1January — the first month of the Gregorian (modern) calendar, read いちがつ. Written 一月 in kanji or as 1月 / １月 with digits. The same kanji form 一月 is also a homograph for a separate word meaning 'one month (duration),' read ひとつき or いちげつ — disambiguated only by reading and context. To avoid the ambiguity in writing, the duration is usually expressed as 一ヶ月 / 一か月 (いっかげつ) or, with okurigana, ひと月.
私の誕生日は一月です。
My birthday is in January.
一月一日は元日で、家族で初詣に行く。
January 1st is New Year's Day, and we go to the shrine for hatsumōde with the family.
一月の東京は乾燥していて、空気がとても冷たい。
Tokyo in January is dry, and the air is very cold.
新しいプロジェクトは来年の一月から始まる予定です。
The new project is scheduled to start in January next year.
2the first month of the traditional lunisolar (kyūreki) calendar — overlapping roughly with what is also called 睦月 (mutsuki). Encountered in classical, historical, or seasonal/poetic contexts (waka, haiku, traditional New Year customs). In everyday modern usage, 1月 by default refers to the Gregorian January (sense 1).
旧暦の一月は、現代の暦ではおよそ二月前後にあたる。
The first month of the lunar calendar corresponds roughly to February in the modern calendar.
古い記録には旧暦一月の年中行事について詳しく書かれている。
Old records describe the annual events of the lunar first month in detail.