What’s kazoedoshi（数え年）?
Age counting method
When you’re born, you are 1 year old
When the new year comes, you turn 2 years old
ex. You’re born on the 31st of December in 2020, you will be two years old on the 1st of January in 2021.
History
Old custom from China
In 1902, the Japanese government made a law that set the rule "a man gets one year older at the last moment of the previous day of his/her birthday" ("man-nenrei"（満年齢） system)
However, Japanese people continued to use kazoedoshi
In 1950, the new law, which said "obey the 1903 law system, not kazoedoshi" took effect
Why?
Kazoedoshi includes the period of development in the womb
Some people say "the first number is one, not zero". For instance, the 1st day, the 1st grade, the 1st century, and so on.
Getting one year older on new year’s day for the viewpoint "elderly is respectable" in Buddhism and Confucianism
Some people say the reason why is the lunar-solar calendar which Japanese society used till 1872. The calendar has a "leap month" due to a complex calculation method (7 times in 19 years). Therefore kazoedoshi system is easy to count age. Source: National Astronomical Observatory of Japan(in Japananese)
Still used in modern Japanese society
"nenki"（年忌）; the anniversary of the death of family in Japanese Buddhism. The third anniversary is held in two-year-after of the family member death, the seventh anniversary is held in six-year-after of the death. All Japanese people hold nenki under kazoedoshi count.
"Shichigosan"（七五三） (Seven, five, three); festival in November for 3-year-old boys and girls, 5-year-old boys and 7-year-old girls at a Shinto shrine or Buddhist temple. Some people count their child’s age in kazoedoshi, others in man-nenrei
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In the world
In the past it was popular in other east Asian countries; China, Korean peninsula, Vietnam
South Korea is the only country that usually uses kazoedoshi system now
