## Information on geographical coordinates, conversion and calculation

WGS84

The World Geodetic System of 1984 is a geodetic reference system used by many GPS devices as a uniform basis for position information on Earth.

Geographic coordinates (WGS84)

The geographical coordinates describe a point by its angular distance from the equator.

On this page the latitude is given in decimal degrees from -90° to +90°, it would also be possible to give from 90° south to 90° north.
The length is given in -180° to +180° East, instead of 180° West to 180° East.

Decimal degree (decimal notation, DD.DDDDDD°)

On this page you can calculate and work with it, as well as Google Maps and Microsoft (Bing) Maps.

This system is used mainly because it can be calculated very well.

An example for coordinates in decimal degree of Berlin (Siegessäule): Lat 52.514487 N, Lng 13.350126 E

The accuracy of this specification depends strongly on the number of decimal places.

With only 2 decimal places there is a possible deviation of up to 1km, with 4 decimal places there is only a deviation of 10m,
Like most systems, we use 6 decimal places, which corresponds to an accuracy of 1 meter.

Degrees Minutes (nautical notation, DD° MM.MMMM')

This is also a common spelling, which is common in geocaching and especially in seafaring, where the minute is usually sufficient as the smallest specification.

An example is 52° 12.2345' N(north), 12° 44.5678' E(east),
where the first number is an integer of the degrees (D=degree) and must be between -180 and 180.

The second number is the minute integer or decimal number from 0 to 59.999999.
For a sufficient accuracy, the same values apply here as for decimal notation.

Degrees Minutes Seconds (historical notation, sexagesimal, DD° MM' SS.SS")

Used e.g. by Wikipedia.

Sexagesimal means, because 1 degree corresponds to 60 minutes, 1 minute corresponds to 60 seconds.

An example is 52° 12' 43.33" N(North), 12° 44' 33" E(East),
where the first number is an integer of the degrees (D=degree) and must be between -180 and 180.

The second number indicates the minutes in whole numbers from 0 to 59,
and the last number indicates the seconds as an integer or decimal number from 0 to 59.999999.
It is interesting to note that a minute of latitude corresponds to about 1.852 km and thus defines a nautical mile.

CH1903 LV03

Swiss Grid, too, are the official Swiss national coordinates.

The starting point of all calculations for Switzerland was fixed at Bern and is Y:600000 East | X:200000 North.

For Liechtenstein the reference point is also Bern, but with the values Y:0 | X:0, so that e.g. Vaduz has the CH coordinates Y 758008 | X 223061, which results in LIE coordinates Y 158008 | X 23061.
However, only the CH coordinates are calculated here. Please pay attention to the values if necessary.

CH1903+ LV95

The current reference system in Switzerland since 2016, mandatory from 2020 at the latest.

The new system is also based on the Bessel 1841 Ellipsiod and differs only very slightly in accuracy (maximum 1.6 metres).

To differentiate, however, 2,000 or 1,000 kilometres were added to the coordinates as an offset, so that the reference point for Bern is now, for example, E 2,600,000 and N 1,200,000.

Here you can see that the designation has also changed from y/x to E/N. Unfortunately still swapped in the order unlike most other systems that use N/E...

UTM-system

The Universal Transverse Mercator is a global coordinate system. It divides the earth's surface (from 80° south to 84° north) in stripes into 6° wide vertical zones.

The basis and name of this system come from Gerhard Mercator, a geographer from the Middle Ages.

Since this system is true to angle, but produces larger areas with increasing distance from the equator, Gauss and Krüger have further developed the transverse Mercator projection. The universal transversal projection is much more accurate, especially for smaller maps, and is used by almost all major map services today.

An example for UTM coordinates is the Arc de Triomphe in Paris with: 31U 448304 5413670

To explain the length zones: (1-60, in the example the 31)
For the UTM system, the Earth is divided into 60 zones from west to east, each strip comprising 6 degrees of longitude.
The zones are numbered from west to east. One begins in the Pacific west of America at the date border with zone 1.

To explain the latitude zones: (C-X however without I and O, in the example the U)
Each UTM longitude zone is divided from south to north into 20 latitude zones (zone fields) of 8° each.

Now the two values Easting and Northing follow.
The Easting or the East value indicates the distance of the point from the specified latitude zone in meters. (+500.000m or 500km to avoid negative values)
The northing is the distance in meters between the point and the equator.
The high value only applies to the northern hemisphere, in the southern hemisphere this value must be subtracted from 10,000,000.
On which hemisphere one is can be easily recognized by the latitude zone. C-M lie on the southern hemisphere, N-X on the northern hemisphere.

UTMREF / MGRS

The UTM reference system or Military Grid Reference System divides the zones of the UTM system into 100 x 100 km plan squares.

These plan squares consist of 2 letters from A to Z, whereby I and O are omitted due to the danger of confusion with 1 and 0.

The first letter indicates the horizontal position within the grid square, also called Easting.
The second letter denotes the vertical position, i.e. the distance to the equator, within the plan square, also called northing.

The values for North and East determine the size of the grid square within which the coordinates are located and must always have the same number of digits. The more digits this number has, the higher the accuracy. The number of digits can be between 1 and 5.

A one-digit number only means an accuracy of 10 km. A 5-digit number, on the other hand, means an accuracy of 1 meter. In principle, the one-digit number 1 corresponds to the 5-digit number 10000.

Gauss-Kruger

The Gauss-Krueger coordinate system is a Cartesian coordinate system which makes it possible to locate sufficiently small areas of the earth in conformity with metric coordinates (right and high value).

In German cartography and geodesy the Bessel ellipsoid is used as reference ellipsoid.

The Gauß-Krüger coordinate system is very similar to the UTM system and differs only in the use of another ellipsoid as a basis. (UTM = WGS84, Gauss-Krueger = Bessel),
and the use of 3° wide strips instead of 6° wide strips as with the UTM.

For a better differentiation of the values for coordinates, the coordinates are called high values and right values.
For the determination the earth is divided into 3° wide stripes from north pole to south pole. The so-called meridian stripes.

To each of these stripes belongs a zone, starting at 0° and zone 0, 3° and zone 1, 6° and zone 2 etc.. The number of degrees divided by 3 results in the zone.
The zone can be recognized by the first number of the right value and thus quickly a rough estimate of the position. The following numbers indicate the distance in meters from the meridian.

To avoid negative numbers, a constant of 500,000 is always added to the right value. If the number is smaller than 500,000, the position of the coordinates is to the left or west of the meridian.

If it is greater than 500,000, it is to the right or east of the meridian. A right value of 4,545,678 is thus to the right of the 12th degree of latitude, namely 45,678 meters or 45.678 km.

At the edge of the zones there may also be overlaps of 20 minutes of longitude which corresponds to about 23 km. Thus, a zone change does not necessarily have to take place at the edge of the zones with every measurement.

Bessel ellipsoid

The Bessel ellipsoid (also Bessel 1841) is a reference ellipsoid for Europe.

The Bessel ellipsoid adapts particularly well to the geoid and the mean earth curvature in Eurasia due to its data base and was therefore used as a basis for many national surveys, e.g. in Germany.

Potsdam date, Rauenberg date, DHDN

The spatial definition of the Bessel ellipsoid to the Earth body (the position of the ellipsoid in the centre of mass of the Earth and its orientation to the Earth's rotation axis)
was carried out for Prussia at that time with the help of the central point Rauenberg in Berlin. After its destruction, the central point of the network was mathematically transferred to the Helmertturm in Potsdam, which is why the geodetic date of this system is often erroneously referred to as the Potsdam date.

This Rauenberg date is also the basis of the German Main Triangle Network (DHDN).

When converting from WGS84 to Gauß-Krüger, the date must be adjusted, otherwise the points will be shifted by about 150 meters.

SRTM

The SRTM data (Shuttle Radar Topography Mission) were recorded during a space mission in 2000. This is a rather high-resolution digital terrain model of the Earth's surface.

The SRTM data cover a large part of the Earth and are freely available with an accuracy of 90 metres (or 30 metres for North America).

SRTM-1 means a resolution of 1 arcsecond which corresponds to about 30 m at the equator. However, these data are only intended for North America.
SRTM-3 accordingly means a resolution of 3 arc seconds and about 90 m at the equator.

The altitude data refer to the worldwide uniform reference system WGS84, which is also used here on this page.

Due to the resolution of 90 meters there are deviations of up to 30 meters especially in steep areas, in flat terrain however the data are very accurate.

NAC (Natural Area Coding, WGS84)

The NAC (abbreviation for Natural Area Coding System) is a new system to standardize geographic coordinates.

Only the date WGS-84 is used.

It consists of 30 common characters from 0-9 and the letters BCDFGHJKLMNPQRSTVWXZ (All English Consonants). So the result is very compact and efficient.
Each of these characters represents a number from 0 to 29.

With NAC, the entire earth is divided into 30 zones of equal size, each with a longitude of 0-360° and a latitude of 0-180°, and the corresponding character is assigned to the result.

The result is a pair of characters. The first character string describes the longitude and the second the latitude. The character strings are separated by a space.

The more characters the pair has, the more accurate are the coordinates. Each of the 30 described squares can be split into 30 more squares to increase the accuracy.

For example, a pair of 4 digits has an accuracy of 25 x 50 meters.

With 5 digits one already reaches an accuracy of about 1 meter, therefore we work here with a character length of 6 characters, which is exact enough for every imaginable case.

W3W (What 3 Words)

The W3W (abbreviation for What 3 Words) has been a global system for addressing geographic coordinates since 2013.

Each position on the map consists of a square of 3 x 3 meters. This is represented by a combination of exactly 3 words. Hence the name: What 3 Words.

These 3 words are separated by a dot and are all written in lower case.

The system is also available in different languages. There is no word in several languages to avoid confusion.
Depending on the language, there are up to 40,000 words which are randomly combined to avoid any relation to neighbours. There is an official app and a website.