Heavenly Stems and Earthly Branches: the sixty-year cycle, explained

Before there were numbered years in China there were named years, and the names still run. 2026 is 丙午 (bǐngwǔ); 2027 will be 丁未. The naming system — the Heavenly Stems and Earthly Branches (天干地支, tiāngān dìzhī), or simply 干支 (gānzhī) — is older than the written classics, appears on Shang oracle bones from the second millennium BCE, and underlies the zodiac animals, BaZi and the traditional calendar. It is also simple enough to learn in an afternoon.

Ten stems

The ten Heavenly Stems are 甲 乙 丙 丁 戊 己 庚 辛 壬 癸 (jiǎ, yǐ, bǐng, dīng, wù, jǐ, gēng, xīn, rén, guǐ). On the oracle bones they named the days of a ten-day week. Later they were mapped onto the five elements in yang–yin pairs:

• 甲 yang wood · 乙 yin wood
• 丙 yang fire · 丁 yin fire
• 戊 yang earth · 己 yin earth
• 庚 yang metal · 辛 yin metal
• 壬 yang water · 癸 yin water

So a stem tells you an element and a polarity at once; that is why a BaZi chart can read the five elements straight off its characters.

Twelve branches

The twelve Earthly Branches are 子 丑 寅 卯 辰 巳 午 未 申 酉 戌 亥 (zǐ, chǒu, yín, mǎo, chén, sì, wǔ, wèi, shēn, yǒu, xū, hài). They mark the twelve months of the solar year, the twelve double-hours of the day (子 hour is 23:00–01:00) and the twelve-year cycle of Jupiter. Each branch has an animal — Rat, Ox, Tiger, Rabbit, Dragon, Snake, Horse, Goat, Monkey, Rooster, Dog, Pig — an element and a polarity, and also "hidden stems" (藏干) that give it a mixed character; 寅, for instance, carries 甲 wood with some 丙 fire and 戊 earth.

Sixty pairs

Pair the stems and branches in step — 甲子, 乙丑, 丙寅 … — and because 10 and 12 share the factor 2, a yang stem always meets a yang branch and a yin stem a yin branch. Only half of the 120 possible combinations occur, and the sequence returns to 甲子 after sixty steps. This is the sexagenary cycle (六十甲子), and it names:

• years — hence a sixtieth birthday (還曆) is the completion of one full cycle;
• months — the month branches are fixed (寅 is always the first month, starting at the Start of Spring); the month stem follows from the year stem;
• days — the day count has run unbroken for well over two thousand years, which is how historians date events recorded only by their cyclic day;
• double-hours — the hour branch is fixed by the clock, the hour stem follows from the day stem.

Those four pairs are the eight characters of BaZi.

Working out a year by hand

Take the Western year. For the stem, use the last digit: 4 → 甲, 5 → 乙, 6 → 丙, 7 → 丁, 8 → 戊, 9 → 己, 0 → 庚, 1 → 辛, 2 → 壬, 3 → 癸. For the branch, divide the year by 12 and take the remainder: 4 → 子, 5 → 丑, 6 → 寅, 7 → 卯, 8 → 辰, 9 → 巳, 10 → 午, 11 → 未, 0 → 申, 1 → 酉, 2 → 戌, 3 → 亥.

2026: last digit 6 → 丙; 2026 ÷ 12 = 168 remainder 10 → 午. The year is 丙午, yang fire over the Horse — "Fire Horse". 2027: 7 → 丁, remainder 11 → 未: 丁未, Fire Goat.

One essential caveat: the cyclic year changes at the Start of Spring (立春, around 4 February), not on 1 January and not at Lunar New Year. Someone born on 20 January 2026 belongs to 乙巳, the previous year. See why the zodiac begins at the Start of Spring and the 24 solar terms.

Relations between branches

Much of BaZi and Six Lines divination is the grammar of how branches interact: six combinations (六合, e.g. 子丑), three harmonies (三合, e.g. 申子辰 forming water), clashes (六沖, e.g. 子午), punishments, harms and destructions. A clash between a year branch and the branch of the current year is the familiar 沖太歲, "clashing with the Grand Duke", that sends people to temples each new year. Our BaZi calculator lists the interactions it finds in a chart and against each coming year.

Why it endured

The 干支 system is a two-gear clock — a ten-tooth wheel and a twelve-tooth wheel — that names time without numbers and without a starting era. Dynasties changed their era names; the cycle kept counting. It still does: open any Chinese almanac, look at the small characters beside today's date, and you are reading the same notation a Shang diviner scratched on a turtle shell.