Okay. No answers. So let's go with conversion of any recipe. There are any number of recipe converters on-line. Here's one:
Recipe Conversion Calculator for Cooking Measurement Conversions
To use it, you enter each ingredient for any recipe that expresses the amount it makes in terms of pan size or volume. We're going to use the servings type conversion by expressing volume as servings, as you'll see.
You can use the Option #1 - Serving. A serving is just one unit, and you want to convert from one number of units to another number of the same units. Now, you don't specify the depth of your pans, so let's just assume any pan you use will be the same depth as any other. We just say it is one unit deep. That way, we can just use surface area for scaling. So how many units is in a 4.5 inch round pan? The actual depth of you pan won't matter, so long as you use a starting recipe designed for the same depth.
That's a circle of radius 2.25. The are is pi x (2.25)squared. Which, rounding, is 3.14 x 5, or 15.7. Call is 16 one-unit servings in that 4.5-inch round pan. That's the number of servings we want to scale up or down to.
So, let's say we find a recipe designed for a 9-inch round pan, a very common thing to use. So, how many servings in the 9-inch round? Half of 9 is 4.5. 3.14 x (4.5)squared is 3.14 x 20.25, which is 63.5 or so. So, 63.5 servings in that 9-inch pan.
So, in out on-line converter, we want to have it convert the recipe from 63 servings to 16 servings. The converter will produce the new quantities for ingredients.
For a square pans, it's easier. Your 7-inch pan has 49 unit servings. A 9-inch pan has 81 unit servings. So, you convert a 9-inch recipe to a 7-inch recipe by converting from 81 servings to 49 servings.
The differences are more dramatic than one might think at first glance, so the converter is a good tool. I actually think the above numbers will work for most of the recipes you find, since those are very common pan sizes. PLUS - Now that we've done all that for the most common 9-inch pans, it's pretty safe to say you can make 1/4 of a 9-inch round recipe for a 4.5-inch round pan. And a little more than half of a 9-inch square recipe to fit a 7-inch square.
You have to make an adjustment if your pan is a different depth from the recipe pan. If yours is deeper, you will want to convert to more serving. Twice as deep, twice the servings. If the recipe pan is deeper, you want to say the recipe is for more servings. Twice as deep recipe pan, say the recipe make twice the calculated unit servings. But if you're okay with both pans being the same depth, just do as above.