I have a closet that is 36.667 sq. ft. it seems that this is just shy of the shiur of 4×4 (Sq.) amos…is it still “proper” to put a mezuza on it OR do we say if it’s patur there’s no reason to? As always, any sources you have on the topic are greatly appreciated.
The minimum size room for a mezuzah is 4 amos by 4 amos, which is approximately 2 X 2 meters (1 amah equals approx. 48 cm, or 60 cm according to Chazon Ish). If the room is 16 square amos in area (192 cm squared), some maintain that there is an obligation of mezuzah even though one of the sides is less than 4 amos in length. In this case, a mezuzah should be fixed without a berachah.
However, if the function of the room is such that it is normal for the room to be small (less than 16 square amos), some maintain that it is obligated in mezuzah, and although most authorities do not agree with this, a mezuzah should preferably be fixed without a berachah. This would apply to a “walk in closet” if it is a normal size for such a storage facility. However, if the room is not a multi-purpose storage facility, but can only be used for hanging clothes, it requires no mezuzah.
Shulchan Aruch, Yoreh Deah 286:13, and Shach 23 (concerning a room that is 192 cm squared but one side is less than 4 amos long); Pischei Teshuvah, YD286:11 citiing from Chamudei Daniel, concerning a small room such as a storage facility; Minchas Yitzchak, Vol. 3, no. 103 (a room that is only intended for hanging up coats, and the like, is not considered a room but only a “hole,” and all concur that it is exempt from mezuzah).