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**Grid references** define locations in maps using Cartesian coordinates. Grid lines on maps define the coordinate system, and are numbered to provide a unique reference to features. This reference is normally based on projected easting and northings

Although professional map-making and use of the grid had existed in China before, the Chinese cartographer and geographer Pei Xiu of the Three Kingdoms period was the first to mention a plotted geometrical grid reference and graduated scale displayed on the surface of maps to gain greater accuracy in the estimated distance between different locations.^{[1]}^{[2]}^{[3]} Historian Howard Nelson asserts that there is ample written evidence that Pei Xiu derived the idea of the grid reference from the map of Zhang Heng (78–139 CE), a polymath inventor and statesman of the Eastern Han dynasty.^{[4]} The American writer Robert K. G. Temple asserts that Zhang Heng should also be credited as the first to establish the mathematical grid in cartography, as evidenced by his work in maps, the titles of his lost books, and the hint given in the *Book of Later Han* (i.e. Zhang Heng "cast a network of coordinates about heaven and earth, and reckoned on the basis of it").^{[5]}

Grid systems vary, but the most common is a square grid with grid lines intersecting each other at right angles and numbered sequentially from the origin at the bottom left of the map. The grid numbers on the east-west (horizontal) axis are called Eastings, and the grid numbers on the north-south (vertical) axis are called Northings.

Numerical grid references consist of an even number of digits. Eastings are written before Northings. Thus in a 6 digit grid reference 123456, the Easting component is 123 and the Northing component is 456.

Grids may be arbitrary, or can be based on specific distances, for example some maps use a one-kilometre square grid spacing.

A grid reference locates a unique square region on the map. The precision of location varies, for example a simple town plan may use a simple grid system with single letters for Eastings and single numbers for Northings. A grid reference in this system, such as 'H3', locates a particular square rather than a single point.

Points can be located by grid references on maps that use a standard system for Eastings and Northings, such as the Universal Transverse Mercator used worldwide, or the Ordnance Survey National Grid used by Ordnance Survey in the UK. These points can then be located by someone else using grid references, even if using maps of a different scale.

In the Universal Transverse Mercator (UTM) system, grid reference is given by three numbers: zone, easting and northing. In the UTM system, the earth is divided into 60 zones. Northing values are given by the metres north, or south (in the southern hemisphere) of the equator. Easting values are established as the distance from the central meridian of a zone. The central meridian is arbitrarily set at 500,000 metres, to avoid negative numbers. A position 100 kilometres west of a central meridian would have an easting of 400,000 metres. Due to its popularity, and worldwide cover, the UTM system is used worldwide by NATO as well as many countries, including Australia and the USA.^{[6]}

In the United Kingdom, a proprietary grid system is used. In Ordnance Survey maps, each Easting and Northing grid line is given a two-digit code, based on the British national grid reference system with origin point just off the southwest coast of the United Kingdom. Since the Eastings and Northings are one kilometre apart, a combination of a Northing and an Easting will give a four-digit grid reference describing a one-kilometre square on the ground. The convention is the grid reference numbers call out the lower-left corner of the desired square. In the example map below, the town Little Plumpton lies in the square 6901, even though the writing which labels the town is in 6802 and 6902, most of the buildings (the orange boxed symbols) are in square 6901.

The more digits added to a grid reference, the more precise the reference becomes. To locate a specific building in Little Plumpton, a further two digits are added to the four-digit reference to create a six-digit reference. The extra two digits describe a position within the 1-kilometre square. Imagine (or draw or superimpose a Romer) a further 10x10 grid within the current grid square. Any of the 100 squares in the superimposed 10×10 grid can be accurately described using a digit from 0 to 9 (with 0 0 being the bottom left square and 9 9 being the top right square).

For the church in Little Plumpton, this gives the digits 6 and 7 (6 on the left to right axis (Eastings) and 7 on the bottom to top axis (Northings). These are added to the four-figure grid reference after the two digits describing the same coordinate axis, and thus our six-figure grid reference for the church becomes 696017. This reference describes a 100-metre by 100-metre square, and not a single point, but this precision is usually sufficient for navigation purposes. The symbols on the map are not precise in any case, for example the church in the example above would be approximately 100x200 metres if the symbol was to scale, so in fact, the middle of the black square represents the map position of the real church, independently of the actual size of the church.

Grid references comprising larger numbers for greater precision could be determined using large-scale maps and an accurate Romer. This might be used in surveying but is not generally used for land navigating for walkers or cyclists, etc. The growing availability and decreasing cost of handheld GPS receivers enables determination of accurate grid references without needing a map, but it is important to know how many digits the GPS displays to avoid reading off just the first six digits. A GPS unit commonly gives a ten-digit grid reference, based on two groups of five numbers for the Eastings and Northing values. Each successive increase in precision (from 6 digit to 8 digit to 10 digit) pinpoints the location by a factor of 10. Since, in the UK at least, a 6-figure grid reference identifies a square of 100-metre sides, an 8-figure reference would identify a 10-metre square, and a 10-digit reference a 1-metre square. In order to give a standard 6-figure grid reference from a 10-figure GPS readout, the 4th, 5th, 9th and 10th digits must be omitted so it is important not to read just the first 6 digits.

**^**Thorpe, I. J.; James, Peter J.; Thorpe, Nick (1996).*Ancient Inventions*. Michael O'Mara Books Ltd (published March 8, 1996). p. 64. ISBN 978-1854796080.**^**Needham, Volume 3, 106–107.**^**Needham, Volume 3, 538–540.**^**Nelson, 359.**^**Temple (1986) 30.**^**[www.icsm.gov.au] Archived 2014-10-08 at the Wayback Machine.