How do I wire a new light sconce to an existing receptacle?

==== realize that the wall has "" wall studs "" that the sheetrock is nailed to and the centers of the wall studs are probably on 16inch centers or they could be on 24inch centers depending on the age of your house == if you have a single story home then you can drill from the attic thru the top plate and hook onto the wall socket and then move down the plate and drill a second hole for the other wall sconce and you must use wall boxes to put the wires into as they are part of the code and it is a requirement to have those boxes as they act as spark arrestor..... consult with the guy on the electrical isle at the Lowe's for correct parts and use 12 gauge with ground wire ......

You can use a receptacle box as a junction box, to add wire upwards inside the wall to a fixture box.

Both boxes would be in the same stud cavity, unless you cut a hole for the fixture box one space over, then drilled the stud between before installing the box, pulling the wire through the stud hole.

Or, if there's unfinished basement below, or attic above, run wire up there, then over to a more distant stud cavity, drilling access down through the top plate or up through the sole plate of the framing. Connecting two fixtures to the one receptacle box would need such an approach.

14/2 w/ground Romex would be fine, connected to the hot & neutral in the existing receptacle box, with new pigtails to the receptacle itself.

If this is immediately confusing, hire it done.

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