You're on the right track in thinking about box fill. You are correct that the scenario you described would be a violation of the NEC regarding box fill.Here’s a breakdown of the issues and some potential solutions, keeping in mind that I am an AI and cannot provide code-compliant solutions and that it's always essential to consult local codes and a qualified electrician for the final decision and implementation.

The Problem: Junction Box Fill Calculation Your Calculation

Your calculation of 14.0625 cubic inches for the box is correct based on the dimensions you provided.

Wire Fill Calculation

You're slightly off on the wire fill calculation. Here's the breakdown based on NEC (National Electrical Code) for 14 AWG conductors: Each 14 AWG conductor = 2.0 cubic inches

Two 14-2 cables

Each 14-2 cable has two current-carrying conductors and one equipment grounding conductor. 2 cables x (2 conductors + 1 ground) = 6 conductors x 2.0 cubic inches = 12 cubic inches

One 14-3 cable

The 14-3 cable has three current-carrying conductors and one equipment grounding conductor. 1 cable x (3 conductors + 1 ground) = 4 conductors x 2.0 cubic inches = 8 cubic inches

Device Fill (if any)

If there are devices such as a dimming module mounted in the box, you have to add the double volume allowance for a number of conductors from the device

Total Fill

12 + 8 = 20 cubic inches minimum

You are

well over the box fill capacity.

SolutionsHere are several possible approaches to consider, ranked roughly in order of desirability (least invasive to most invasive, assuming that is the customer's desire), but also considering safety and code compliance:1.

Inspect The Existing Junction Box Thoroughly

Check for Listed Cubic Inch

Ensure that the junction box is not marked in a way you've overlooked, and look at other similar boxes.2.

If Using Shallow Housing Recessed Lights. Some shallows come with a larger junction box that may accommodate the wires.3.

Remote Junction Box



Description

This involves installing a larger junction box above the ceiling (in the attic or accessible space) and extending wires from that box down to the recessed light.

Pros

Solves the box fill issue without cutting into the finished ceiling. Provides easier access for future maintenance. Allows for use of standard, readily available junction boxes.

Cons

Requires access to the space above the ceiling. Adds more labor and materials. May require running additional conduit or cable protection if the wiring runs through inaccessible spaces.4.

Larger Recessed Housing



Description

Find a different 5" recessed housing that is rated to accept a higher box fill

Pros

Solves the box fill issue without cutting into the finished ceiling.

Cons

May not exist.5.

Install a Junction Box Into the Ceiling



Description

Cut a hole in the ceiling to install a larger junction box closer to the recessed light location.

Pros

Solves the box fill issue.

Cons

Requires cutting into the finished ceiling (which the owner doesn't want). Aesthetically undesirable.

Important Considerations



Accessibility

Any junction box you install must be accessible. That means you can't bury it in the ceiling without a cover that can be removed.

Local Codes

Always check with your local electrical inspector about what is allowed in your jurisdiction. Local codes can be more restrictive than the NEC.

Professional Help

If you're unsure about any of these steps, or you run into complications, it's best to consult with a licensed electrician.

Recommendation:*Start with the least invasive options, like inspecting the original box. If those don't work, move to a remote junction box in the attic. While the remote junction box requires more labor and access, it generally provides the most code-compliant and maintainable solution while minimizing disruption to the finished ceiling. Flag for review