Sexagenary Cycle: Why Saju Counts in 60s (the Gapja Cycle)

The sexagenary cycle, called the 60 gapja (육십갑자 yuksip gapja, 六十甲子) in Korean, is a repeating list of 60 two-character labels made by pairing the 10 Heavenly Stems with the 12 Earthly Branches. It starts at 甲子 gapja and ends at 癸亥 gyehae, then starts again. Saju uses it to name the year, month, day and hour of your birth.

Why 60 and not 120? Because the stems and branches move forward together, one step at a time, and only meet again at the same starting point after 60 steps. That is also why a Korean 60th birthday is a big deal.

Let’s count it out with the Moon Rabbit.

Why 10 and 12 make 60

Imagine two gears. One has 10 teeth (the stems), the other has 12 (the branches). Each tick, both gears turn one tooth:

Tick 1: 甲 gap + 子 ja = 甲子 gapja
Tick 2: 乙 eul + 丑 chuk = 乙丑 eulchuk
Tick 3: 丙 byeong + 寅 in = 丙寅 byeongin
…
Tick 11: the stems run out and restart, so 甲 gap meets 戌 sul: 甲戌 gapsul
…
Tick 60: 癸 gye + 亥 hae = 癸亥 gyehae

The gears line up at 甲子 again only after 60 ticks, because 60 is the least common multiple of 10 and 12.

Half of all imaginable pairs never happen. There is no 甲丑, for instance. Stems and branches alternate yang and yin, and because they step forward together, a yang stem always lands on a yang branch and a yin stem on a yin branch. Ten stems times twelve branches would be 120; polarity matching leaves exactly 60.

A brief history of counting in sixties

This is one of the oldest continuously used counting systems in the world.

Days first. Stem-branch day labels appear on the oracle bones of the Shang dynasty in the late second millennium BC. Eclipse records in the Spring and Autumn Annals, covering 722 to 481 BC, show the 60-day count running without a break from that period onward, and it has kept going ever since.
Years later. Using the cycle to label years began around the middle of the third century BC and became standard for administration in the Western Han dynasty.
Spread across East Asia. The cycle became part of calendars in Korea, Japan and Vietnam, and it still names famous events. Korea’s Imjin War (1592–1598) is named after the 壬辰 imjin year, 1592.

The current cycle began with a 甲子 year in 1984, and the next 甲子 year arrives in 2044.

How the cycle labels each level of time

Saju uses the same 60 labels at four scales. Here’s how each keeps count:

Scale	How it advances	Saju detail
Year	one step per year	changes at Ipchun (입춘), around February 4
Month	one step per solar-term month	12 months × 5 years = 60
Day	one step per day, nonstop	unbroken since antiquity
Hour	one step per double-hour	12 double-hours × 5 days = 60

Two neat patterns hide in that table. Months cycle through all 60 labels every five years, and the year’s stem decides where the months begin: in a 甲 or 己 year, the first month, 寅 in (Tiger), is 丙寅. Hours cycle through all 60 every five days, and the day’s stem sets the first hour: on a 甲 or 己 day, the 子 Rat hour is 甲子.

Try the year formula. For a year AD, subtract 3, divide by 60 and take the remainder; that’s the year’s position in the cycle (a remainder of 0 means position 60). For 2026: 2026 − 3 = 2023, and 2023 divided by 60 leaves 43. Position 43 is 丙午 byeong-o, the Fire Horse. For 2027, the answer is 44, 丁未 jeong-mi, the Fire Goat. Just remember that in saju the new year label switches on at Ipchun, not on January 1.

Days can’t be guessed from the date. Because the day count simply rolls on regardless of months, leap years or new moons, a day pillar has to be looked up in an almanac, a manseryeok (만세력), or calculated by software. Korea’s astronomy institute, KASI, publishes calendar data that almanac makers rely on.

The 60 labels as personalities

Each of the 60 combinations is also read as a character in saju. Readers often give them nature names by combining the stem’s element with the branch’s animal:

Example	Reading	Imagery
甲子 gapja	yang wood + Rat	a young tree over winter water
丙午 byeong-o	yang fire + Horse	midday sun, a galloping horse
丁卯 jeong-myo	yin fire + Rabbit	a lamp in a spring garden
癸亥 gyehae	yin water + Pig	deep winter rain, the cycle’s quiet end

Your day pillar, one of these 60, is often treated as a shorthand personality. That’s why Korean saju fans will ask “what’s your ilju (일주)?”, meaning “which of the 60 is your day pillar?”

Hwangap: the 60-year homecoming

Because the year cycle repeats every 60 years, the year pillar you were born under returns in your 61st year of life by Korean reckoning, which is your 60th birthday internationally. Koreans mark this with hwangap (환갑, 還甲), literally “return of the gap,” the first stem. Japan has the same idea as kanreki (還暦), “return of the calendar.”

Traditionally, hwangap is a large family celebration, a way of honoring a full cycle of life. It’s also a lovely illustration of what the 60 gapja really is: not an abstract table, but a clock that everyone in the family can feel ticking.

FAQ

What is the sexagenary cycle?

It is a repeating sequence of 60 labels, each made by pairing one of 10 Heavenly Stems with one of 12 Earthly Branches, from 甲子 to 癸亥. It has been used in East Asia to label days since ancient times, and later years, months and hours. Korean saju reads your birth moment as four of these labels, called the four pillars.

Why is the cycle 60 and not 120?

Stems and branches advance together, one step each time, so they only return to 甲子 after 60 steps, the least common multiple of 10 and 12. Because both sequences alternate yang and yin, a yang stem always meets a yang branch and a yin stem a yin branch. Mismatched pairs such as 甲丑 never occur, leaving exactly 60 combinations.

What is my year in the 60 gapja cycle?

Subtract 3 from the year, divide by 60 and take the remainder; that is its position, with 0 meaning 60. For example, 1990 gives position 7, 庚午 Metal Horse, and 2026 gives position 43, 丙午 Fire Horse. If you were born in January or early February, check whether your birthday came before Ipchun, around February 4, because saju would then use the previous year.

What is hwangap in Korea?

Hwangap (환갑, 還甲) is the Korean celebration of a 60th birthday, marking the return of one’s birth-year stem-branch pair after a full 60-year cycle. The name means “return of the gap,” referring to the first stem. Japan’s equivalent is kanreki. Traditionally it is a significant family occasion, honoring a complete turn of the calendar.

Try it with the Moon Rabbit

See all four of your 60-cycle labels laid out in the pro manseryeok chart, or check today’s fortune to meet today’s day pillar.

Saju is a cultural tradition, not a science. SajuBunny readings are for fun and self-reflection, not professional advice.

Sources

For fun and self-reflection. Saju is a traditional way of looking at yourself, not a prediction or professional advice.