How many 12 AWG conductors fit in a 4 by 4 by 2 1/8 inch box?

That box is 30.3 cubic inches and 12 AWG counts as 2.25 cubic inches each, so 13 conductors is the limit before you count clamps, devices, or grounds.

Do ground wires count in box fill?

Yes, but all equipment grounding conductors together count as a single conductor volume under 314.16(B)(5), based on the largest ground present.

How much volume does a receptacle add to box fill?

A device on a yoke or strap counts as two conductor volumes based on the largest conductor connected to it, so a receptacle wired with 12 AWG adds 4.5 cubic inches.

Can I install 20 number 12 wires in a 4 by 4 junction box?

No, not in any standard 4 by 4 box. Section 314.16(B) of the NEC assigns a free space volume to each conductor, and Table 314.16(B) gives 12 AWG a value of 2.25 cubic inches. Twenty 12 AWG conductors require 45.0 cubic inches of box volume all by themselves. The largest common 4 by 4 by 2 1/8 inch metal square box is 30.3 cubic inches. Even a 4 11/16 by 4 11/16 by 2 1/8 inch box is only 42.0 cubic inches, which is still short.

Run the count the way an inspector will

Section 314.16(B)(1) counts each conductor originating outside the box and terminating or spliced inside as one. A conductor that passes through without a splice also counts as one, unless it is looped and unbroken with at least twice the minimum required free conductor length in 300.14, in which case it counts as two.

Section 314.16(B)(2) adds one conductor volume for each internal cable clamp, and only one total no matter how many clamps you have. External cable connectors do not count.

Section 314.16(B)(4) adds two conductor volumes for each yoke or strap containing a device, based on the largest conductor connected to it. A single receptacle costs you 4.5 cubic inches at 12 AWG.

Section 314.16(B)(5) adds one conductor volume total for all equipment grounding conductors in the box, regardless of how many there are, and one more if a second set of isolated grounds is present.

Common 4 by 4 volumes

4 by 4 by 1 1/4 inch square: 18.0 cubic inches, 8 conductors at 12 AWG. 4 by 4 by 1 1/2 inch square: 21.0 cubic inches, 9 conductors. 4 by 4 by 2 1/8 inch square: 30.3 cubic inches, 13 conductors. Add a plaster ring and you gain whatever the ring is stamped with, commonly 3.6 to 9.0 cubic inches. Section 314.16(A) requires you to use the volume marked on the box or listed in Table 314.16(A), and any assembled extension ring or plaster ring must be durably marked with its own volume before you can count it.

What to do instead

Use a 4 11/16 box with a 2 1/8 inch depth and an extension ring, or step up to a listed pull box or a small wireway. If the run is really carrying that many conductors, a wireway sized per 376.22 is usually cheaper and neater than stacking rings. Do not forget 314.28 if the box also serves as a pull or angle point for raceways, because that section imposes its own straight pull and angle pull dimensions that have nothing to do with box fill.

Field takeaway

Twenty 12 AWG conductors need at least 45.0 cubic inches before you add clamps, devices, or grounds. Pick the box off the volume math, not off what fits when you push hard.