Physically far; distant; located a long way away.
私の家から駅までは遠いので、自転車で行く。
The station is far from my house, so I go by bike.
山の向こうに遠い町が見えた。
I could see a distant town beyond the mountain.
彼の実家はここから遠い。
His parents' home is far from here.
Distant in time; remote (e.g. a long time ago or far in the future).
それは遠い昔の話だ。
That is a story from a long time ago.
問題は遠い将来にやってくるかもしれない。
The problem may occur in the distant future.
Distant in relationship or kinship; having little connection or involvement with someone.
彼は私の遠い親戚だ。
He is a distant relative of mine.
彼女とは仕事上の付き合いだけで、関係は遠い。
I only have a working relationship with her; we're not close.
Far from something in quality or degree; not similar or close (e.g. far from the truth or ideal).
その説明は事実から遠く、信用できない。
That explanation is far from the truth and can't be trusted.
期待から遠い成果に終わってしまった。
It ended up being an outcome far from what was expected.
Hard of hearing; used in expressions like 耳が遠い to mean difficulty hearing.
最近、祖母は耳が遠くなった。
Lately my grandmother has become hard of hearing.
Nearsighted (used in phrases like 目が遠い to indicate difficulty seeing close or certain details).
彼は目が遠いので、細かい字を読むのに老眼鏡が必要だ。
He has trouble seeing fine print, so he needs reading glasses.