Run it backwards from the flue
The flue is the fixed part. It was built with the house, it is surrounded by masonry, and changing its section means rebuilding a chimney or lining it. The opening is the cheap part: a steel smoke guard bolted across the top of the firebox, a raised hearth, or a course of firebrick laid on the floor all reduce the opening area without touching the structure. So the arithmetic that helps is not what flue this opening wants; it is what opening this flue corresponds to.
On the numbers the form opens with: a 36 by 29 inch opening is 1,044 square inches, or 7.25 square feet. A flue measuring 7.5 by 11.5 inside is 86.25 square inches. That is 8.26 percent, or 1 to 12.10. At a ratio of 1 to 10, the same flue corresponds to an opening of 862.5 square inches, which at the same 36 inch width is 23.96 inches high. The opening is 5.04 inches taller than that, and 5.04 inches is a piece of steel angle.
| Ratio | Opening area it corresponds to | Height at 36 in wide | Against the 29 in as built |
|---|---|---|---|
| 1 to 8 | 690 sq in | 19.17 in | −9.83 in |
| 1 to 10 | 862.5 sq in | 23.96 in | −5.04 in |
| 1 to 12 | 1,035 sq in | 28.75 in | −0.25 in |
Those three ratios are shown because you will hear all three quoted, not because this page endorses any of them. Which one applies to a particular fireplace depends on the flue shape, on the chimney height, on whether the fireplace has glass doors, and above all on the code your jurisdiction has adopted, which differs by state and by city. The building department and a certified sweep settle it. What the table is for is showing how sensitive the answer is: the gap between the loosest and the tightest ratio quoted is nearly ten inches of opening height on this fireplace, which is most of it.
Where a ratio stops being the answer
A fireplace that smokes with an opening well inside whatever ratio applies has a different problem, and there are a lot of candidates. The throat above the fire and the damper in it can be narrower than the flue, in which case the flue section is not the constraint at all. The smoke chamber above the throat can have a step or a rough unparged face that trips the flow. The firebox can be too shallow front to back for its opening, which sends the fire smoke forward rather than up. The chimney can be too short relative to the ridge beside it, or badly placed for the wind. And the whole thing can be perfectly built and still spill because a 600 CFM range hood two rooms away has pulled the house negative — the makeup air calculator puts a number on how easily that happens.
Then there is temperature. An open fireplace on an exterior masonry chimney has a large cold mass to warm before it drafts properly, and the chimney draft calculator shows exactly how much of the draft depends on the gas staying hot. A fireplace that smokes only in the first ten minutes and only in mild weather is describing that problem and not a ratio problem.
Net area, and the argument about rectangles
Flue area here means the actual inside section, and it should be measured or taken from the manufacturer rather than read off the nominal size. A tile sold as 8 by 12 has wall thickness on every side and is meaningfully smaller inside. Beyond that, some sizing methods discount a rectangular flue against a round one of the same area, on the grounds that the corners carry slow-moving gas and contribute less than their share. Whether that discount is applied, and how much, is a method question for whoever is doing the design and for the code being worked to. This page reports the geometric area and states no discount, so if your method applies one, apply it to the number here rather than expecting the page to have done it.
What an open fireplace costs you in heat
Worth saying plainly while you are here: an open masonry fireplace burning at a moderate rate is exhausting a large volume of already-heated house air up the flue for as long as it burns, and in many houses the net effect over an evening is a loss. The radiant heat on your face is real and the heat balance for the building is often negative. That is not an argument against fireplaces, which people have for reasons that are not thermal, but it is the reason an insert with a properly connected liner is a different appliance in every sense. The wood stove sizing calculator covers what that does to the arithmetic, and the delivered BTU per pound field is where the whole difference lives.
Questions people ask
What ratio should I be using?
This page will not tell you, and it is not being coy. Fireplace flue sizing is set by the code your jurisdiction has adopted, and the figure differs for round and rectangular flues, changes with chimney height, and is applied differently to a fireplace with glass doors than to a fully open one. The three ratios shown in the results and the guide are there so you can see how much difference the choice makes, which on the default fireplace is nearly ten inches of opening height. The building department and a certified sweep tell you which one applies to yours.
My fireplace smokes. Will a smoke guard fix it?
It changes the one variable that is cheap to change, so it is a reasonable thing to try under advice, and the calculator tells you how much opening height a stated ratio corresponds to. But a fireplace can smoke because of the throat, the smoke chamber, the firebox depth, the chimney height, wind, a cold exterior flue, or the house being pulled negative by an exhaust fan, and none of those are ratio problems. If a fireplace has always smoked from new, the ratio is a good first thing to measure. If it started smoking recently, something changed, and finding out what changed matters more than the arithmetic.
Do I measure the flue inside or use the nominal tile size?
Inside, always, and it makes a real difference. A tile sold as 8 by 12 has wall thickness on all four sides and the actual inside section is smaller, by an amount that depends on the maker and the standard. Using the nominal 96 square inches instead of a true 86.25 shifts the ratio on the default fireplace from 1 to 12.10 to 1 to 10.88, which is enough to change what you would do about it. Get the real figures from the manufacturer or measure a spare tile.
Does a rectangular flue count the same as a round one of the same area?
Not in every method. The corners of a rectangular section carry slower gas and lose more heat per unit of flow, which is why some sizing approaches discount a rectangle against a round flue of equal area. This page reports the plain geometric area and applies no discount, so if the method you are working to uses one, apply it yourself to the figure here. The flue size calculator on this site shows the underlying difference: an 8 by 12 rectangle has about 15 percent more wall perimeter per square inch of flow area than a round flue of the same section.
Can I make the opening smaller by narrowing it rather than lowering it?
Arithmetically yes, and the results show the width that a given ratio corresponds to at your current height. In practice the height is the dimension usually reduced, because the smoke that spills does so at the top of the opening and lowering the lintel line acts directly on it, while narrowing the sides does not. That is a comment on how fireplaces behave rather than a recommendation. Anything structural at the front of a firebox, including hanging steel from the lintel, is work to discuss with a mason or a certified sweep.