EPSG:9657 DEPRECATED

Note: These formulas have been transcribed from EPSG Guidance Note #7-2. Users are encouraged to use that document rather than the text which follows as reference because limitations in the transcription will be avoided.

In Europe, national height systems are related to the pan-European height system through three transformation parameters and the formula:

Ht = Hs + A + [IncLat * rhoO * (Lat – LatO)] + [IncLong * nuO * (Long – LongO) * cos(Lat)]

where
Ht = gravity-related height value in the target vertical coordinate reference system.
Hs = gravity-related height value in the source vertical coordinate reference system.
A is the value of the vertical offset to be applied.
IncLat is the value in radians of the inclination parameter in the latitude domain, i.e. in the plane of the meridian, derived at an evaluation point with coordinates of LatO , LongO.
IncLon is the value of the inclination parameter in the longitude domain, i.e. perpendicular to the plane of the meridian.
rhoO is the radius of curvature of the meridian at latitude LatO, where rhoO = a(1 – e^2)/(1 – e^2 * sin^2(LatO))^1.5
nuO is the radius of curvature on the prime vertical (i.e. perpendicular to the meridian) at latitude LatO, wh		ere nuO = a /(1 – e^2 * sin^2(LatO))^0.5
Lat , Long are the horizontal coordinates of the point in the ETRS89 coordinate reference system, in radians.
LatO , LongO are the coordinates of the evaluation point in the ETRS89 coordinate reference system, in radians.

The horizontal location of the point must always be given in ETRS89 terms. Care is required where compound coordinate reference systems are in use: if the horizontal coordinates of the point are known in the local CRS they must first be transformed to ETRS89 values. The method is reversible.