As we already have a Sun calculator - Sunrise and sunset calculator I thought about the one for the Moon.
And what's the first thing that comes to mind about the Moon - it has phases. And also, during the Full moon, the werewolf turns into a wolf. So let's find moon phases.
It appears that many moon calculators on the internet use the algorithm by Stephen R. Schmitt. It's described here.
The idea is simple (that's why it's mostly used, I guess). Given date converts into Julian days calculation and then the number of days is substituted from the magic Julian date 2451550.1.
It's 14:24 6 January 2000, and I suspect this is a day of a new moon cycle at the moment of algorithm development.
The acquired difference of days is divided by the length of a moon month - 29.530588853, and the remainder of the division allows to define the age of the moon and so the phase.
The interesting thing is that we have only 4 moon positions - new moon, first quarter, full moon, and third quarter. In English sources, there are names for the thing between,
The gap between the new moon and the first quarter is called Waxing Crescent.
The gap between the first quarter and the full moon is called Waxing Gibbous.
The gap between the full moon and the third quarter is called Waning Gibbous.
The gap between the third quarter and the new moon is called Waning Crescent.
Enter the date. The calculations are made from 00:00 Greenwich Time.