Not used as a standalone noun in modern Japanese. Appears almost exclusively in the set phrases 途方に暮れる (to be at a loss) and 途方もない (extraordinary, absurd). The glosses 'way', 'destination', and 'reason' reflect the underlying meaning that feeds into these idioms.
See also: 途方に暮れる · 途方もない (とほうもない)
The expression 途方に暮れる describes a state of being completely at a loss, not knowing what to do.
途方もない is used, as in 途方もない金額, to describe something so extreme it defies common sense.
Standard kanji spelling; almost always used in set phrases.
Kana spelling is common in everyday writing, especially when the word appears in fixed expressions.
途 (way, road) + 方 (direction, side). The combination originally meant 'way' or 'direction', but in modern Japanese it survives only in fixed idiomatic expressions.