Your Hour Animal Is a Different Animal
Most people who know their Chinese zodiac animal only know one of two traditional animals assigned to them. The second one comes from the clock, not the calendar.
The day has its own 12-animal cycle
Alongside the well-known 12-year cycle, traditional Chinese astrology divides each day into 12 two-hour blocks called Shichen (時辰). Each block is ruled by one of the same 12 animals used for years — Rat, Ox, Tiger, Rabbit, Dragon, Snake, Horse, Goat, Monkey, Rooster, Dog, Pig — running in the same fixed order, just against the clock instead of the calendar.
The 12 blocks and their boundaries
The blocks use fixed clock hours, not solar time adjusted for location: 23:00-01:00 is Rat, 01:00-03:00 is Ox, 03:00-05:00 is Tiger, 05:00-07:00 is Rabbit, 07:00-09:00 is Dragon, 09:00-11:00 is Snake, 11:00-13:00 is Horse, 13:00-15:00 is Goat, 15:00-17:00 is Monkey, 17:00-19:00 is Rooster, 19:00-21:00 is Dog, and 21:00-23:00 is Pig. Notice the Rat block wraps midnight — 11pm and 12:30am both fall inside it.
Why this needs your exact birth time
This is the same problem Western astrology has with the Ascendant, or with a Moon sign computed near a sign change: the hour animal depends on which two-hour block your birth falls into, and being born a few minutes before or after a boundary — say 10:58pm versus 11:02pm — puts you in a completely different animal. A birth certificate that only records "around 11pm" or rounds to the nearest half hour isn't precise enough. If you don't know your exact birth time, the honest answer is that this can't be calculated for you — not a rounded guess dressed up as a result.
It's independent of your year animal
Your hour animal and your year animal are calculated completely separately and don't influence each other — someone born in the Year of the Dragon can have any of the 12 hour animals depending on their birth time, including Dragon itself by coincidence. Synastri's /chinese-zodiac page includes a calculator for this: enter a birth time and it applies the fixed Shichen table above, for entertainment, not a scientifically validated system.
Two signs, one honest verdict — how you actually fit together.
Compatibility