有空(yǒu kōng) - to be free, to have time to spare in Mandarin

有空 (yǒu kòng) is the everyday way to ask whether someone is free. It is a verb phrase, not an adjective, so it is negated with 没 and not with 不: 没有空, never 不有空. The 有 can drop in casual speech, leaving 有空没有 or just 空不空 in some regions.

It is also the softest way in Chinese to make an open invitation. 有空来玩 and 有空聊 are the equivalents of "come round sometime" and "let's catch up", and like the English they commit nobody to anything. Take one as a firm arrangement and you will be waiting a while.

Two traps. First the tone: the 空 here is kòng, fourth tone, the reading that means a gap, not kōng meaning empty, and 有空 spoken with a first tone sounds like a different word. Second, 有空 is about a free slot, not about being unoccupied in general. To say you are not busy, 不忙 (bù máng) is the natural answer.