Eli5: Calories. How do they work with weight? Would 100 calories of sugar be the same as 100 calories of protein? How many would result in gaining or losing a inch off your waist?
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Calories is just how much energy is in something.
Some things are more calorie dense than others. For fats sugars and protein the calories are as follows:
Carbohydrates(sugar): 4 calories per gram
Fat: 9 calories per gram
Protein: 4 calories per gram
In order to lose a kilo of bodyfat you need to be in calorie deficit summing up to 7700 calories.
As for inches off your waist that varies drastically person to person. Different sizes and some store fat differently.
Calories are a way to measure the amount of chemical energy in a substance. It answers the question of “how much energy can be released by breaking this substance down?”
100 calories of sugar are equivalent to 100 cals of protein, yes.
There is no flat out answer for your last question. Everyone has different daily demands for calories.
For a calorie as a unit of measure, it doesn’t matter if it’s sugar or fat or protein or gasoline. For how our bodies react to, digest, and store that calorie, it matters somewhat. Sugar is “easy energy” the calories arrive in spike and are likely to be stored as fat if they aren’t used up. This put the Krebs cycle into “fat storage” mode. Fats are also easy energy, but the Krebs cycle is in “fat usage” mode. Protein is harder to convert to energy, so it tends to be a more spread-out energy supply rather than a spike. It also doesn’t convert to fat, so you can have “rabbit starvation” where a person eats a ton of protein with no fat or cards and slowly starves (if a person only eats rabbits).
The are the same in terms of calories; that’s like asking which weighs more, a pound of feathers or a pound of lead.
But you don’t want to go using that lead to stuff a pillow. That sugar won’t be as filling and won’t satisfy you for as long as you’ll be hungry and back for more sooner. The source of that sugar also likely doesn’t have much else you need with it while the protein probably does, so you get more useful things with protein than just calories.
As others said the last can’t be said for sure, but the rule of thumb (that I was taught) is for men, 11 calories per pound of desired weight and 10 for women. So a man who wants to be 180lbs should eat 1980 calories. But you’ll want to be under that to reach it quicker. There’s just no way to tell when that would take an inch off a specific person’s waist.
No one’s addressed your second question so I will. There’s no real ratio of calorie to inches on the waist, as where you store fat is 99.999% genetic. But, a pound of fat is roughly 3,500 calories, so a typical weight loss regimen is to cut out (and or burn more) about 500 cal per day to ultimately lose a pound per week. This is where the food source matters. Protein (and fat and complex carbs) will help you feel more full than simple carbs (sugar, candy, sweet drinks). This can help with fat loss as you don’t feel so hungry.
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