Ordnance Survey National Grid
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The Ordnance Survey National Grid reference system is a system of geographic grid references used in Great Britain, different from using Latitude and Longitude. It is often called British National Grid (BNG).^{[1]}^{[2]}
The Ordnance Survey (OS) devised the national grid reference system, and it is heavily used in their survey data, and in maps (whether published by the Ordnance Survey or commercial map producers) based on those surveys. Grid references are also commonly quoted in other publications and data sources, such as guide books or 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 is a similar system created by the Ordnance Survey of 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. Europeanwide agencies also use UTM when mapping locations, or may use the military grid reference system (MGRS) system, or variants thereof.
General
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.
The Airy ellipsoid is a regional best fit for Britain; more modern mapping tends to use the GRS80 ellipsoid used by the GPS (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 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).^{[3]} 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 southwest of the Isles of Scilly. The distortion created between the OS grid and the projection is countered by a scale factor in the longitude to create two lines of longitude with zero distortion rather than one. Grid north and true north are only aligned on the 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 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 OSTN02.^{[4]} This models the detailed distortions in the 1936–1962 retriangulation, and achieves backwards compatibility in grid coordinates to submetre accuracy.
Datum shift between OSGB 36 and WGS 84
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.
But Great Britain has not shrunk by 100+ metres; a point near Land's End now computes to be 27.6 metres closer to a point near Duncansby Head than it did under OSGB36.^{[5]}
Datum shift between OSGB 36 and ED 50
These two datums are not really 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.
Grid letters
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, almost all of which lies below mean high tide.^{[6]}
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 northwest corner to Z in the southeast 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.
It would be possible to extend the grid system over Ireland, completing the S and N squares and introducing what would become the R and M squares (with the arrangement of first letters following the same pattern as for the second letter). However, there is no motion for this at the moment, and the accuracy of the projection would start to diminish in the west of Ireland, more than 8 degrees from the central meridian. Theoretically, the system extends far over the Atlantic Ocean and well into Western Europe with square AA near Iceland and square ZZ in northern Italy. In fact, Rockall is mapped by the Ordnance Survey, but is usually shown as an inset without gridlines on a mainland sheet. However, the grid can be extended to put Rockall in grid square MC as shown in this 1:50,000 mockup.
Grid digits
Within each square, eastings and northings from the origin (south west corner) of the square are given numerically. For example, NH0325 means a 1 km square whose southwest corner is 3 km east and 25 km north from the southwest 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.
Allnumeric grid references
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 allnumeric 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 2letter square. For example, within the context of a location known to be on OS Landranger sheet 41 (which extends from NN000500 in the southwest to NN400900 in the northeast) 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 twoletter 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.
Summary parameters of the coordinate system
 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]}
 Semimajor axis a: 6377563.396 m
 Semiminor axis b: 6356256.909 m
 Flattening (derived constant): 1/299.3249646
Notes
 ↑ http://spatialreference.org/ref/epsg/27700/
 ↑ http://communityhub.esriuk.com/geoxchange/2012/3/26/coordinatesystemsandprojectionsforbeginners.html
 ↑ OS Net, The true origin
 ↑ "Surveying guidelines". Ordnance Survey.
 ↑ Using an online calculator (e.g., this one) or the doityourself Transverse Mercator formulas we find that OSGB 134300 metres East 25,300 metres North is 50.067712° N 5.713449° W OSGB36; the OS website tells us that same point is 50.068307 N 5.714433 W ETRS89. At 340,500 metres East 973300 metres North we get 58.643850N 3.025201W OSGB36 and 58.643460N 3.026781W ETRS89. Numerous online calculators will give the distances between those sets of latlons, or do it yourself with Vincenty's formulae; it turns out to be 970195.4 metres on the Airy spheroid and 970167.8 on the GRS80/WGS84. Archived 5 June 2010 at the Wayback Machine.
 ↑ Standing, 2006
 ↑ Scale factor is defined by its base10 logarithm of (0.9998268 − 1) exactly.
 ↑ The defining Airy dimensions are a = 20923713 "feet", b = 20853810 "feet". In the Retriangulation the base10 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.
See also
 World Geodetic System
 Irish grid reference system
 United States National Grid
 Tetrad, Hectad, Myriad
 International Map of the World#Map Indexing System
 Cassini Grid
References
 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.
External links
 Ordnance Survey Guide to the National Grid
 Ordnance Survey Guide to coordinate systems
 Ordnance Survey coordinate transformer
 Interactive Ordnance Survey Mapping showing grid references
 FieldenMaps.info Coordinate Converter  Multipleformat coordinate 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
 JavaScript source code for OS coordinate transforms
 .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