Projection parameters
Symbol  Parameter 

a  Semimajor axis of reference ellipsoid 
f  Ellipsoidal flattening 

Origin latitude 

Origin longitude 

False Northing 

False Easting 

Latitude of computation point 

Longitude of computation point 
N  Northing of computation point 
E  Easting of computation point 
The following equations are divided into three sections:
NZGD1949 geographic to NZMG projection
The conversion of NZGD1949 geographic coordinates (θ, λ) to NZMG projection coordinates ( N , E ) is achieved in several steps.
The conversion requires the latitude and longitude expressed in decimal degrees (north and east are positive). The constants are provided on the NZMG page and coefficients used in these formulae are listed below.
Note: NZMG applies to coordinates referenced to NZGD1949. Coordinates from other datums, such as NZGD2000 or WGS84, must be converted to NZGD1949 before these formulae can be applied.
Calculate ΔΨ and Δλ using:
Calculate a complex polynomial function of the complex number θ = ΔΨ + iΔλ using the formula:
Express the complex number z in terms of its real and imaginary parts z = x + iy and calculate the northing N and easting E from x and y as:
NZMG projection to NZGD1949 geographic
The conversion from NZMG to latitude and longitude involves an iterative approximation to reverse step 2 above. This starts with the easting E and northing N. The steps to calculate latitude and longitude are as follows. Note that the constants and coefficients used in these formulae are listed below. Derive the complex number z as the following steps.
Note: NZMG applies to coordinates referenced to NZGD1949. Coordinates from other datums, such as NZGD2000 or WGS84, must be converted to NZGD1949 before these formulae can be applied.
Determine the complex number θ as a series of approximations θ_{0} , θ_{1} , θ_{2} and so on. The first approximation is:
Successive approximations are obtained by applying the formula:
Two iterations of this formula will give millimetre transformation accuracy.
Express θ in terms of its real and imaginary parts θ = ΔΨ + iΔλ and calculate the latitude and longitude as follows
NZMG coefficients
Coefficient  Real Part  Imaginary Part 

A_{1}  0.6399175073  
A_{2}  0.1358797613  
A_{3}  0.063294409  
A_{4}  0.02526853  
A_{5}  0.0117879  
A_{6}  0.0055161  
A_{7}  0.0026906  
A_{8}  0.001333  
A_{9}  0.00067  
A_{10}  0.00034  
B_{1}  0.7557853228  0 
B_{2}  0.249204646  0.003371507 
B_{3}  0.001541739  0.041058560 
B_{4}  0.10162907  0.01727609 
B_{5}  0.26623489  0.36249218 
B_{6}  0.6870983  1.1651967 
C_{1}  1.3231270439  0 
C_{2}  0.577245789  0.007809598 
C_{3}  0.508307513  0.112208952 
C_{4}  0.15094762  0.18200602 
C_{5}  1.01418179  1.64497696 
C_{6}  1.9660549  2.5127645 
D_{1}  1.5627014243  
D_{2}  0.5185406398  
D_{3}  0.03333098  
D_{4}  0.1052906  
D_{5}  0.0368594  
D_{6}  0.007317  
D_{7}  0.01220  
D_{8}  0.00394  
D_{9}  0.0013 