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Looking at the individual kanji according to a dictionary:
丈 means height, stature, length
夫 means husband, man
大 means big, great

They seem unrelated to what these words using the kanji mean:
丈夫 means healthy, strong
大丈夫 means safe, all right, okay

How did these words end up with these meanings?

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2 Answers 2

up vote 8 down vote accepted

A summary of the gogen-allguide reference for 大丈夫:

丈 refers to a measure of height; about 3m by the 尺貫法{しゃっかんほう} system (traditional Japanese standard) but less in older Chinese measures. One 丈 referred to the height of a man.

夫 here means 'man', so when these words were imported from China, 丈夫 meant a fully grown man and 大丈夫 was a great/splendid man. From there 大丈夫 started to be used to mean "exceptionally strong", "exceptionally reliable", "exceptionally healthy", and from there the other meanings developed.

(大丈夫/丈夫 do not mean the same things in Chinese).

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In modern Chinese, "大丈夫" means "big husband". – Joe Z. Jan 29 '13 at 4:08

I think they seem related.

A tall man is a strong/healthy man. A really tall man is someone who is well/alright (i.e. without any problems).

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