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.
If there is a requirement to change the linear unit of a vertical axis, the following formulae can be used:
for the forward transformation: X2 = (X1 * U1) / U2
for the reverse transformation: X1 = (X2 * U2) / U1
where U1 and U2 are unit conversion ratios for CRS1 and CRS2 respectively. U = [(factor b) / (factor c)] from the EPSG Dataset Unit of Measure table, populated with respect to the SI base unit, for linear units the metre.
Then
for the forward transformation:
X2 = (X1 * (b1 / c1)) / (b2 / c2) = (X1 * b1 * c2) / (b2 * c1)
for the reverse transformation:
X1 = [X2 * (b2 / c2)]/ (b1 / c1) = (X2 * b2 * c1) / (b1 * c2)