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This one may seem surprising at first glance. Looking at the characters it looks like 환갑[還甲] literally means “return-shell/armor”. The thing is though, 갑[甲] – besides the literal meaning “shell” – is also the name of the first of the ten so called Heavenly Stems 천간[天干] which were used in labeling successive things (much like we use the letters of the alphabet). Together with another similar system, the twelve Earthly Branches 지지[地支], they were also used to label years (the system is a bit difficult to follow at first, I’ll describe it below for those who are interested). So the first year was 갑자[甲子], the second 을축[乙丑] and so on, until the 60th year 계해[癸亥]. In the 61st year you would have cycled back and start with 갑자[甲子] again. So 환갑 means “return to the first year of the 60-year cycle, complete a 60-year cycle”, hence “60th birthday”.

For those who are interested in how the cycle works, first here are the Heavenly stems and Earthly Branches, in order with their Korean readings:

- Stems: 갑 甲, 을 乙, 병 丙, 정 丁, 무 戊, 기 已, 경 庚, 신 辛, 임 壬, 계 癸
- Branches: 자 子, 축 丑, 인 寅, 묘 卯, 진 辰, 사 巳, 오 午, 미 未, 신 申, 유 酉, 술 戌, 해 亥

Now to get the labels for years in order, we simply start by combining the first Stem with the first branch, then the second stem with the second branch and so forth:

- 갑자 甲子
- 을죽 乙丑
- 병인 丙寅
- 정묘 丁卯
- 무진 戊辰

and so forth. That works fine until we get to 10: 계유 癸酉. But now we have run out of Stems! What to do? We simply start the Stems from 갑 甲 again while the Branches just go on where they left off:

11: 갑술 甲戌

12: 을해 乙亥

Now we reached the last Branch. As you would expect, we now simply start the Branches from 자 子, too, while the Stems just continue where they happen to be:

13: 정자 丁子

14: 병축 丙丑

15: 무인 戊寅

And so on.

In short, each year you count up to the next element in **both** the Stems and the Branches, and once you have reached the last one of either, you just loop back to the first element in the next year. You do that until in year 60, you have reached 계해 癸亥. Now both Stems and Branches have reached their final element at the same time, so in year 61 both loop back and you are back at 1: 갑자 甲子 again.

Now, you might wonder, if there are 10 Stems and 12 Branches, aren’t there 120 possible combinations? Why is the cycle just 60 years rather than 120? Well, since both rows are counted up at the same rate and both rows have an even number of elements, any loop back to the first element can only happen on an uneven year. As a result, even Stems can only pair up with even Branches, uneven stems only with uneven Branches (and vice versa). This halves the length of the circle to 60.

It's the Japanese kanreki=還暦, but it would be on New Year's (or Chinese New Year's or February fourth here which with the time difference is the third back there and so Groundhog Day, or in an even older version around the winter solstice) of your sixtieth calendar year (数え年) so you'd really be fifty eight. Unless your birthday is that day and then you'd be fifty nine . . .

We called it the Chinese Zodiac, but it's also the Chinese Calendar, or kyureki 旧暦 in Japan, oh and 甲 is any western year ending in four: ~4 AD . . .