The measurement of the Batim-Understanding the 4×4 Chabad Batim:
Letter of law: The length and width of the Batim [i.e. Ketzitza] do not have any [minimum or maximum] size. [Nonetheless, one cannot make them too big that they won’t rest on the head properly, and may also not make them too small, due to the difficulty in writing such small Parshiyos.] The Titura, however, has a minimum length and width of more than one fingers worth [i.e. more than 2 centimeters].
Opinion of Geonim: The Geonim, however, state that the Bayis [i.e. Ketzitza] of the Shel Rosh is to initially be 2 by 2 fingers worth [which is 4 by 4 centimeters], and the Bayis of the Shel Yad is to initially be 1 by 1 fingers worth [which is 2 by 2 centimeters], although it is not invalid if made will be less your measurement.
Final ruling and custom: Practically, although the custom is not like the opinion of the Geonim, one is to suspect for it and do so. [Indeed, the Chabad custom is like this latter approach to make the Batim/Ketzitza 4×4 centimeters. Now, although this ruling only applies to the Tefillin Shel Rosh, practically this size is followed also for the Tefillin Shel Yad. This was like was the custom of other Gedolei Yisrael, and many sects of Jewry of previous times, and in fact they would wear Tefillin of even much larger size, such as 7×7 cm. Practically, today, the standard size of regular Batim is 3-3.5 centimeter square for the Ketzitza, and a total of 5 by 5 centimeters with the Titura, and thus fulfills the above stringency when measured together with the Titura. Standard Chabad Batim are made 4×4 centimeter for the Ketzitza, and another 1-2 centimeters for the Titura. This applies for both the Shel Yad and Shel Rosh, although some are accustomed to get a smaller size for the Shel Yad so it properly fit on the bicep of a Bar Mitzvah boy.]
 See Admur 32:63; Michaber 32:41; Piskeiy Teshuvos 32:67
 Admur 32:63; Michaber 32:41; Tur 32:41; Ittur Tefillin 3 in name of Rif; Semag Asei 25; Orchos Chaim Tefillin 26 in name of Rav Haiy Gaon
 M”B 32:189; Biur Halacha 32:41; Keses Hasofer 21:7; See Piskeiy Teshuvos 32:66
 Admur ibid based on Rosh
 Shimusha Raba, brought in Tur 32:41, Rosh, Admur ibid, M”A 32:56, Beis Yosef 32; Bach 32 that a Baal Nefesh is to make it 4×4 by both Shel Rosh and Shel Yad; Igeres Hakodesh 10 of Admur; Os Chaim 32 that so was custom of Arizal; See article of Rav Ginzberg in Hiskashrus For all the details on the subject
 So is evident from Admur ibid who defines Batim as the Ketzitza and not Titura; Tur 32:41; P”M 32 A”A 56 in name of Rashi; Os Chaim Vehsalom 32:19; Igros Kodesh 11:364
Other opinions: Some opinions interpret this measurement to include also the Titura. [M”B 32:189; Keses Hasofer 21:7; See Igros Kodesh 11:364; Piskeiy Teshuvos 32:66 footnote 471] According to this opinion and ends up get almost all Tefillin today follow the stringency of the Shimusha Raba
 Admur ibid; Elya Raba; M”B 32:189; Piskeiy Teshuvos 32:66
 Tur ibid
 Igros Kodesh 11:306 [it is known that this is our custom]; 364 [Custom of Mehadrin]; 13:251; 15:437; Admur ibid rules that the Geonim rule that the Batim are to be 2×2 fingers [4×4 cm] and hence we are stringent like their opinion, as rules Admur; See Admur Igeres Hakodesh 10 that the Tefillin are to be 2×2 fingers
 See Igeres Hakodesh ibid; See Bach ibid who writes the 4×4 applies to both the Shel Rosh and Shel Yad; Makor Chaim 32:41 that both Batim are to be the same size; Piskeiy Teshuvos ibid footnote 468 that it is done due to Hiddur Mitzvah; See article of Rav Ginzberg in Hiskashrus
 See Darkei Chaim Veshalom 15; M”B 27:4
 As rules the M”B and other Poskim ibid; See Piskeiy Teshuvos 32:66
 See Chapter 2 Halacha 7 in Q&A!