Both come up with the same reading and definition in Jisho.org (round/circular), and both are listed as common words. Is there any preference between the two or should I simply learn both as interchangeable?
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This jisho has the info: http://wwwjdic.org (Jim Breen's WWWJDIC). Both spellings are marked with a P which means both are preferred. – Kaz May 11 '12 at 15:00
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丸い generally refers to spherical objects like a globe.
円い generally refers to circular objects like a circle drawn on a page. Perhaps also a physical object which is flat and round in shape (a 円 (yen) coin for example)

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Thank you! I seem to remember now seeing that somewhere, but Jisho wasn't much help to me. – tsukaima May 11 '12 at 02:03
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It should be noted that you can write `丸く描く` but you wouldn't write `円く描く` even if drawing a circle on a page. – Jesse Good May 11 '12 at 02:48
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3@Jesse I agree that 丸く might be more common, but do you have evidence that 円く is wrong? A similar point, though: to write まる, you would use 丸 even if it means a circle, maybe to avoid confusion with 円{えん} which is a word meaning circle by itself, whereas there's no 丸{がん} by itself AFAIK. – dainichi May 11 '12 at 03:01
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1@dainichi: Unfortunately, I don't have any evidence, so maybe I shouldn't say it is wrong, just more common as you mention. Also, you make a good point about まる only can be written as 丸, that is the reason we have 日の丸 and not 日の円 because the 訓読み for まる is 丸 only. – Jesse Good May 11 '12 at 03:16
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円 is usually read えん, and reading it まる sounds like ateji, and is less common. 丸い should be used.
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+1: I tend to agree, just remember there are certain "special" words that use `円い` instead, for example `円い月` and `円い人柄`. – Jesse Good May 11 '12 at 20:45