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Transformation between RT 90 and SWEREF 99 is done using a so-called direct projection.
About RT 90 and SWEREF 99
The 1990 Swedish coordinate system (RT 90) is a two-dimensional reference system that was the basis for production of the official Swedish maps until 2006. The plane coordinates from the Gauss-Krüger (Transverse Mercator) projection used for the official Swedish maps have the system notation RT 90 2.5 gon V 0:‑15.
The reference frame SWEREF 99 is a Swedish realization of the European three-dimensional reference system ETRS89 and agrees with WGS 84 within 8–9 decimetres. Therefore for normal GNSS applications in Sweden WGS 84 and SWEREF 99 are, in principle, interchangeable. Corrections from SWEPOS for differential GNSS applications are given relative to SWEREF 99.
The map projection SWEREF 99 TM is used for production of the official Swedish maps since 2007.
Transformation between RT 90 and SWEREF 99
Transformation between RT 90 and SWEREF 99 is done using a so-called direct projection. With this method, transformation is done using a Gauss-Krüger projection (pdf, new window) of latitude and longitude in one geodetic reference system directly to plane coordinates in another; in this case SWEREF 99 latitude/longitude and RT 90 2.5 gon V.
The following parameter values should be used for the direct projection between RT 90 and SWEREF 99:
| Parameter | Value |
|---|---|
| Projection type | Transverse Mercator (Gauss-Krüger) |
| Reference ellipsoid | GRS 80 |
| Semi major axis (a) | 6378137 |
| Inverse flattening (1/f) | 298.257222101 |
| Central meridian | 15°48'22.624306' East Greenwich |
| Latitude of origin | 0° |
| Scale on central meridian | 1.00000561024 |
| x0, false northing | -667.711 m |
| y0, false easting | 1500064.274 m |
NOTE: Parameter values for the GRS 80 ellipsoid should be used.
Because the system differences cannot be modelled in analytical form an exact transformation between RT 90 and SWEREF 99 is not possible. The transformation gives a mean error just under 0.07 m and a maximum error just over 0.2 m.
The accuracy of the transformed coordinates can be increased by the addition of a correction model (interpolation of residuals). The correction model is made available in e.g. our coordinate transformation software Gtrans. The method of interpolation of residuals is briefly described in the article Correction Model to Rectify Distorted Coordinate Systems (pdf, new window).
Transformation from/to other projection zones
As mentioned above, the direct projection parameter values refers to the 2.5 gon V projection zone of RT 90 and geographic coordinates (latitude/longitude) in SWEREF 99. If RT 90 coordinates in another projection zone than 2.5 gon V is to be transformed, a coordinate conversion must be done from the projection zone in question to 2.5 gon V, before the direct projection is performed. If the transformation resultat is to be delivered in any of the thirteen local SWEREF 99 projection zones, a map projection is required to convert latitude/longitude into plane coordinates.
The corresponding procedure applies to transformation in the opposite direction; i.e. from SWEREF 99 to RT 90.
Interactive transformation
Transformation between RT 90 and SWEREF 99 can be done interactively, using the direct projection, via the Coordinate transformation service.
Direct projection
Lantmäteriet's Geodesy Department has developed a method (projection fitting) that can be used for computation of parameter values for direct projection of latitude and longitude in one geodetic reference system, to plane coordinates in another for the Gauss-Krüger (Transverse Mercator) projection.
With this method, parameter values have been computed for transformation between SWEREF 99 and RT 90 by direct projection. It is therefore possible to transform plane coordinates between SWEREF 99 and RT 90 without the need for height values, unlike the previously used three-dimensional similarity transformation; see below.
The previously used three-dimensional similarity transformation
Prior to 2006 we recommended to perform the transformation between RT 90 and SWEREF 99 using a three-dimensional similarity transformation – a 7‑parameter transformation. Traditionally, the transformation between two reference systems (different geodetic datums) is performed using such a transformation. A complication in this connection is that although only plane coordinates are transformed, height information is required. Thus, the transformed plane coordinates are dependent on height information.
The direct projection and the three-dimensional similarity transformation give almost the same accuracy, but not identical results. The difference between plane coordinates obtained by direct projection and coordinates transformed with the three-dimensional similarity transformation is generally less than 0.1 m, but can in certain areas be as large as 0.3 m.
In case the three-dimensional similarity transformation has been used, and someone wants to transform the coordinates back to the original system, it is recommended that the inverse transformation is used. Parameter values and formulae for the three-dimensional similarity transformation are published in the report LMV-rapport 2001:7 (in Swedish). The Geodesy Department provides the report upon request.
Control points
Control points can be found in this document (pdf, in Swedish, new window).
Questions and answers
Yes, PROJ supports transformation of Swedish national coordinate and height systems. See Swedish transformations in PROJ (pdf, in Swedish, new window) for a brief introduction to the most common transformations.