Chinese Zodiac Calculator

What this calculator does

The Chinese zodiac assigns one of twelve animal signs and one of five elements to every birth year, repeating on a 12-year (animal) and 10-year (element) cycle. This calculator uses your birth year - and, optionally, a partner's birth year - to compute:

• your Chinese zodiac animal and element
• your partner's Chinese zodiac animal and element
• a compatibility score and label between the two signs
• a checklist of personality traits for both signs, and which traditional compatibility relationship (if any) applies

Formula used

Animal sign cycles every 12 years, anchored so that 1900 falls on the Rat:

$$animalIndex = ((year - 4) \bmod 12 + 12) \bmod 12$$

Element cycles every 10 years in pairs (two years per element - Wood, Fire, Earth, Metal, Water):

$$elementIndex = \left\lfloor \frac{(year - 4) \bmod 10}{2} \right\rfloor$$

Compatibility between your animal index and your partner's is determined, in order of priority:

1. Same sign - identical animal index. A strong match.
2. Clash - indexes exactly 6 apart (opposite points on the 12-year cycle). A challenging match.
3. Secret friends - indexes that sum to 1 (mod 12). One of six traditional harmony pairs (e.g. Rat & Ox, Tiger & Pig). An excellent match.
4. Same trine group - indexes that share the same remainder mod 4 (the zodiac splits into four trine groups of three animals each, spaced four years apart, e.g. Rat, Dragon, Monkey). An excellent match.
5. Neutral - none of the above. A moderate match.

Example

Someone born in 1995 has animalIndex = ((1995-4) mod 12 + 12) mod 12 = 11 -> Pig, and elementIndex = floor(((1995-4) mod 10)/2) = floor(1/2) = 0 -> Wood. So 1995 is the year of the Wood Pig.

Their partner, born in 1998, has animalIndex = ((1998-4) mod 12 + 12) mod 12 = 2 -> Tiger, element index floor(((1998-4) mod 10)/2) = floor(4/2) = 2 -> Earth - the Earth Tiger.

Checking compatibility: Pig is index 11, Tiger is index 2. They aren't the same sign, the difference (9) isn't 6, but 11 + 2 = 13, and 13 mod 12 = 1 - so Pig and Tiger are secret friends, one of the six traditional harmony pairs, making this pairing an excellent match.

Notes

• The Chinese zodiac is traditionally based on the lunar calendar, and the Lunar New Year usually falls in late January or February. If you were born in January or early February, your true zodiac year may be one year earlier than your calendar birth year - check a lunar calendar for the exact cutoff date in your birth year if you're right on the border.
• Chinese astrology is a cultural and traditional belief system, not a scientific one - treat the compatibility result as a fun conversation starter rather than a definitive judgment about a relationship.