I've got a document in which I'm defining counterclockwise and mentioning that it is sometimes also called anti-clockwise. The document is in American English, and generally in line with the Chicago Manual of Style. CMoS seems to suggest counterclockwise (no hyphen), but anti-clockwise seems to me to be a predominantly British-English term, and the OED seems to indicate that the hyphen should be present there. Should I hyphenate either or both of counterclockwise and anti-clockwise? Why?
I think you will find counterclockwise to be most often unhyphenated and anti-clockwise/anticlockwise to be as often hyphenated as not (and it appears that the unhyphenated version is gaining traction)
EDIT: A little more evidence (note that counter clockwise shows hits for both counter clockwise and counter-clockwise, and the same for anti clockwise) to clear up the issue.
It appears to me that the unhyphenated form "wins" for both words.
Very good question. Typically, terms coined as combinations of two words to create a word of a different type, or with an uncommonly-used prefix to the word, are hyphenated. As in my previous sentence, the adverb "uncommonly" and the verb "used" are hyphenated to create a single adjective "uncommonly-used", modifying the noun "prefix". Similarly, novel uses of prefixes like pre-, sub-, anti-, pro-, non-, etc. are hyphenated when the term is first coined. However, if a hyphenated term passes into common use and becomes thought of as its own word and not just a modification of another, it often becomes acceptable to omit the hyphen.
My vote is that both the hyphenated and non-hyphenated spellings are perfectly acceptable. As far as the will of the mob goes, the Google test says that your initial premise is backwards; "anticlockwise", unhyphenated, is far and away the more common spelling of that word (24m results for the unhyphenated word; only 2.9m for hyphenated), while the hyphenated "counter-clockwise" is the more common spelling there, but not by nearly as much (6.5m hyphenated to 4.9m unhyphenated).
-thanks to snumpy for pointing out that hypens break NGrams - use spaces instead
Use them as you have found them. It is, as you say, usual to hyphenate anti-clockwise (as it is for the vast majority of words beginning "anti-"; the only counterexample that comes to mind is antimacassar).
It is not usual to hyphenate counterclockwise, and there is no reason why you should. Hyphenation usually occurs where the compound term is not so well established as to be written as a single word, or where to drop the hyphen would make the word cumbersome as a matter of English orthography. "Anti-" falls into the latter category.