1. Grid Coordinates

UTM zones on an equirectangular world map with irregular zones in red. https://handwiki.org/wiki/index.php?curid=2055446

Easting and northing are geographic Cartesian coordinates for a point. Easting is the eastward-measured distance (or the x-coordinate) and northing is the northward-measured distance (or the y-coordinate). When using common projections such as the transverse Mercator projection, these are distances projected on an imaginary surface similar to a bent sheet of paper, and are not the same as distances measured on the curved surface of the Earth.

Easting and northing coordinates are commonly measured in metres from the axes of some horizontal datum. However, other units (e.g., survey feet) are also used. The coordinates are most commonly associated with the Universal Transverse Mercator coordinate system (UTM), which has unique zones that cover the Earth to provide detailed referencing.

1.1. Notation and Conventions

Locations can be found using easting/northing (or x, y) pairs. The pair is usually represented conventionally with easting first, northing second.

For example, the peak of Mount Assiniboine (at 50°52′10″N 115°39′03″W) in UTM Zone 11 is represented by 11U 0594934 5636174. Subset conventions can also be used, such as a truncated grid reference,^[1] where the general location is already known to participants and may be assumed. Because the (leading) most significant digits specify the part of the world and the (trailing) least significant digits provide a precision that is not needed in most circumstances, they may be redundant for trekking use. This permits users to shorten the example coordinates to 949-361 by concealing 11U 05nnn34 56nnn74.

Usually associated with a map projection is a natural origin, e.g., at which the ellipsoid and flat map surfaces coincide.^[2] To ensure that the northing and easting coordinates on a map are not negative, map projections may set up a false origin, specified in terms of false northing and false easting values, that offset the true origin. Otherwise, negative northing and easting values indicate a position south and west of the origin, respectively.

2. Grid North

Grid north (GN) is a navigational term referring to the direction northwards along the grid lines of a map projection. It is contrasted with true north (the direction of the North Pole) and magnetic north (the direction in which a compass needle points). Many topographic maps, including those of the United States Geological Survey and Great Britain's Ordnance Survey, indicate the difference between grid north, true north, and magnetic north.^[3]

The grid lines on Ordnance Survey maps divide the UK into one-kilometre squares, east of an imaginary zero point in the Atlantic Ocean, west of Cornwall. The grid lines point to a Grid North, varying slightly from True North. This variation is zero on the central meridian (north-south line) of the map, which is at two degrees West of the Prime Meridian, and greatest at the map edges. The difference between grid north and true north is very small and can be ignored for most navigation purposes. The difference exists because the correspondence between a flat map and the round Earth is necessarily imperfect.

At the South Pole, grid north conventionally points northwards along the Prime Meridian.^[4] Since the meridians converge at the poles, true east and west directions change rapidly in a condition similar to gimbal lock. Grid north solves this problem.

3. Types

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, i.e. if the smallest unit is 100 metres, it refers to a point 12.3 km east and 45.6 km north from the origin.

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 view may use a simple alphanumeric 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.^[5]

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 an origin point just off the southwest coast of the United Kingdom . The area is divided into 100 km squares, each of which is denoted by a two-letter code. Within each 100 km square, a numerical grid reference is used. 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 above, 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 Easting and Northing values. Each successive increase in precision (from 6 digit to 8 digit to 10 digit) pinpoints the location more precisely 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.

Amateur radio operators use the Maidenhead Locator System to succinctly describe their geographic coordinates. It alternates pairs of letters and pairs of numbers to encode latitude and longitude to increasing specificity. The grid runs from A to R in both longitude and latitude starting from (-180°, -90°), and these are then divided into single-digit values in both directions. The location EM, for example, covers 20° by 10° and runs from the central United States through its southeast, and EM48 is 2° by 1° in size and lies in eastern Missouri, including St. Louis.