Right now (late 2015), the difference is about 256 miles.
The geographic north pole is the point where the north end of the
Earth's rotation axis sticks out of the ground. As long as the Earth
continues to spin on the same 'pencil', the geographic poles don't move.
The magnetic north pole is the point on Earth that magnetic compasses
point to. The magnetic poles are the result of the flowing, shifting liquid
iron in the Earth's core, and they move. The magnetic north pole is presently
somewhere in the Canadian Arctic territory, about 256 miles south of the
geographic pole, and moving westward towards Russia at about 35 miles a year.
