In our NJ town, one fills out the paper work for the permit outlining the plans to the best of their ability; then the code official makes any changes and/or corrections needed. Hopefully it is the same in your town. Before you make yourself nuts trying to figure out what would be the correct formula..contact the town construction code office, as ask if they can help you with that part. IMO, they most likely will be happy to do so.

Or...contact the NJ Department of Community Affairs construction code division. I have found them to be extremely helpful more than once in the past on code questions with regard to our home improvement projects.

As a general rule, this is why it is never a good idea for one to advise another that it is OK to not get permits as long as one follows code. Code is not all that clear to those who are not well versed in such...this is a classic example how it can indeed be quite confusing.

I believe what the formula is trying to determine is if the mechanical room is an unconfined space. If the space is big enough then it is assumed that there will be enough leakage from little cracks for the combustion air to draw from. If your total basement was big enough then you would have to cut grilles in the wall btw the mechanical room and the finished basement. That way the equipment could draw air from the finished portion. This may not be acceptable if your equipment is noisy. If in your case the basement is not big enough then you will have to draw combustion air from the outside.
How difficult would that be for you? If you don't like that idea then you could fill out the paperwork and wait for the official to tell you what is acceptable.

funnycide is correct.

The purpose of the formula is to determine the physical area in cubic footage required to provide an adequate supply of combustion air.

For example, you have two furnaces @ 82k/btu each and a water heater at 75k/btu for a total of 239k/btu.

We then divide the btu x 1k and multiply by 50 to determine the required cubic footage of the room or structure where the combustion equipment is. In this case it would be:

239kbtu x 50 = 11,900cu.ft.

We then divide the total cubic feet by the actual ceiling height to determine the square footage. In this example bdl99 has stated that the actual ceiling height would be less than 8' so for the purpose of illustration let us assume the actual ceiling height will be 7'.

11,900cu.ft / 7' = 1,707sq.ft.

If the structure was greater than 1,707sq.ft it would be considered to be an "unconfined space" and no additional air would be required, however if the combustion equipment was in a smaller utility space we would need to make provision to allow air to transfer from the remaining portion of the structure into the combustion area.

In this example the required square footage exceeds the total square footage of the structure so it is then classified as a "Confined Space" and we need to make provison for sufficient outside makeup air to meet the needs of the combustion equipment.

Once we determine we need to provide a source of make up air we then need to determine the method that we will use to supply the air. The method could be a direct opening through and outside wall, a vertical duct from an attic space above or a crawlspace below or a horizontal duct from outside.

When making a direct opening through the wall we could have a single opening or we could have two openings, one within the top 12" of the combustion area and a second one within 12" of the floor of the combustion area.

In this case the combustion area is in a basement so it is highly unlikely that we can provide an air intake at the floor level so we would use the formula for a single opening.

For a single opening direct to the outside the formula is;

1sq.in/4kbtu/hr

The total btu/hr was 239,000btu.

239,000btu / 4,000btu = 59.75sq.in.sq.

Using the square root of 59.75 we can then determine that the air intake opening must be 7.72" x 7.72" or equivalent.

A 9" diameter round opening in the wall would provide 63.61sq.ft which would be just slightly larger than our required opening.

I dont know much about gas appliances but quick search for filling out that form said...    *Do not include direct-vent gas appliances. Direct-vent draws combustion air from the out-doors and vents to the outdoors.

Does a gas waterheater waste indoor conditioned air to heat water ?

Here is a link that might be useful: form calculation instructions from nj town

You are correct that a gas water heater uses conditioned air for combustion. There is also losses of conditioned air to bathroom or range hood exhaust fans, however this is not a bad thing. As that slight amount of conditioned air is exhausted to atmosphere it results in an equal amount of infiltration of outside air into the structure.

If we did not have a small percentage of infiltration there would be an extreme risk of oxygen depletion or the levels of chemicals offgassing from the building materials or furnishings reaching a dangerous level.