What the ratio is and where it comes from
The opening area is width times height in inches. The flue must supply a cross-section of at least a tenth of that for a lined round or square flue, or about an eighth for an unlined masonry one. The reasoning is straightforward: the opening is where air enters and the flue is where it leaves, and a chimney that cannot carry away what the opening admits will spill the difference into the room. Not the only variable, but it is the one that can be checked from the floor with a tape measure.
Why an oversized opening is so common here
Two reasons, both historical. Older fireplaces were often built generously because they were the heating system, not an amenity, and the flue was sized to whatever the mason built instead of to a ratio. And second, fireplaces get modified, a surround removed, a hearth extended, an opening enlarged during a renovation, without anybody recalculating what the flue can carry. A fireplace that smoked from the day it was altered is nearly always this, and the timing is the strongest clue there is.
Reduce the opening, do not enlarge the flue
Enlarging a masonry flue means taking the chimney apart, which is rarely proportionate. Reducing the opening is a smaller intervention with a long history: a smoke guard across the top of the opening, a raised hearth, or a permanently built-up lintel line. Each reduces the opening area until the ratio comes back into range, and each can be tested temporarily with a piece of sheet metal before anything is made permanent. That test is the cheapest diagnostic in this entire subject.
What the check does not settle
Passing the ratio does not guarantee a fireplace drafts, and failing it does not prove that the opening is the only problem. Flue height, offsets, a rough or badly formed smoke chamber, a blocked flue, a house too tight to supply combustion air, and competing appliances all matter. What the ratio does is remove or confirm one large variable cheaply, before anybody spends money on the others. That is why it belongs first, not last.