-을까요?

V/Adj/이다, 아니다 + 을까(요)? 1. When asking the listener’s opinion or thoughts with guessing. (Do you think/guess~?) When speaking with friends, ‘-요’ is omitted.

괜찮을까?

Do you think it's okay? (Will it be okay?)

이 영화가 많이 무서울까요?

Do you think this movie will be very scary?

수지 씨가 지금 도착했을까요?

Do you think Suji has arrived now?

V + 을까(요)? 2. When asking to do something together in a polite questioning sentence. (Shall we, Should I~?) This usage extends from meaning 1, as we're essentially asking for the listener's opinion about performing an action together.

우리 수업 할까요?

Shall we start the class?

같이 커피 마실까요?

Shall we drink coffee together?

우리 전화할까?

Should we call each other?

• -을래요? VS -을까요?

They are interchangeable when the speaker suggests doing something together.

을래요?(would~)	을까요?(should~)
우리 전화할래요? O	우리 전화할까요? O
- Subject: I X 제가 전화할래요? X 네가 전화할래? O Would you like to call?	- Subject: You X 제가 전화할까요? O Shall I call? 네가 전화할까? X
- It can’t be used to make a suggestion to an older listener. 사장님, 저희 전화할래요? X → It sounds rude	- It can be used for an older listener. 사장님, 저희 전화할까요? O

• For meaning 2, since it is a suggesting sentence, it cannot express tense.

갔을까요? X

• For meaning 2, since it is a suggesting sentence, it cannot express tense.

갔을까요? X