This article is from the Stardates in Star Trek FAQ, by Andrew Main firstname.lastname@example.org with numerous contributions by others.
It turns out that the stardate rate has to change sometime between ST:TMP and
STII:TWOK, as well as sometime before ST:TMP. The details of that period,
encompassing ST:TMP, can't be calculated until this bit, for the remainder of
the classic films, has been done.
The reference points to use for this are STIII:TSFS (SD 8210.3; late 2285) and
STVI:TUC (SD 9521.6; conjectured to be 2293). The gap is 1311.3 units,
covering 7-8 years. A suitable rate is 0.5 units per day. (0.48u/d --
0.02u/hour -- is also within the possible range.)
Similarly to the first period of stardates, it can be assumed that any exact
multiple of 0.5 units is midnight. This means that the days on which
STIII:TSFS and STVI:TUC start will start at stardates 8210.0 and 9521.5
respectively. The calculation of exactly which dates these are must wait
until the details of the intermediate stardate rate have been calculated.