calculated from that. The flattening is exactly 69903 divided by 20923713.

In geography, **latitude** is a geographic coordinate that specifies the north–south position of a point on the Earth's surface. Latitude is an angle which ranges from 0° at the Equator to 90° at the poles. Lines of constant latitude, or *parallels*, run east–west as circles parallel to the equator. Latitude is used together with longitude to specify the precise location of features on the surface of the Earth. On its own, the term latitude should be taken to be the *geodetic latitude* as defined below. Briefly, geodetic latitude at a point is the angle formed by the vector perpendicular to the ellipsoidal surface from that point, and the equatorial plane. Also defined are six *auxiliary latitudes* that are used in special applications.

A **geographic coordinate system** (**GCS**) is a coordinate system associated with positions on Earth. A GCS can give positions:

The **World Geodetic System** (**WGS**) is a standard for use in cartography, geodesy, and satellite navigation including GPS. This standard includes the definition of the coordinate system's fundamental and derived constants, the ellipsoidal (normal) Earth Gravitational Model (EGM), a description of the associated World Magnetic Model (WMM), and a current list of local datum transformations.

The **prime meridian** is a geographical reference line that passes through the Royal Observatory, Greenwich, in London, England. It was first established by Sir George Airy in 1851, and by 1884, over two-thirds of all ships and tonnage used it as the reference meridian on their charts and maps. In October of that year, at the behest of US President Chester A. Arthur, 41 delegates from 25 nations met in Washington, D.C., United States, for the International Meridian Conference. This conference selected the meridian passing through Greenwich as the official prime meridian due to its popularity. However, France abstained from the vote, and French maps continued to use the Paris meridian for several decades. In the 18th century, London lexicographer Malachy Postlethwayt published his African maps showing the "Meridian of London" intersecting the Equator a few degrees west of the later meridian and Accra, Ghana.

In geodesy, a **reference ellipsoid** is a mathematically defined surface that approximates the geoid, which is the truer, imperfect figure of the Earth, or other planetary body, as opposed to a perfect, smooth, and unaltered sphere, which factors in the undulations of the bodies' gravity due to variations in the composition and density of the interior, as well as the subsequent flattening caused by the centrifugal force from the rotation of these massive objects . Because of their relative simplicity, reference ellipsoids are used as a preferred surface on which geodetic network computations are performed and point coordinates such as latitude, longitude, and elevation are defined.

The **transverse Mercator** map projection is an adaptation of the standard Mercator projection. The transverse version is widely used in national and international mapping systems around the world, including the UTM. When paired with a suitable geodetic datum, the transverse Mercator delivers high accuracy in zones less than a few degrees in east-west extent.

A **geodetic datum** or **geodetic system** is a coordinate system, and a set of reference points, used for locating places on the Earth. An approximate definition of sea level is the datum WGS 84, an ellipsoid, whereas a more accurate definition is Earth Gravitational Model 2008 (EGM2008), using at least 2,159 spherical harmonics. Other datums are defined for other areas or at other times; ED50 was defined in 1950 over Europe and differs from WGS 84 by a few hundred meters depending on where in Europe you look. Mars has no oceans and so no sea level, but at least two martian datums have been used to locate places there.

The **Irish grid reference system** is a system of geographic grid references used for paper mapping in Ireland. The Irish grid partially overlaps the British grid, and uses a similar co-ordinate system but with a meridian more suited to its westerly location.

The **retriangulation of Great Britain** was a triangulation project carried out between 1935 and 1962 that sought to improve the accuracy of maps made of Great Britain. Data gathered from the retriangulation replaced data gathered during the Principal Triangulation of Great Britain, which had been performed between 1783 and 1851. The retriangulation involved erecting around 6,500 concrete pillars on British hilltops, which were used as reference points for the triangulation. Today, use of the trig points and the results of the retriangulation have been replaced by a network of global navigation satellite system stations known as OS Net, which is able to achieve an accuracy of 3 millimetres (0.12 in) over the length of the country compared to 20 metres (66 ft) achievable by use of the trig points.

The **Military Grid Reference System** (**MGRS**) is the geocoordinate standard used by NATO militaries for locating points on Earth. The MGRS is derived from the Universal Transverse Mercator (UTM) grid system and the Universal Polar Stereographic (UPS) grid system, but uses a different labeling convention. The MGRS is used as geocode for the entire Earth.

The **Swiss coordinate system** is a geographic coordinate system used in Switzerland and Liechtenstein for maps and surveying by the Swiss Federal Office of Topography (Swisstopo).

**ED50** is a geodetic datum which was defined after World War II for the international connection of geodetic networks.

The **Universal Transverse Mercator** (**UTM**) is a system for assigning coordinates to locations on the surface of the Earth. Like the traditional method of latitude and longitude, it is a horizontal position representation, which means it ignores altitude and treats the earth as a perfect ellipsoid. However, it differs from global latitude/longitude in that it divides earth into 60 zones and projects each to the plane as a basis for its coordinates. Specifying a location means specifying the zone and the *x*, *y* coordinate in that plane. The projection from spheroid to a UTM zone is some parameterization of the transverse Mercator projection. The parameters vary by nation or region or mapping system.

The **North American Datum** (**NAD**) is the horizontal datum now used to define the geodetic network in North America. A datum is a formal description of the shape of the Earth along with an "anchor" point for the coordinate system. In surveying, cartography, and land-use planning, two North American Datums are in use for making lateral or "horizontal" measurements: the North American Datum of 1927 (NAD 27) and the North American Datum of 1983 (NAD 83). Both are geodetic reference systems based on slightly different assumptions and measurements.

**ECEF**, also known as **ECR**, is a geographic and Cartesian coordinate system and is sometimes known as a "conventional terrestrial" system. It represents positions as X, Y, and Z coordinates. The point is defined as the center of mass of Earth, hence the term **geocentric coordinates**. The distance from a given point of interest to the center of Earth is called the **geocentric radius** or **geocentric distance**.

A "**quadrangle**" is a topographic map produced by the United States Geological Survey (USGS) covering the United States. The maps are usually named after local physiographic features. The shorthand "**quad**" is also used, especially with the name of the map; for example, "the Ranger Creek, Texas quad". From approximately 1947-1992, the USGS produced the 7.5 minute series, with each map covering an area one-quarter of the older 15-minute quad series, which it replaced. A 7.5 minute quadrangle map covers an area of 49 to 70 square miles. These maps employ the 1927 North American Datum (NAD27); conversion or a change in settings is necessary when using a GPS which by default employ the WGS84 geodetic datum. Beginning in 2009, the USGS made available digital versions of 7.5 minute quadrangle maps based on GIS data that use the NAD83 datum, which is typically within one meter of WGS84, or within the uncertainty of most GPS coordinate measurements. On a quadrangle map, the north and south limits are not straight lines, but are actually curved to match Earth's lines of latitude on the standard projection. The east and west limits are usually not parallel as they match Earth's lines of longitude.

The **Helmert transformation** is a transformation method within a three-dimensional space. It is frequently used in geodesy to produce distortion-free transformations from one datum to another. The Helmert transformation is also called a **seven-parameter transformation** and is a similarity transformation.

The article Transverse Mercator projection restricts itself to general features of the projection. This article describes in detail one of the (two) implementations developed by Louis Krüger in 1912; that expressed as a power series in the longitude difference from the central meridian. These series were recalculated by Lee in 1946, by Redfearn in 1948, and by Thomas in 1952. They are often referred to as the Redfearn series, or the Thomas series. This implementation is of great importance since it is widely used in the U.S. State Plane Coordinate System, in national and also international mapping systems, including the Universal Transverse Mercator coordinate system (UTM). They are also incorporated into the Geotrans coordinate converter made available by the United States National Geospatial-Intelligence Agency. When paired with a suitable geodetic datum, the series deliver high accuracy in zones less than a few degrees in east-west extent.

The **IERS Reference Meridian (IRM)**, also called the **International Reference Meridian**, is the prime meridian maintained by the International Earth Rotation and Reference Systems Service (IERS). It passes about 5.3 arcseconds east of George Biddell Airy's 1851 transit circle or 102 metres (335 ft) at the latitude of the Royal Observatory, Greenwich. It is also the reference meridian of the Global Positioning System (GPS) operated by the United States Department of Defense, and of WGS84 and its two formal versions, the ideal International Terrestrial Reference System (ITRS) and its realization, the International Terrestrial Reference Frame (ITRF).

**Web Mercator**, **Google Web Mercator**, **Spherical Mercator**, **WGS 84 Web Mercator** or **WGS 84/Pseudo-Mercator** is a variant of the Mercator projection and is the de facto standard for Web mapping applications. It rose to prominence when Google Maps adopted it in 2005. It is used by virtually all major online map providers, including Google Maps, Mapbox, Bing Maps, OpenStreetMap, Mapquest, Esri, and many others. Its official EPSG identifier is EPSG:3857, although others have been used historically.

- Ordnance Survey (1946) A brief description of the National Grid and reference system. London: His Majesty's Stationery Office.
- Ordnance Survey A guide to coordinate systems in Great Britain: An introduction to mapping coordinate systems and the use of GPS datasets with Ordnance Survey mapping; Version 2.2 December 2013 [accessed 13 February 2014].
- Ordnance Survey's Grid script: a brief introduction to the National Grid Reference; Version November 2011 [accessed 13 February 2014].
- Standing, Peter (2006)
*OV0000 a unique grid square at Beast Cliff*, Geograph Project, UK, web article [accessed 11 June 2007] - "The National Grid FAQs". Ordnance Survey. Retrieved 13 February 2014.

- Ordnance Survey Guide to the National Grid
- Ordnance Survey Guide to coordinate systems
- Interactive Ordnance Survey Mapping showing grid references
- FieldenMaps.info Co-ordinate Converter - Multiple-format co-ordinate transformer for Great Britain & Channel Islands
- Programs to convert Ordnance Survey grid references
- Open Source Javascript Conversion Library
- GPL Java Conversion Library
- Perl Conversion Library
- The sole part of Great Britain that lies in the OV square
- Convert between Latitude/Longitude & OS National Grid References (JavaScript source code)
- .Net library to convert between lat/lon in various coordinate systems and grid reference
- UK Grid Reference Finder. Web utility to find a UK grid reference

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