Hiking with a backpack is a heck of a lot more work than hiking without one. It feels harder, but also you're burning more calories — which is important to know as you're planning your snacks and meals for the trip.
This calculator from Outside Online will tell you how many calories you burn if you tell it your weight, the weight of your pack, how fast you hike, how steep the hills are, and how soft or bumpy the ground is.
Play with the numbers, keeping calories constant, and you can find out more than just how much food to pack. For example, how much faster could you go if you lightened your pack by ten pounds?. Or if you know how fast you hike on flat ground, how many miles can you plan to cover on hilly terrain?
In case you're wondering who went to the effort to figure out this equation in the first place: it's the military, which needs to be able to put packs on people's backs, understand how far they can realistically go in a day, and how much to feed them as they do it. It turns out that when you're planning a backpacking trip, you need to know pretty much the same things.