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Home > Geodetic System > Coordinate conversion > Height conversions > Ellipsodial to mean sea level (normal-orthometric heights) conversion

Ellipsoidal to Mean Sea Level (Normal-Orthometric Heights) Conversion

There are two types of height available in New Zealand. Precise leveling-derived mean sea level (MSL) normal-orthometric heights and GNSS derived ellipsoidal heights.

These heights relate to different surfaces, normal-orthometric heights to the quasigeoid and ellipsoidal heights to the ellipsoid. Furthermore the normal-orthometric heights are in terms of 13 separate datums that are offset from the quasigeoid.

Heights can be converted between systems if the quasigeoid height (eg NZGeoid05) at the location is known and also the offset for the datum that the normal-orthometric height is in terms of (see figure below).

Figure 1: Heights converted between different systems.
Figure 1: Heights converted between different systems

Use the equations below to convert:

  • ellipsoidal heights to MSL (normal-orthometric heights)
  • MSL (normal-orthometric heights) to ellipsoidal heights
  • MSL (normal-orthometric heights) to MSL (normal-orthometric heights).

Alternatively, use the advanced online conversion tool. Read instructions for carrying out height conversions.

Ellipsoidal to MSL Datum Height Conversion

The NZGeoid05 model can be used to transform heights between the ellipsoidal and normal-orthometric systems:

  • Determine NZGD2000 coordinate (latitude, longitude) and ellipsoidal height ( h ) for point to be converted
  • Determine NZGeoid05 value ( z ) by interpolating the grid at the above coordinate. This can be computed online or by downloading the NZGeoid05 model
  • Determine the offset ( o ) for the output levelling datum
  • Use the following equation to determine the normal-orthometric height ( H ).
  • Ellipsoidal to MSL equation.

MSL Datum to Ellipsoidal Height Conversion

The NZGeoid05 model can be used to transform heights between the normal-orthometric and ellipsoidal systems:

  • Determine NZGD2000 coordinate (latitude, longitude) and normal-orthometric height ( H ) for point to be converted
  • Determine NZGeoid05 value ( z ) by interpolating the grid at the above coordinate. This can be computed online or by downloading the NZGeoid05 model
  • Determine the offset ( o ) for the output levelling datum
  • Use the following equation to determine the NZGD2000 ellipsoidal height ( h ).
  • MSL to Ellipsoidal equation.

MSL Datum to MSL Datum Conversion

The datum offsets can be used to transform heights between different normal-orthometric systems:

  • Determine the offset ( o1 ) for the "from" levelling datum
  • Determine the offset ( o2 ) for the "to" levelling datum
  • Use the following equation to convert the normal-orthometric height in MSL datum 1 ( H1 ) to MSL datum 2 ( H2 ).
  • MSL to MSL datum equation.
Figure 2: MSL Datum to MSL Datum Conversion.
Figure 2: MSL Datum to MSL Datum Conversion
 
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