What is the sexagenary cycle?

It is a 60-year cycle made by pairing 10 Heavenly Stems with 12 Earthly Branches. Because 10 and 12 repeat together only every 60 years, each combination such as jiǎ-zǐ recurs once per 60 years, giving every year a unique two-character name within the cycle.

How are the stem and branch calculated?

Using the anchor that 1984 is jiǎ-zǐ (cycle position 1), the stem index is (year minus 4) modulo 10 and the branch index is (year minus 4) modulo 12. The branch maps to the familiar zodiac animal and the stem encodes the five element and yin or yang polarity.

Where does the zodiac animal come from?

The animal is determined entirely by the Earthly Branch: zǐ is the Rat, chǒu the Ox, and so on through hài the Pig. So the 12-animal zodiac is just the branch cycle expressed with animal names.

Why does the year change at Chinese New Year, not 1 January?

The traditional Chinese year begins at the lunar New Year, which falls between late January and mid-February. A date in January or early February of a Gregorian year may still belong to the previous sexagenary year, so check the lunar New Year date for birthdays near the boundary.

What do the five elements mean here?

Each pair of stems shares one of five elements — Wood, Fire, Earth, Metal, Water — in alternating yang then yin polarity. So jiǎ is Yang Wood and yǐ is Yin Wood. This gives each year a richer character than the animal alone, as in a Fire Horse or Water Rat year.

Chinese Sexagenary Cycle Converter

Every year in the traditional Chinese calendar carries a two-character name from the sexagenary cycle: a Heavenly Stem paired with an Earthly Branch. This tool converts any Gregorian year into that name, along with its zodiac animal, its five-element polarity, and where it sits in the 60-year cycle.

How it works

The cycle pairs 10 stems with 12 branches. Anchored on the known fact that 1984 is jiǎ-zǐ (the first position in the cycle), the indices are simple modular arithmetic:

stemIndex   = (year − 4) mod 10
branchIndex = (year − 4) mod 12
cyclePos    = ((year − 4) mod 60) + 1

The branch index selects both the branch character and its zodiac animal, while the stem index gives the element and yin/yang polarity. Because 10 and 12 have least common multiple 60, the full stem-branch pairing repeats every 60 years.

Example and tips

1984 is jiǎ-zǐ, a Yang Wood Rat year and the start of the cycle. 2025 is yǐ-sì, a Yin Wood Snake year, and 2026 is bǐng-wǔ, a Yang Fire Horse year. Remember that the Chinese year turns at the lunar New Year, not on 1 January — so someone born in late January or early February should confirm that year’s New Year date before assigning their stem-branch and animal.