-(으)ㄹ까요?: Shall We, and Am I Right?

-(으)ㄹ까요? does two things that feel unrelated in English and sit comfortably together in Korean.

같이 갈까요? — Shall we go together? (a suggestion)
비가 올까요? — Do you think it’ll rain? (wondering)

Same ending. What changes is who the subject is.

Building it

Take the stem and check the last letter.

Vowel → -ㄹ까요
Consonant → -을까요
ㄹ → -까요, and the ㄹ stays

가다   →  갈까요?
먹다   →  먹을까요?
살다   →  살까요?      ← ㄹ does not drop
공부하다 → 공부할까요?

That ㄹ behaviour is worth noticing. Before -(으)니까 and -(스)ㅂ니다 the ㄹ disappears — 사니까, 삽니다. Here it does not. There is no unifying rule to derive; each ending has to be learned with its own ㄹ behaviour.

Drop the 요 for casual speech: 갈까? 먹을까?

Job one: suggesting

When the action is something you and the listener could do together:

• 커피 마실까요? — Shall we get coffee?
• 이거 시킬까요? — Shall we order this?
• 내일 만날까요? — Shall we meet tomorrow?

Because it is a question, it leaves room to decline. That is the whole reason to prefer it over -읍시다, which proposes rather than asks and can land as an instruction when said to someone senior.

If you learn one way to suggest something in Korean, learn this one.

Job two: wondering

When the subject is not you-and-them, there is nothing to propose, so the ending can only mean I wonder:

• 비가 올까요? — Do you think it’ll rain?
• 그 사람이 올까요? — Will he come, do you think?
• 이게 맞을까요? — Is this right, I wonder?

Rain cannot be invited anywhere. The subject rules out the first reading, and Korean speakers do not experience any ambiguity.

For wondering about the past, insert the past marker:

갔을까요? — Do you suppose they went?
어제 비가 왔을까요? — Do you think it rained yesterday?

The one you will use most

어떨까요? — 어떻다 (to be how) + -(으)ㄹ까요.

내일은 어떨까요? — How about tomorrow?
이렇게 하면 어떨까요? — What if we did it this way?

It floats an idea without committing to it, which makes it extremely useful in any situation where you are not the one who decides. 될까요? (would that work?) does similar duty.

Quick reference