Ganzhi (Chinese 干支, gānzhī — "stems and branches"; also 六十甲子, liùshí jiǎzǐ — "the sixty [pairs from] Jia Zi") is the complete cycle of combinations of the 10 Heavenly Stems (T013, 天干 Tian Gan) and the 12 Earthly Branches (T014, 地支 Di Zhi), yielding 60 unique pairs.

The Math of 60 Pairs

Why 60. 10 stems × 12 branches = theoretically 120 combinations, but due to the alternation of Yin / Yang (even stems with even branches, odd with odd) only 60 are actually used.

Use as a Time Unit

• 60-year cycle (Yuan, 元) — the main macrocycle
• 60-month cycle (5 years)
• 60-day cycle (~2 months)
• 60-hour cycle (2.5 days, each "hour" = 2 modern hours)

A Unique Combination of Element and Polarity

Each pair carries a code. Each of the 60 pairs carries a unique combination of element (Wu Xing, T010) and polarity (Yin / Yang, T058). The first pair: Jia Zi (甲子, Yang Wood + Rat).

Ganzhi in Ba Zi

Four pillars = four Ganzhi pairs. The entire Ba Zi system (#10) is based on four pillars of destiny, each one a Ganzhi pair: year, month, day, hour of birth. These 4 pairs = 8 signs, hence the name "Ba Zi" (八字, "eight signs").