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.
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