Rat and Ox compatibility
Combination
The Rat is the branch 子, Yang Water. The Ox is 丑, Yin Earth. Here is how the two branches meet in the tables Korean saju uses, and how their elements relate.
By the tables, the Rat and the Ox have a combination and no friction marks. This is usually called an easy pairing.
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Branches: 子 and 丑
Six harmony (六合)
子 and 丑 form a six harmony, one of the six closest pairings, said to make Earth. It is usually read as easy cooperation: plans click and small things get forgiven.
Elements: Water and Earth
Earth controls Water in the controlling cycle. The Ox side tends to set the frame and the Rat side tends to feel it. Read gently it is structure, read harshly it is pressure. Agreeing who decides what usually helps.
子 is Yang and 丑 is Yin: one of each.
Groups you share
Both are in the winter group (亥子丑), which the tables call a directional set (方合).
How to read this
A zodiac sign is one character out of eight in a saju chart. For two people, the birth-day pairs, the balance of elements and timing usually say more than the signs do. Treat this page as a tendency, for fun and self-reflection, not a verdict on anyone.

A sign is just one character
Two full charts have sixteen. Enter your birthday, then theirs, and the Moon Rabbit works out your compatibility score for free, on your device.
Questions
Are the Rat and the Ox compatible?
By the tables, the Rat and the Ox have a combination and no friction marks. This is usually called an easy pairing. It is one character each, so treat it as a tendency. The full charts of both people say more.
Which signs are traditionally closest to the Rat and the Ox?
By the tables, the Rat’s closest partner (six harmony) is the Ox and its three-sign teammates are the Monkey and Dragon. For the Ox, the closest partner is the Rat and the teammates are the Snake and Rooster.
Is zodiac compatibility the same as saju compatibility?
No. Zodiac compatibility compares only the two birth-year signs. Saju compatibility compares both full charts, especially the birth-day pairs and how the elements fill each other in. SajuBunny shows that score for free.