[1] 586/13; Michaber 586/9 [4 fingers]

Other opinions: Some Rishonim rule that the Shofar is to have a minimum Shiur of three Tefach. One Tefach of the hand and one Tefach protruding from each end. [Rabbeinu Gershom Maor Hagoleh Chulin 89a; Kol Bo p. 69] Some Poskim write based on this that that initially it is proper that the Shofar be at least three Tefachim of length in order to fulfill one’s obligation according to all opinions. [Piskeiy Teshuvos 586/8; Rivivos Efraim 4/144 in name of Emek Bracha; Yalkut Yosef Moadim p. 43]

[2] Gra”ch Naa”h in Shiureiy Torah p. 249

Other Poskim: The Chazon Ish rules that a Tefach is 9.6 cm.

[3] The reason: The reason for why the Shofar must have a minimum length of one Tefach is because it is required to be of a size that when the blower holds it in his hands, which means within his four fingers, the Shofar will be visible [i.e. protruding] from both sides of his hand. Now a Tefach is four thumb widths and hence when held within four fingers a Shofar of one Tefach will slightly protrude from both sides of his hand and be visible. The reason for why the Shofar is required to protrude from either side of his hand is because otherwise it appears as if one is blowing from inside his hand. This measurement of one Tefach applies to all people and hence even if the blower has big hands which are larger than a Tefach, and hence a Tefach long Shofar is not visible when covered by his four fingers, nevertheless the Shofar is valid, as the measurement was given in accordance to the common hand of a person. [Admur ibid; Beis Yosef in name of Rosh and Ran; Levush 586; Mateh Yehuda; Kaf Hachaim 586/89]

Is this measurement Biblical or Rabbinical? Some Poskim rule that the above Shiur of one Tefach is only Rabbinically required, however Biblically any measurement suffices. [Peri Chadash; Levush 586; Kaf Hachaim 586/89]