Mishnah Berurah — משנה ברורה

4 cubits - The pious trait is to [not move without a yarmulke] even less than 4 cubits, and [to do so] even when sleeping at night. There are those who lean towards saying that [moving] even 4 cubits [without a yarmulke] isn't prohibited according to [Jewish] law except for [those who are] modest in their ways. However, the Ta"z has already written below in siman 8 that in our time it is entirely prohibited according to [Jewish] law to have one's head uncovered, even when sitting in his house - see there for the reason. And so too writes Mahar"i Bruna. And Magen Avraham writes that even for minors it is correct to habituate them in covering their heads, in order to instill an awe of heaven, as it was brought, (Shabbat 156) "Cover your head so that an awe of heaven will be upon you." And know also that regarding uncovered heads, it is enough to cover one's head with a hand, and similarly, if one is checking their head for lice, it is permitted to not cover one's head. And see further in Pri Megadim who wrote that for moving 4 cubits in the open air, covering one's head with a hand is not sufficient.