Size of Cap or YarmulkaThe reason R. Appel uses the vague term "reasonable size" is that R. Moshe Feinstein never defines a minimum size. R. Eliezer Waldenberg (Tzitz Eliezer 13:13) points out that this information is missing. All R. Moshe Feinstein says is that the yarmulka must be of the size that one's head is generally considered by people to be covered. R. Ovadiah Yosef (Yechaveh Da'as 4:1) writes that a yarmulka must be big enough and properly placed so that it can be seen from all sides.
As long as it is considered a head covering, a yarmulka, or cap, of any reasonable size suffices, inasmuch as it complies with the requirement to cover the head as a sign of piety (midat hasidut), and likewise removes the concern lest one appear to be following the customs of the heathens. While one who is more strict in his observance will take care to cover the greater part of the head, a head covering of any reasonable size nonetheless meets the basic requirement, and can be worn in the house or on the street, and even while reciting blessings or during prayer.
A stricter view is that of the Chazon Ish. Piskei Teshuvos (2:9 n. 58) quotes from sources that state that the Chazon Ish held that a yarmulka must cover the majority of one's head.