I need ~8-10 sq ft of additional exhaust vents to accommodate a new 7600 cfm whole house fan. Uncertain if add'l soffit vents needed for adequate ventilation flow through attic. Planning to install 3 dormer vents near ridge. Two screened gable vents (2 ft x 1 ft) installed when house was built.
Okay looks like several folks have no idea what a whole house fan is or how it works. You need to check your fan rating to see how many CFM it will move. Then you need to take that number and divide it by 750 to see how many square feet of vent openings you need. The square feet of opening depends on the type of vent you have. The vents could be ridge vents, gable vents, turbine vents or any combination thereof. Check the square feet of opening for each vent you have and add it up. If it’s not more than the fan rating divided by 750, you need more. If you are installing a 2 speed fan, make sure you are using the higher cam rating.
If the TOTAL attic venting (ridge, soffit, gable, turbines, vent cans, etc. combined) is more than the fan requires, you're fine. If it's not enough, figure how much more you need to add to satisfy the fan, then balance that to provide 50-60% of the total attic ventilation as intake (soffits or low on the roof) and 40-50% as exhaust (gables or high on the roof). When you run the house fan, it can pressurize the attic and exhaust out of all the vents, including the soffits. Since you only run the fan a short time in the morning, before the attic heats up, there won't be any issue with air going out the soffits instead of in. When you turn off the fan and the attic heats up, the airflow will return to normal - in the soffits and out the ridge and gables.
A whole house fan needs 1 ft^2 NFVA per 750 CFM. A 36" whole house fan moving 7600 CFM from the house into the attic needs a total of 7600/750 = 10.13 ft^2 or about 1460 in^2 of net free vent area (NFVA) from the attic to the outside.
1460*40% = 584, 1460*50% = 730, 1460*60% = 876. Thus, you should aim to have 730 to 876 in^2 NFVA in your soffits and 584 to 730 in^2 for exhaust as high as practical.
FWIW, a combination of soffit & ridge vent (or near the ridge) is better than soffit & gables. The gables don't remove the hot air from above them or as effectively from the center of the house.
Hmmm...I think we're discussing two different things. Attic vents are in terms of "square inches." Room vents are discussed in terms of cfm.
Attic vents, Soffit vents, etc. are placed for "cross-ventilation" and generally not motorized.
Equipment measured in cfm is sized for make-up air, exhaust ventilation, etc. The 7600 cfm fan you mention should not be bringing in air from the attic nor exhausting air from the house into the attic.
If you have a ventilation system (HVAC system) that can bring in 7600 cfm "fresh air", then you need to exhaust about the same.
If you have an exhaust fan that exhausts 7600 cfm, then you need a "relief" air vent...it does not need to be motorized...just a relief grille (with damper).
I've been researching the same in an improvement to a house we are closing on soon, so felt I should share what I've found. Adding to a few answers here, your attic ventilation needs to satisfy two states: when the whole-house fan is on, and when it is off. The latter is harder, so let's start there.
Generally speaking, attic ventilation should be "vertical", with intakes at the soffits (or, more generally, in the lower-third of the roofline), and exhaust at the highest points possible (minimally, in the upper-third of the roofline). A good roof ridge-line vent is ideal for this, as it plus balanced soffit vents tend to promote flow across the entire inside surface of the roof, which is what you want. But, you have gable vents which are decent but far from ideal (generally, they only promote flow out the ends of the attic, or cross-ventilation if the wind is in the right direction, which allows for hot spots through the rest). An ideal retrofit would be to replace the gable vents (cover them from the inside with plastic sheeting, as they can do more harm than good) and instead put in ridge-cap venting to match the soffit venting you (hopefully) already have. That said, that is a bit more work than just adding box or near-ridge-line rectangle vents, so you might want to put that off until the next time you redo your roof tiles.
The second thing to note is that the upper vents (gable vents + dormer/box vents + ridge cap vents) should never be larger (in net free ventilation area) than the intakes, or you will tend to pull warm, moist air from inside the house rather than from the soffits (as another has pointed out, this is great for increasing the radon counts in your house as well, which is a really bad outcome, and one that I am personally interested in as well as our house already has a radon hazard being mitigated).
Generally speaking, the total ventilation area for static venting (with no whole house fan on) is the square footage of your attic floor / 150. That is, if you have a ranch home of 1500 square feet, you will need 10 square feet of net free ventilation area (NFVA). The "net free" is important, because this isn't just the area of the vent, but rather that minus the effective obstruction area of any louvers, mesh netting, etc. Note that there are circumstances here you can have half as much (area / 300), but those are specific circumstances and over-sizing ventilation is far better than under-sizing it, so some contractors will just ignore that. Moreover, the "when built" net-free ventilation area is inevitably larger than the "after the homeowner has failed to clear out the vents for a few years" NFVA, and so oversizing here is definitely going to keep you out of trouble when you forget to do maintenance (not that I am saying you would, but I do know myself, so...)
When you figure out the NFVA you will need, you want at least 50% of that to be in the intakes, and the remainder in high-on-the-roof ventilation. I have seen ratios as high as 90:10 allowed for intake:exhaust, but the ideal is as close to 50:50 as possible. In that hypothetical 1500 sq ft ranch with attic over everything, that means 5 sq ft of soffit vents and 5 sq ft of ridge or other "high" edge venting.
When you look at the venting, envision the paths the air will take. Air will take the "easiest" path possible through the attic. If you have "mid-level" intakes (ex, gable vents) as large as the "high-level" exhausts, much of the "pull" from the exhausts will be satisfied by the mid-level intakes instead of pulling from the low-level soffit vents. Again, this is why generally gable vents are no longer seen as a good roof ventilation option. Similarly, if your "exhaust" is primarily gable vents, and intakes of soffit vents, you can imagine that most of the air leaving through a gable vent will be coming from the soffits closest to it, not from those in the "middle" of the roof plane. If you are going to keep gable venting, you should plan on adding more ventilation (generally via box or near-ridgeline vents) more towards the "center" (horizontally) of the roof plane but (again) as high up as possible.
Okay, with that in place, and I assume this is already a working system today, let's consider the whole house fan being on. When the whole-house fan is on, you will have a lot of windows open in the lower parts of the house, compensating for the air being drawn up through the house. This will lower the pressure slightly in the house (that's how air moves when you are "pulling" it out), which will again draw up radon slightly, but that effect should be more than compensated for by the outside (radon-free) air coming in as natural ventilation. In the attic, though, you have a "push" system in place, which means you are pressurizing the attic. That air needs to go somewhere instead of just pressurizing. So, we need that same ventilation in the attic that we needed with the fan off, except that now everywhere is exhaust. That includes the soffits as well as gables / ridge venting / box vents etc.
Generally speaking (and different manufacturers will have very different formulas here, so make sure you use the one matched to your particular whole house fan), you have sized the whole house fan based on the square footage of the house, allowing for at least 4 exchanges of air in the house per hour. So, in that 1500 sqft ranch, assuming 10 foot ceilings to make the math easy, we have 15,000 cubic feet, which means you will want about 1000 cubic feet of exhaust per minute (15,000*4/60). But, maybe you put in 3000 cuft/min fan instead, allowing for a whopping 12 air exchanges per minute. Size the attic exhaust for the fan you actually buy, not for the minimal size. At some point, someone is going to put that sucker on "high" and you want the attic to remain unpressurized even then.
Okay, now back to the attic exhaust. Again, each manufacturer has a different formula for this, so make sure you follow the one for your manufacturer, but again it will generally be the cfm (cubic feet per minute) of the fan divided by some factor (units of ft/min) to give minimum exhaust ventilation in the attic. Again, remember that all vents are exhaust here when the WHF is on. A common number is 200ft/min, which would mean for our 3000 cfm fan we would need 15 square feet of NFVA. So, for this ranch with an oversized WHF, we now need to come up with another 5 square feet of ventilation.
Do not just add top-of-roof exhaust venting. That will upset the balance when the WHF is off, leading to a low-pressure attic drawing conditioned air from the house. Your first instinct should be to add to the intake vent system, perhaps adding new soffit vents, perhaps replacing them with more efficient venting, etc. For every square foot you add to intake, add the same to exhaust (ie, the ridge-cap venting, near-ridge venting, etc). Adding to intake is a lot more work than adding a new box exhaust fan up top; no one likes working that far in the eaves. But, if you just add exhaust instead of intakes the "exhaust" you add will end up acting as an intake instead, short-circuiting the ventilation and leaving you with mold, ice dams, and all the other hallmarks of poor attic ventilation.
Last thing to note is that soffit vents are very commonly obstructed, because they are a horizontal surface and "stuff" is generally above them. That is only compounded by them sometimes acting as intake and other times as exhaust (when the WHF is on). If baffles weren't properly installed in the attic or have since deteriorated/failed, the soffits may be covered by insulation. Cobwebs, dust+grime, critter nests, etc, all can clog up soffit vents (you are cleaning those out yearly, right?) Make sure on the worst day of the year, before you go at the vents with a leaf blower to clear them out / go up to the attic to maintain them, there is still more airflow on the intakes than on the exhaust.
Finally, if you do add "upper-third exhaust" venting, place it to make the side-to-side flow from the soffits up to the vents better. Making gable vents larger will allow more air to leave, but will make the vertical flow worse than if instead you place a few near-ridgeline vents in the center third of the roof plane (these are generally placed on the non-street-facing side of the roof, not on both sides).
There are other nuances involving using powered attic fans, which will allow for more flow through undersized venting, but using simple static venting is always the best initial approach, making for fewer things that can fail at any time.