Why are studs centered at 16 and 24 in wall construction?

Answer 1

Stud placement is geared toward having support at the ends or joints in sheetrock ,decking and plywood. These sheets are 48" x 96" (4' x 8"). 19 1/4" is sometimes used for roof framing as well.

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Since the sheetrock is 48" wide, 16" makes three studs per sheet, and 24" makes 2 studs per sheet. 16 and 24 both go evenly into 48 (and 96).