I had the same question! I called a nice guy at Kuchenprofi USA and he measured the funnel for me. No contact info found on Amazon. The opening that goes in the bottle is 1 and 3/8 inches. Hope that's helpful :)
The Kuchenpro 18/10 Stainless Steel Funnel with Filter fits into an Ocean Spray 3 liter Cranberry Juice container and has an added white handle, to boot for easy handling. For reusable oil, a paper towel inside the funnel and held in place by the filter is a good idea. For other cooking oil like for fish seared over a gas grill grate in a cast iron skillet, I use a separate O.S. 3 liter bottle.
If the question is how much does this hold, probably 4 ounces or more.
So if you are willing to pour slowly yes, you could easily pour a gallon or more.
If you want to pour an gallon into it all at once no way.
If you want to strain a gallon of fluid, it will depend on how fine the screening is that you are going to use, I would suggest buying a 1 gallon mason jar and then using a filter in the band and pour it through that. If a big mesh is OK use stainless steel sprouting insert inside the band, in place of a lid, for finer filtration I would use cheese cloth or a coffee filter with the sprouting insert. Or simply buy a large Melita Style coffee unit and use a coffee filter and pour into that. I use such a set up with large coffee filters to filter a quart or more. Works well and the Melita style coffee pot makes it easy to pour into smaller containers. Or go straight into a gallon wide mouth mason jar.
I would also look at beer brewing supplies if you want to filter large amounts, as they are often filtering 5 gallons or more.
Top diameter (I.D.) 4.75 inches - diameter at bottom 1.5 inches (Thickness of wall is about 1/16 inch but very solid) and 3.5 inches top to bottom. The inner removable fine sieve is 2.5 inches (O.D.) and 1 inch deep. This is German made (Solingen) noted for highest quality steel and engineering overkill.