The energy and Young's modulus as a function of tube length for (10, 10) armchair single-walled carbon nanotubes (SWCNTs) are investigated by using a linear scaling self-consistent-charge density functional tight binding (SCC-DFTB) method. It is found that the formula derived from total energy for a zigzag SWCNT [Physica B404, 3930 (2009)] can be also used to explain these calculated length-dependent properties. Moreover, a transition occurs from fast change of length-dependent properties of the SWCNT to their slow change. This transition corresponds to the SWCNT's length of about 5 nm. The length for the armchair SWCNT is about one half of that of the corresponding Zigzag SWCNTs. In addition, a definition of volume for a short SWCNT is discussed.