OK, I did some poking around on the forum but I have some specifics that I would like to receive feedback on if possible. I have an old home, the ceiling "joists" are 2X4 with 16" on center spacing. I am doubling them up to, in a sense, make 4X4 because I don't like how unsturdy they feel. Also, I am looking to add storage in the attic. I am curious to know if this will work:

I have 2X4s at 16" on center that I doubled up in addition to adding a cross brace between them every ~42". All of this over a 13.5' span, is this enough reinforcement to support decent storage? Is there a website where I could calculate my lb/ft^2 ratio?

Well, we don't know the species and grade of the 2x4's so we don't know what they can carry, but generally speaking, it's the depth of the member that counts, not the width, so you may have doubled the width, but the depth is still the same. You could get some sagging ceilings below if you store too much up there.

This is what information is necessary to design floor joists:
1. The span of the member
2. The loads to be carried
3. The species and grade of wood to be used
Attic loads by code are live load of 20 pounds per square foot, plus dead load of 10 pounds per square foot, Total Load 30 pounds per square foot. The span is the distance between supports.

The strength of a piece of lumber can vary greatly according to the species and grade. That information is stamped on each piece of lumber as a code. The symbols vary slightly from one kind of lumber to another.

The building code has span tables in it, which simplifies the design process. You just pick the species and grade of lumber, the spacing of the joists, and where those two lines cross in the tables will be the maximum span. I believe you can view the New York State Residential Code online, and refer to those tables to get your answer.

Again, generally speaking, 2x4 floor joists would be insufficient even for an attic floor. Your span is very near the outer limit for some 2x8's, suck as #2 Douglas Fir / Larch, and way past the limit for some species and grades having less strength.

Hmmmm.... Interesting comments. Well, I know that the 2x4s I put up were SPF. The old ones I was told by a contractor were the equivalent of today's 2x6s because it is the full 2x4 and the grain is much tighter because they cut from old trees back then as opposed to newer (20-25) year old trees as they do now. So, would my best bet be to replace the joists to 2x8's for the area designated for storage? I don't mind replacing them since it wouldn't be more than maybe 10 joists to replace.

Why keep guessing? Find a qualified design professional to inspect your house and do the calculation, which takes about thirty seconds, and you'll have what you need without overspending. What the contractor told you about the original joists may be a little bit right, but a 2x4 still isn't going to span over 13 feet adequately, new wood or old.

I did some work on a 100-year-old house where the floor joists spanned almost 20 feet and were 2x6. That's impossible nowadays, but it turned out that those joists were oak, not a softwood like we use now, and they were perfectly capable of spanning that distance.

Alright, sounds good, thanks for the insight.

One thing that is generally misunderstood is that the tightness of grain (old wood or hardwoods like oak) doesn't make the wood stronger. Allowable stresses for oak and other hardwoods are no better than many softwoods.
This is a general statement and not a hard and fast rule, but does hold true for most cases.

That being said, Richard is right regarding the depth. The strength is a function of the depth squared. So you would only have to increase the depth by a factor of roughly 1.35 to get the same boost as adding another 2x4. I don't believe the cross-bracing will add strength to the system.
One other thing to consider, the two 2x4's will not take equal load just because they are both 2x4's. Since they are deflecting together, they will share the load based on their relative stiffnesses (EI). Just to think about it is an extreme case (to help you visualize it) - Think about adding a 4" steel beam next to the 2x4. You can imagine that it under equal loads they would deflect differently (with the 2x4 deflecting much more). Because of the required compatibility of deformations (this just means that you would assume some nomimal deflection - say 1" - then back out what through analysis equations what load will cause that same exact deflection in each member and you will see that the ratio of loads causing that equal deflection is the same as the ratio of EI). This is an extreme example just to help you visualize the principle. It won't be as pronounced with two wood members, but will be something to consider nonetheless.