EPSG:9824

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.

The standard Transverse Mercator formulas (coordinate operation method 9807) are modified as follows:

Zone number, Z, = [(int((Long - LongI) / W) mod(360 / W)) + 1] with Long, LongI and W in degrees. 
where (LongI) is the Initial Longitude of the zoned grid system (the western limit of zone 1)
and W is the width of each zone of the zoned grid system.

In the formula above, mod = (a - floor(a / b) * b) where 'floor' is defined as rounding toward negative infinity. Z is in the range 1 ≤ Z ≤ (360/W) and for UTM 1 ≤ Z ≤ 60.

Then,
   Long0  = LongI + (Z * W) – (W/2)

For the forward calculation,
   Easting, E =  Z*10^6 + FE + k0.nu[A + (1 - T + C)A^3/6 + (5 - 18T + T^2 + 72C - 58e'^2)A^5/120]
   
and in the reverse calculation for longitude, 
   D = (E – [FE + Z*10^6])/(nu1.k0)