Doors – How to frame a door in a passageway

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I'd like to add a door into the entrance of a passageway which leads into the bedrooms.
The entrance dimensions are 87 1/4 X 39 3/4 and is drywall.
it seems the standard door widths are 36 X 80, so it seems I will need to add a frame.
I've looked at some doors and the "assembled" height/width seems to be 1.75 inches over the doors widths – what does this mean?
What would be the best method of building a frame to support a door on this size, especially the top as I have just over 6 inches I'll need to build up.
What would the internal dimensions need to be to support a door 36 X 80?
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Best Answer

The recommended rough opening for a 36" x 80" door, is 38 1/2" x 82". So you're basically looking at something like this.

Door opening

Basically, you'll have to fill the purple area with framing. Which means you might have to either use thin planks on the sides, or cut into the walls to install framing.

The rough opening (blue) around the jamb (brown) will be left open, and shims will be used to make sure the jamb is perfectly level and plumb. This area will be covered by the casing, once the door is trimmed out.

Finally the door (green) will be fitted within the jamb.

The 1 3/4" you're seeing as "assembled" dimensions, includes the door, the small gap between the door and the jamb (3/16"), and the jamb itself (11/16"). This is typical of prehung doors.