The custom for men to wear a kipa all day began as a pious practice, and over time became a binding custom. Wearing it provides an opportunity to sanctify God’s name, since by doing so the person is declaring he is a believing Jew, faithful to the Torah. When one is in synagogue, praying, or studying Torah, it is even more important to wear a kipa, as this has been the practice since medieval times. Some maintain that a kipa must cover the majority of a man’s head, in which case its diameter should be at least 14 cm (5½ inches). Many say this size is required only in synagogue or while praying. Still others are lenient and say a small kipa is sufficient, even in a synagogue.
While women do not traditionally wear a kipa, married women are halakhically required to cover their hair. It is unfortunate that some do not do so. Having said that, even if a married woman does not normally cover her hair, she should do so in synagogue and while praying or studying Torah.