There is no absolute set answer. The necessary joist height (thickness) depends in part on the distances you are trying to span. It also depends on the load you will be putting on the joist, how widely you space your joists, and the type of wood your joists are made of. A good grade of 2X10 lumber might be used for joists spaced 16 inches apart where the longest clear span is no more than say 15 feet. If you needed to span a room that is 20 feet across with lumber of the same quality, you might need to use 2x12s that were spaced no wider than every 12 inches. You mentioned a 7000 square foot home. I would lay odds that you intend to have large open rooms downstairs. That fact alone means you will need thicker joists. The whole issue of space between the floors for can lights and ductwork is secondary compared to making sure that your joists will support the load that is put on them. This is NOT an area that a novice should be playing around in. I have an undergraduate minor in physics and despite having recently read far more about joist loads and span table that I ever wanted to, and I can barely comprehend the subject. I would NEVER trust myself to actually try to determine the proper size joists for a house without help from a structural engineer. And frankly, I rather doubt most architects - who are only required to take a very minimal amount of physics to get their degrees - really understand span load tables either. I suspect (pray) they confer with qualified structural engineers whenever they are designing anything out of the ordinary. But, let me give you two examples and tell a cautionary tale... In our current house, the joists are 2x12 lumber. (I know b/c several years ago I repaired the sheetrock in the dining room after we had a leaking pipe.) However, our current house is a very simple rectangular shape of only 1900 sq feet. It has a central staircase with rooms on either side. The joists between the 1st and 2nd floor run perpendicular to the staircase and the widest room they have to span is only 14.5 ft wide. The HVAC unit also sits in the middle of the house (behind and just to one side of the staircase) so the AC ducts run parallel to the joists (i.e., each duct lies between two joists) to reach the rooms on either side of the staircase. A soffit over my kitchen cabinets houses a duct that runs perpendicular to the joists from the HVAC unit to the back of the house. Parallel ducts T out of the top of this to reach the rooms that are at the back of the house. No holes had to be cut thru the joists to accomodate the ductwork. Meanwhile, all our upstairs plumbing is centralized over a single "wet wall" so all the drainage pipes run straight down. Again, no need to cut holes thru those 12 inch joists. The only holes drilled through our 12 inch joists are little tiny ones that accomodate electrical wiring. Now the second example and the cautionary tale... Our new home - still under construction - is a 3200 sq ft house with a much more complex design with much larger rooms downstairs. I will also have two large cast-iron bathtubs upstairs and wanted to be sure their weight, when filled, would not be a problem. My architect and his engineer specified 18" deep open-web trusses spaced 16 inches on center. To save money however, my builder elected to use 18 inch i-beams joists made of oriented strand board (OSB) instead. (Actually OSB is stronger than real lumber when used for ibeams.) The engineer at the lumber store where my builder bought his lumber package told the builder he could place safely place the OSB ibeam joists 24 inches apart. I was out of town for several days while framing was going on so first time I saw the i-beam trusses, my builder was already framing up the second floor. I immediatley insisted that he stop what he was doing and verify with his engineers that he would be able to cut large enough holes thru the ibeams to accomodate my HVAC ducts BEFORE he went any further. I should have just told my builder he had to follow the specs but I was trying to be reasonable. I told him that IF holes could be cut through those ibeam joists large enough to accomodate HVAC ducts without compromising their structural integrity, he could go ahead and use them. But, if not, he needed to back up, take down the second floor framing, and replace the ibeams with the open web trusses specified in the plans. Two days later, in one of many many lies he told me, my builder said he had checked with his engineer and that the HVAC ducts would be "no problem"... that I should "trust him" and "let him do his job" because he was a professional. Foolishly, I did so. Later - after my house was fully framed, sheathed, roofed, shingled, sided with Hardie, had all windows and doors installed, and the exterior was painted - I learned for the first time what my builder meant by "no problem." It meant he had unilaterally decided that he would move the two HVAC units and ductwork up into the attic so holes would not have to be cut thru the ibeams for the ductwork! He completely ignored the fact that this decision meant the HVAC would no longer be in the heated and cooled envelope of the house which would increase my utility bills AND require him to purchase larger and more costly HVAC units; that running flex duct down from the attic to the first floor rooms required chases which took significant amounts of space out of each of my bedroom closets; and that positioning two HVAC units and a spiderweb of flex duct in the attic made it completely impossible to ever consider putting in an attic bedroom - which was the whole reason I had elected to have a 12/12 stick built roof in the first place! But my cautionary tale continues... It then turned out that the necessary holes for the plumbing drainage pipes was too much for the joists! In some cases the joists span distances of 25 feet. Once the plumber cut a 4 inch diameter hole through several joists to accomodate a toilet drainage pipe, the joists started bowing inward. I noticed rather quickly that the sub-floors on the second floor were no longer level. My builder tried to tell me that it was "normal" for the subfloors to bow a little but that putting the final layer of flooring on top would correct the problem! HAH! By this point, I was long past trusting anything the man said. We are building out in the country where no inspections are required except for septic systems but I had included in my contract a provision allowed me to call in an independant third-party inspector at any point. The contract stated that the third-party inspector's finding and recommendations regarding the safety or structural integrity of any element in the house would be controling. In other words, if the inspector said something needed to be done, builder had to do it at his cost. The inspector required my builder to go back and put an additional 18 inch i-beam joist between every pair of existing joists that had had a hole cut thru it. So now the joists are spaced every 12 inches instead of every 24 inches and the second floor no longer bows. I don't know what it cost my builder to put in the additional joists and then to replace the drain pipe he had to cut... but I'd lay odds the total cost was more than if he'd used the open web trusses in the first place. In case you're wondering, we ultimately fired the builder and filed suit against him after even more issues reflecting his incompetance and dishonesty. Now I'm the GC to finish the build... and believe me, I'm relying heavily on my third-party inspector to help me get things done right! The bottom line, simply by asking "10 inches or 18 inches? which one is the correct answer?" you reveal that you have a lot to learn before you proceed. You might start by reading this link. Here is a link that might be useful: Tutorial on joist design

My guess is that as long as it isn't directly underneath some huge point load (like a valley rafter or the jack studs of a large-headed opening above) the answer is "probably". If the framing was laid out neatly, there is another stud bay or rafter bay above the joist bay you're using. Make the hole as neatly as possible, try not to destroy the band. If you would feel better, add a vertical 2x4 leg on the flat to each side of the hole. This will support the bottom plate above you, and hopefully prevent the band from crushing under load. Casey

Apparently everyone has a different code book than I do. Section R502.8.1 of my IRC book limits the depth of a notch to D/6 [not D/3] so the maximum notch depth for a 2x8 is 1.2" [not 2.42"]. I hope no one is taking the deeper notching advice seriously. There also seems to be confusion about the difference between "acceptable engineering practice" and residential building code prescriptions. The code allowances for notches on the tension side of a joist is based on long time field observations where the adjacent joists are assumed to help support a weakened joist via the floor sheathing. In this prescription the code doesn't consider the potential for excessive floor bounce nor is that a consideration anywhere else in the code. "Acceptable engineering practice" is based primarily on the Timber Construction Manual and would require a joist to provide support for the original design loads for it's entire length. That would result in a maximum notch at the 1/3 point of your example of approximately .6" which is half the code allowable depth and one fourth the D/3 depth claim. Sometimes the building code is not more restrictive than the rules of good design and common sense.

"The pre-made repair plate is quite thin and it's made for a small hole in the joist, not for most of it cut away. So no, they haven't done calculations for me. " Did you read the listing? It is designed for more than the maximum cutting, but yes, it still has limits. If you need a PE sealed fix to satisfy an AHJ, open your wallet. It should only be under $1,000 to examine the joist, determine the loads, and design a fix. PE stamps come with liability, so they are not used for free. Or you can just guess (but be careful, your comment about "repair plate is quite thin" indicates you may be in over your head. Even thin metal has surprising strength when formed and applied correctly. All the metal is fixing is the maximum shear load the joist is designed to carry so it does not need to be especially heavy if it is formed and fastened correctly.