Equations for vertical datum transformations

Elevations can be converted between vertical datums with simple additional and subtraction. The values being added or subtracted are determined from a reference surface such as a geoid or vertical datum relationship grid.

Vertical datums

Gravity and the geoid

Vertical datum relationship grids

The formulae used for these transformations are formally defined in the standard LINZS25009 (Standard for New Zealand Vertical Datum).

Standard for New Zealand Vertical Datum 2016

Convert data between vertical datums by using our online coordinate converter or the vertical datum conversion form. Both give examples of the expected input data depending on the options chosen.

To convert larger datasets such as point clouds, more technical instructions are provided in the Medium post: Reprojecting point clouds to NZVD2016

Online coordinate converter 

Vertical datum conversion form

New Zealand Geodetic Datum 2000 to New Zealand Vertical Datums 2016

This is the official formula to convert New Zealand Geodetic Datum 2000 heights to New Zealand Vertical Datum 2016, using a geoid model (New Zealand Quasigeoid 2016 (NZGeoid2016)) to transform heights.

New Zealand Geodetic Datum 2000

New Zealand Vertical Datum 2016

New Zealand Quasigeoid 2016

The process is:

1. Determine the NZGD2000 ellipsoidal height (h)
2. Determine transformation value (N) by interpolating the NZGeoid2016 grid 
3. Calculate the NZVD2016 height (H_NZVD), using:

H_NZVD = h – N

Local vertical datum to New Zealand Vertical Datum 2016

This is the official formula to convert a local vertical datum height to New Zealand Vertical Datum 2016, using a vertical datum relationship grid. 

Local mean sea level datums

New Zealand Vertical Datum 2016

Vertical datum relationship grids

The process is:

1. Determine the local vertical datums height (H_A) for the point.
2. Determine transformation value (o_A) by interpolating the vertical datum relationship grid
3. Calculate the NZVD2016 height (H_NZVD), using:

H_NZVD = H_A- o_A

Local vertical datum to New Zealand Geodetic Datum 2000

This is the official formula to convert a local vertical datum height to New Zealand Geodetic Datum 2000, using a vertical datum relationship grid and a geoid model (New Zealand Quasigeoid 2016 (NZGeoid2016)).

Local mean sea level datums

New Zealand Geodetic Datum 2000

Vertical datum relationship grids

New Zealand Quasigeoid 2016

The process is:

1. Determine the local vertical datum height (H_A) for the point.
2. Determine transformation value (N) by interpolating the NZGeoid2016 grid 
3. Determine transformation value (o_A) by interpolating the vertical datum relationship grid
4. Calculate the NZGD2000 height (h), using:

h = H_A + N - o_A