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.

What is the Chinese Sexagenary Cycle Converter?

Convert any Gregorian year to its Chinese sexagenary cycle name — the Heavenly Stem and Earthly Branch pair — with the zodiac animal, the five-element and yin/yang polarity, and its position in the 60-year cycle. Runs in your browser. It runs free in your browser on Gera Tools, with nothing uploaded.

Chinese Sexagenary Cycle Converter

Name: Chinese Sexagenary Cycle Converter
Creator: Gera Tools
License: https://creativecommons.org/licenses/by/4.0/

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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.

The ten Heavenly Stems

Stem	Pinyin	Element	Polarity
甲	jiǎ	Wood	Yang
乙	yǐ	Wood	Yin
丙	bǐng	Fire	Yang
丁	dīng	Fire	Yin
戊	wù	Earth	Yang
己	jǐ	Earth	Yin
庚	gēng	Metal	Yang
辛	xīn	Metal	Yin
壬	rén	Water	Yang
癸	guǐ	Water	Yin

Each element appears twice in succession — once as Yang, once as Yin — before the cycle moves to the next element.

The twelve Earthly Branches and their animals

Branch	Pinyin	Animal	Branch	Pinyin	Animal
子	zǐ	Rat	午	wǔ	Horse
丑	chǒu	Ox	未	wèi	Goat
寅	yín	Tiger	申	shēn	Monkey
卯	mǎo	Rabbit	酉	yǒu	Rooster
辰	chén	Dragon	戌	xū	Dog
巳	sì	Snake	亥	hài	Pig

The 12-animal zodiac is simply the Earthly Branch cycle expressed with animal names. The branch also carries its own element and yin/yang attribution in traditional Chinese cosmology, though the tool focuses on the stem-derived element that is most commonly used.

Worked examples

1984 — jiǎ-zǐ (甲子), Yang Wood Rat, cycle position 1. The start of the current 60-year cycle.
2000 — gēng-chén (庚辰), Yang Metal Dragon. The Dragon is one of only two years without a real-world animal counterpart (the other being the Goat/Ram/Sheep, which varies by translation).
2025 — yǐ-sì (乙巳), Yin Wood Snake, cycle position 42.
2026 — bǐng-wǔ (丙午), Yang Fire Horse, cycle position 43.

The lunar-year boundary

The Chinese sexagenary year begins at the lunar New Year, which falls somewhere between 21 January and 20 February in the Gregorian calendar. A person born in late January or early February should check the exact New Year date for that year before assigning their zodiac animal and stem-branch — they may belong to the previous year’s cycle. For example, someone born on 15 January 1984 belongs to the previous year’s cycle (guǐ-hài, Yin Water Pig, 1983) rather than the famous jiǎ-zǐ Rat year. This boundary is a frequent source of confusion in Western zodiac charts that assume 1 January.