How many cables are you allowed to run through a single hole in a wooden floor joist?
Nonmetallic-Sheathed Cable

The Answer

According to the National Electrical Code, you can have 4 12/2 nonmetallic sheathed cables through a single bored hole that is fire- or draft-stopped using thermal insulation, caulk, or sealing foam, or where proper spacing is not maintained for more that 24 in. If you maintain proper cable spacing (which is defined by individual cable manufacturers) where not passing through joists, you can jam as many cables as you like (without damaging the cables) through a bored hole (that is not fire- or draft-stopped using thermal insulation, caulk, or sealing foam).

The Work

Article 334.80 tells you that you can use the 90°C column from Table 310.15(B)(16) for derating, but the final value must not exceed the 60°C column.  If you look at Table 310.15(B)(16), you'll find that 12 AWG copper wire is rated at 30 amperes at 90°C and 20 amperes at 60°C.

Table 310.15(B)(3)(a) tells you that with 7-9 current carrying conductors, you'll have to derate the ampacity by 70%.  So with the information from Table 310.15(B)(16), and Table 310.15(B)(3)(a). The math is quite simple.

4-6 current carrying conductors
30 amperes * 80% = 24 amperes
7-9 current carrying conductors
30 amperes * 70% = 21 amperes
10-20 current carrying conductors
30 amperes * 50% = 15 amperes

Which shows that you can have between 7 and 9 current carrying conductors through the bored hole, before the wires are derated below 20 amperes (from Table 310.15(B)(16) 60°C column). Since each 12/2 cable has 2 current carrying conductors, you can figure that only 4 cables can pass through the bored hole (2 * 4 = 8).

The Codez


  National Electrical Code 2014
  
  Article 334 Nonmetallic-Sheather Cable: Types NM, NMC, and NMS
  
  II. Installation
  
  334.80 Ampacity. The ampacity of Types NM, NMC, and NMS cable shall be determined in accordance with 310.15. The ampacity shall be in accordance with the 60°C (140°F) conductor temperature rating. The 90°C (194°F) rating shall be permitted to be used for ampacity derating purposes, provided the final derated ampacity does not exceed that for a 60°C (140°F) rated conductor. The ampacity of Types NM, NMC, and NMS cable installed in cable tray shall be determined in accordance with 392.11.
  Where more than two NM cables containing two or more current-carrying conductors are installed, without maintaining spacing between the cables, through the same opening in wood framing that is to be fire- or draft-stopped using thermal insulation, caulk, or sealing foam, the allowable ampacity of each conductor shall be adjusted in accordance with Table 310.15(B)(3)(a) and the provisions of 310.15(A)(2), Exception, shall not apply.
  Where more than two NM cables containing two or more current-carrying conductors are installed in contact with thermal insulation without maintaining spacing between cables, the allowable ampacity of each conductor shall be adjusted in accordance with Table 310.15(B)(3)(a).
  
  Article 310 Conductors for General Wiring
  
  310.15 Ampacities for Conductors Rated 0–2000 Volts.
  (B) Tables.
  (3) Adjustment Factors.
  (a) More Than Three Current-Carrying Conductors in a Raceway or Cable. Where the number of current-carrying conductors in a raceway or cable exceeds three, or where single conductors or multiconductor cables are installed without maintaining spacing for a continuous length longer than 600 mm (24 in.) and are not installed in raceways, the allowable ampacity of each conductor shall be reduced as shown in Table 310.15(B)(3)(a). Each current-carrying conductor of a paralleled set of conductors shall be counted as a current-carrying conductor.
  Where conductors of different systems, as provided in 300.3, are installed in a common raceway or cable, the adjustment factors shown in Table 310.15(B)(3)(a) shall apply only to the number of power and lighting conductors (Articles 210, 215, 220, and 230).