Eino Uikkanen's homepage > About the coordinate systems - updated 29.3.2022


About this document

This document is written by Eino Uikkanen and professor Martin Vermeer for anyone who wants to get basic understanding of the coordinate systems. Document presents Finnish and global coordinate systems.

Finnish version of this article: Oppijakso koordinaatistoista

1. About the coordinate systems

1.1 Basic information of coordinates

Geographical coordinate systems provide the basis for expressing the exact position of any geographical location as unique coordinate values. The most widely used and oldest way of expressing the locations on the earth is dividing the earth into parallels and meridians and expressing the positions as latitude, longitude, and height. Other coordinate systems used are, e.g.

Earth-centered, three-dimensional coordinates are used only in scientific work.

Grid coordinates are used to present a limited geographical area with a coordinate system, which approximates a rectangular grid. The UTM coordinate system, for example, is a widely used grid coordinate system.

A coordinate system is always based on a coordinate reference system, i.e., the determination of how and on what basis the coordinate values of the points in the coordinate system are determined and measured.

The actual coordinate system consists of a selected set of fixed and identifiable marked points, whose coordinate values have been measured and marked according to the selected coordinate reference system. Such a point defining the coordinate system can be, for example, a bolt struck in the rock in the terrain or, a fixed GPS measuring station. This set of points defining the coordinate system is called “coordinate reference frame”. For example, the EUREF-FIN coordinate system currently in use in Finland is defined by thousands of points measured and marked in the terrain and many permanent GPS measuring stations.

The earth is a challenging object for determining coordinate systems, as the earth is unstable in many ways. The continental plates of the earth move relative to each other at a rate of several centimeters, even 10 cm, per year. During the year, the position of the Earth's axis of rotation wanders along an irregular circle of about 10 meters in width as the sum of many different movement cycles. There are many other smaller phenomena, which move parts of the earth with respect to each other and occur in different cycles.

As the movement of the continental plates significantly exceeds the accuracy requirements of the coordinate systems in a relatively short time, the coordinate systems intended for normal practical use must be fixed to the continental plates. Therefore, the EUREF-FIN coordinate system used in Finland and the other European coordinate systems are fixed to the stable part of the Eurasian continental plate. Since the coordinate points move with the continental plate, the movement of the continental plate does not affect the coordinate systems.

In earlier times, the instability of the earth was not a problem in the coordinate system definitions, because the coordinate systems were local and the requirements for the accuracy and compatibility of the coordinate systems were much lower than today. Most countries had their local coordinate systems, which could differ significantly. For example, the coordinate values of the KKJ coordinate system, which was used in Finland until the early 2000s, the coordinate values differ from the current globally compatible EUREF-FIN coordinate system up to nearly 200 meters.

Global, cross-border functions and systems, e.g., satellite navigation systems, require global coordinate systems alongside country-specific and other local coordinate systems.

The best known and most widely used global coordinate system is the WGS84 coordinate system used by the GPS system. The WGS84 coordinate system was created by the United States Department of Defense. In global coordinate systems, the effect of the earth’s instability cannot be eliminated by fixing the coordinate systems to continental plates. As a result of that, the coordinate points are in constant motion to different directions making the coordinate values dependent on time. Therefore, the applications utilizing global coordinate systems have either to consider the time dependence or to accept the inaccuracy caused by the earth’s instability in the coordinate values. As a result, the WGS84 coordinate system is not suitable for use in mapping work or any high-precision tasks. However, global coordinate systems like WGS84 are most suitable for positioning and navigation purposes, where the accuracy requirements are lower.

The most accurate and up-to-date information on the movements of the earth and its surface is produced by an international scientific service called “International Earth Rotation and Reference Systems Service” (IERS). The IERS service is provided by an international surveying-science organization called “International Association of Geodesy” (IAG). This organization has produced a global coordinate system called “International Terrestrial Coordinate Reference System” (ITRS) and a set of corresponding coordinate frames called “International Terrestrial Reference Frame” (ITRF). ITRF is based on a dense network of measuring stations located around the globe. IERS maintains coordinate data globally with scientific accuracy using existing observational data. Because the coordinate points are in constant motion, IERS maintains information about the direction, velocity, and coordinate values of the coordinate points at certain points in time.

Constantly moving or changing coordinate values are ill-suited for everyday use. Therefore, IERS regularly publishes coordinate values at specific times. IERS names the resulting coordinate systems according to the time epochs. For example, ITRF89 refers to the coordinate values of the ITRF coordinate frame at time 1989, or epoch 1989.0. Correspondingly, for example, the ITRF coordinate frames ITRF90, ITRF91, …, ITRF2005, ITRF2008, and ITRF2014 have been published.

The current Finnish coordinate system and most other European coordinate systems are based on the European Terrestrial Reference System 89 (ETRS89). The ETRS89 coordinate system is coincident with ITRS at the epoch 1989.0 and fixed to the stable part of the Eurasian Plate. Various realizations of ETRS89, i.e., coordinate frames, have been created at different times in different European countries. The name of the Finnish national ETRS89 realization, i.e., the coordinate frame, is EUREF-FIN.

1.2 Finnish EUREF-FIN coordinate frame

At the beginning of the 21st century, the current EUREF-FIN coordinate frame, a national realization of the pan-European ETRS89 coordinate frame, was introduced in Finland. This means that the points in the EUREF-FIN coordinate frame are measured and determined according to the ETRS89 coordinate frame.

The EUREF-FIN reference frame consisted originally of 100 points (benchmarks), which were measured and marked in the terrain, and of 12 permanent GPS measuring stations. Since then, the EUREF-FIN reference frame has been hierarchically densified into thousands of points in different phases and by different actors.

The predecessor of the EUREF-FIN coordinate frame was the KKJ coordinate frame, which was introduced in 1970. Although the transition from the KKJ coordinate frame to the EUREF-FIN coordinate frame started in the early 2000s, coordinates according to the KKJ coordinate frame continue to appear in various lists, old documents, etc. for a long time to come.

To convert KKJ coordinates to current EUREF-FIN coordinates, several freely available conversion programs are available as web services. The most comprehensive of these is the coordinate transformation service developed at the Finnish Geodetic Institute. This service is currently embedded in the Paikkatietoikkuna online map service: https://kartta.paikkatietoikkuna.fi/?lang=en

All mapping and measurement work in Finland is carried out in the EUREF-FIN coordinate system. The GPS system, on the other hand, uses the WGS84 coordinate system. EUREF-FIN and WGS84 are two different coordinate systems: EUREF-FIN is local, fixed, and more accurate, WGS84 is global, variable, and less accurate. However, the difference between EUREF-FIN coordinates and WGS84 coordinates is so small that it can be ignored in most applications used by average spatial data users, e.g., in positioning and navigation applications.

EUREF-FIN coordinates can be presented in several different formats. These formats with respective coordinate value samples are listed in the table below. For comparison, the coordinates of the same point in the outdated KKJ coordinate system are included.

All EUREF-FIN coordinate entries in the list are thus different representations of the coordinate values of the same point in the same EUREF-FIN coordinate system.

Coordinate system

Coordinate format

Latitude/ Northing

Longitude/ Easting

EUREF-FIN- Geographical coordinates

EUREF-FIN

ddd mm ss.sss…

60 11 19

24 48 30

EUREF-FIN

ddd mm.mmmm…

60 11.32

24 48.50

EUREF-FIN

ddd.ddddd…

60.188611

24.808333

EUREF-FIN projected coordinates

EUREF-FIN

ETRS-TM35FIN

6674433.905

378465.407

EUREF-FIN

ETRS-TM35

6674433.905

378465.407

EUREF-FIN

ETRS-TM34 (*)

6678508.217

711131.053

EUREF-FIN

ETRS-GK25

6675102.149

489365.946

KKJ-coordinates (KKJ is obsolete and is based on a different basis of the calculation than EUREF-FIN)

KKJ

KKJ universal coordinates in meters

6677236.864

3378586.032

(*) = Sample point is on UTM-zone TM35, outside UTM-zone TM34, but presented as an example as UTM-zone TM34 coordinates.

1.2.1 EUREF-FIN Geographical coordinates

Geographic coordinates can be expressed in degrees, degrees and minutes, or degrees, minutes and seconds. Using geographical coordinates when transmitting coordinate information lowers the risk of misunderstandings. It is also worth remembering that the EUREF-FIN coordinate system and the WGS84 coordinate system differ so little, that it seldom matters, whether we refer to EUREF-FIN or WGS84.

On Finnish maps, geographical coordinates are presented in degrees and minutes.

The Emergency Response Centre Agency in Finland recommends that the coordinates are given in degrees and minutes, as Emergency Response Centre Agency's information system uses the format ddd ° mm.mmm, i.e. degrees, minutes and decimals.

1.2.2 ETRS-TM35FIN coordinates

The ETRS-TM35FIN coordinate format is a grid coordinate system covering entire Finland. Zone 35 of the global UTM coordinate system coincides with the ETRS-TM35FIN coordinate system, but the ETRS-TM35FIN extends beyond the UTM zone throughout Finland.

ETRS-TM35FIN coordinates provide us with a coordinate system as close as possible to a rectangular plane grid, where the unit is a meter. Because of the curvature of the earth’s surface, this is not entirely possible, but in a limited area, even in an area of the size of Finland, we get very close. Therefore, ETRS-TM35FIN coordinates can, with reasonable accuracy, be used to perform calculations as if they were rectangular grid coordinates.

As an example and demonstration of how close the ETRS-TM35FIN grid is to a metric rectangular grid, we calculate the distance between two Finnish cities Vaasa and Kotka using two methods:

The ETRS-TM35FIN-coordinates for these cities are in meters: 

The difference between the northern coordinates is 308216 meters, and the difference between the eastern coordinates is 263798 meters. The distance calculated by the Pythagorean theorem is 405693 meters. The actual shortest distance along the earth's surface is 405733 meters. The difference between the results of these two calculations was only 40 meters. Between Helsinki and Sodankylä the distance calculated along the earth's surface is 811755 meters and the distance calculated from the ETRS-TM35 coordinates by the Pythagorean theorem is 811481 meters. Thus, the difference between the results of the distance calculations between Helsinki and Sodankylä will be 274 meters, which is 0.034% of the total distance.

The ETRS-TM35FIN coordinate system does not fully correspond to the rectangular metric grid coordinate system but differs from it by an amount called the projection error. However, this is not an actual error but a difference that is known and can be accurately calculated. It is worth noting that the projection error only affects the properties of the projection, such as scale or area, and not the coordinate values. Thus, coordinate values are not less accurate where there is a larger projection error.

The grids of the ETRS-TM35FIN coordinate system are indicated on the Finish maps with black lines in the UTM zones 34 and 36 and with black crosses in the UTM zone 35.

1.2.3 ETRS-TMnn, nn = 34, 35 or 36, coordinates

UTM coordinate system zones 34, 35, and 36 do overlap the area of Finland and are marked on the Finnish maps with purple lines. These UTM-coordinates are based on EUREF-FIN and are thus distinguished from standard UTM-coordinates with the prefix “ETRS-“; ETRS-TM34, ETRS-TM35, and ETRS-TM36. ETRS-TM35 coincides with the ETRS-TM35FIN coordinate system within the UTM zone width.

1.2.4 ETRS-GKnn, nn = 19, 20, … , 31, coordinates

The ETRS-GK coordinate system is used in applications that require a projection error smaller than in the ETRS-TM35FIN coordinates. This is achieved by using a narrow, one-degree zone width. Therefore, 13 ETRS-GK zones, ETRS-GK19 - ETRS-GK31, are needed to cover the entire area of Finland. Municipalities select the GK zone that best covers the municipality's area. If the municipality's area extends to several GK zones, the municipality may choose one GK zone and use it with extended zone width (e.g. the city of Lahti).

ETRS-GK coordinates are not marked on Finnish maps.

1.3 On the accuracy of coordinate values

The discussions of the theoretical differences between coordinate systems and, for example, the magnitude of computational errors in transformations between coordinate systems easily gives the impression that the sources of the errors in the coordinate values are limited to these sources. However, there are several other sources of errors in the coordinate values and the biggest source of errors is human processing of the coordinate values. For example, when determining coordinate values from a paper map or an application, the thickness of the pen or the resolution of the map application can considerably exceed the errors that occur in other processing.

Basic geodetic and cartographic work, GPS technology, and user navigation work are all about making measurements, and whenever measurements are made, errors are made too. The total error is accumulated from the errors made at different stages. The steps listed below do inevitably result in measurement or calculation errors, even if the operation itself is error-free.

1.4 Summary of the coordinate systems - what is good to remember from the above

Until recently, different countries and regions in the world have applied different and mutually incompatible coordinate systems. Today, most coordinate systems of different countries are as compatible as the slightly unstable surface of our planet allows. Until the beginning of the 21st century, Finland also applied a local coordinate system, Finnish National Grid Coordinate System KKJ. KKJ differed significantly from Finland's current EUREF-FIN coordinate system, which is compatible with global coordinate systems.

Today, different countries have largely compatible coordinate systems. The development of coordinate systems to the current accuracy and compatibility has been made possible by the development of measurement and other technology, not least space technology, the use of positioning satellites orbiting our planet. On the other hand, the same development, as well as globalization, has required higher compatibility of the coordinate systems.

The current coordinate systems in most countries are somehow based on a global coordinate system called the International Terrestrial Reference System (ITRS). This coordinate system is maintained by an international scientific service called International Earth Rotation and Reference Systems Service (IERS). The coordinate system currently in use in Finland is called EUREF-FIN. The EUREF-FIN coordinate system was introduced in the early 2000s. EUREF-FIN is based on the common European coordinate system ERTS89 and ETRS89 is based on the global ITRS coordinate system.

The Finnish EUREF-FIN coordinates can be presented as geographical coordinates in different formats, as coordinates of the nationwide ETRS-TM35FIN grid coordinate system, as UTM coordinates or as coordinates of the 13-zone ETRS-GK coordinate system. The conversions between the different representations are purely mathematical and can thus be done to any desired accuracy. Even though these are different representations of the same coordinate system, they may be called coordinate systems.

The GPS system uses the global WGS84 coordinate system. As a global system, the WGS84 coordinate system is less accurate than coordinate systems which are fixed to continental plates. However, the differences are so small that they are irrelevant to the average user, for example in navigation.

For emergency messages and other urgent transmissions of coordinate data, it is recommended to use geographical coordinates in the format ddd ° mm.mmm ', i.e. degrees, minutes, and decimals.

2. About the map projections

2.1 A map projection is always a compromise

The surface of the globe can not be accurately projected on a plane map; only some properties of the spherical surface can be presented accurately or with minor distortion on the plane while other properties are presented with bigger distortion. Therefore, a large number of different map projections, which preserve different properties unchanged or almost unchanged, have been developed over time. For example, a projection may correctly preserve shapes, angles or areas, represent latitudes and/or longitudes in straight lines, or, for example, present lines with constant bearing as straight lines.

When choosing a suitable map projection, it is necessary to consider which properties of the spherical surface are appropriate to preserve on this particular map. The appropriateness of the projection depends on e.g. the size and shape of the area to be described and the purpose of the map.

For example, the features of the quite commonly known Mercator-projection support very well the ocean navigation, but show the areas near the polar regions much larger than areas near the equator. The user of the Mercator projection must either understand and accept this scale distortion or choose another projection and give up the maritime features of the Mercator projection - the map projection is always a compromise.

2.2 A map projection is an effective communication tool – for a good or evil purpose

With thematic maps made to present some specific information, a projection can be chosen that gives the map user the most accurate idea possible of what is presented on the thematic map. Indeed, a projection that is ill-suited to presenting a case may give the map researcher an incorrect picture of the matter presented, even if the map and the information presented on it are correct in themselves. This can and will be used to deliberately mislead the map user.

2.3 Map projection and coordinate system

The map projection and the coordinate system can be selected independently. Sometimes, however, it is appropriate to select a particular projection with a particular coordinate system. For example, ETRS-TM35FIN or some other large plane coordinate system should be presented in a similar projection so that the grid formed by the coordinate lines is displayed on the map regularly.