3- and 7-parameter similarity transformations (NZGD1949 to NZGD2000)

There are 3 main methods used to transform New Zealand Geodetic Datum 1949 (NZGD1949) coordinates (latitude and longitude) to New Zealand Geodetic Datum 2000 (NZGD2000):

3-parameter similarity
7-parameter similarity
distortion grid transformations.

Similarity transformations convert the coordinate of a point from one ellipsoid to another. Similarity transformations account for the difference between the ellipsoids of different geodetic datums but do not account for distortions within the datums themselves. Internal distortions of a datum are better modelled using a distortion grid.

Geodetic datums
Reference ellipsoids
NZGD1949 - NZGD2000 Distortion Grid

The formula used to calculate a similarity transformation is on the Equations for Datum Transformations page.

NZGD1949 is a horizontal datum so any transformations which include NZGD1949 are horizontal only. Heights cannot be transformed in terms of NZGD1949.

Similarity transformations are defined in the standard LINZS25000 Standard for New Zealand Geodetic Datum 2000 - LINZS25000 and are summarised in the NZGD2000 LINZG25700 fact sheet:

Factsheet: New Zealand Geodetic Datum 2000 - LINZG25700

PDF

210.71 KB

Note

The two common conventions used to define similarity transformations, Helmert and Bursa-Wolf, use different signs to describe the rotation components. The transformations used in New Zealand follow the Helmert convention. Always check that your transformation software is applying the correct rotation directions.

Three-parameter transformation

The 3-parameter transformation calculates the differences between datums using an X, Y, Z system. It defines one datum with its centre at 0,0,0, and the centre of the other datum at a distance (T_X, T_Y, T_Z) metres away.

The 3-parameter transformation from NZGD1949 to NZGD2000 has an estimated accuracy of +/- 5m. The transformation parameters are:

Translation (metres)
T_X	T_Y	T_Z
54.4	-20.1	183.1

This transformation can be reversed (to convert from NZGD2000 to NZGD1949) by reversing the signs of the listed parameters.

Equations used for datum transformations

Seven-parameter transformation

The 7-parameter transformation calculates the differences between datums using an X,Y,Z system. It defines one datum with its centre at 0,0,0, and the centre of the other datum at a distance (T_X, T_Y, T_Z) metres away, as well as rotations around each axis (R_X, R_Y, R_Z), and a scale factor.

The 7-parameter transformation from NZGD1949 to NZGD2000 has an estimated accuracy of +/- 4m. The transformation parameters are:

Translation (metres)	Rotation (seconds of arc)	Scale change (ppm)
T_X	T_Y	T_Z	R_X	R_Y	R_Z	Δ_S
59.47	-5.04	187.44	-0.470	0.100	-1.024	-4.5993

This transformations can be reversed (to convert from NZGD2000 to NZGD1949) by reversing the signs of the listed parameters.