A Yarmulka should be big enough that one’s head is covered . There is an opinion to cover the majority of his head.

If a man is indoors and has nothing with which to cover his head, he may cover it with his hands, however, when outdoors he should cover his head with a sleeve. Even when indoors, when saying a ברכת הנהנין or davening, one should not rely on his hand, rather he should cover his head with a sleeve, unless he has no other choice.