Thickness of wall cement board

My toilet closet sits 13" exactly from plumbing wall. I will be putting cement board and then tile on the wall. I talked to a tile technician in a tile store and he told me the average tile thick ness is about 5/16" and mortar thickness is about 1/4". Since my toilet requires 12" from finish wall I may have problem with installing it if I put standard 1/2" cement board on the wall. Is it possible to put 1/4" cement board, will it affect tile installation? I have no problem adding more studs for strength to create say 8" o.c. instead of 16" o.c. that I have now.I can also add horizontal boards between vertical studs.
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If you applying the tile backerboard over an existing wall the 1/4" hardibacker is fine with no additional studs or support required. If you have 13" from the stud wall to the center of the toilet flange you can use 1/2" hardibacker or durock applied directly to the studs and you will be fine. For thinset you lay up the mortar using a trowel with a 1/4" notch but by the time you press the tile into place you don't use the full 1/4".
BTW, the 12" out is from the finished wall. With most toilets there is still a little gap to the wall.
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Colbyt
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I do not have any exiting wall. So 13" is from plumbing wall (edge of studs)_ to the center of toilet closet. Is it fine distance? I am afraid if I will put 1/2" cement board then 5/16" tile thickness plus 1/4" mortar thick ness I will get less or exactly 12" from finish tiled wall. In some worse scenario 12" toilet may not fit.

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