THE ACTUAL WEIGHT LOSS FORMULA
PEOPLE MISINTERPRET OR MISATTRIBUTE
IT'S FAT LOSS, NOT "WEIGHT LOSS"!
The basic goal of weight loss is to lose fat.
The purpose may be for appearance, but usually the objective is also for health and energy. The latter two, of course, affect how you feel - which in turn is a measure of quality in life.
True long term weight loss is loss of fat - but short term weight loss can be mistaken for loss of fat, as it can be "misleading". When I say "misleading", I mean that it leads us to the wrong conclusions. If I have a massive weight loss rapidly in, say, the Atkins Diet, I think, therefore, that it must be very effective.
But I shouldn't forget that my goal is really fat loss, not temporary rapid weight loss due to less water in the body, loss of muscle, and less retention of waste products of digestion and energy production. Surely, we want only fat loss, not muscle mass loss. Indeed, the loss of muscle mass will cause a reduction in metabolic rate, which is the opposite of burning more fat!
Also desirable besides fat loss is the reduction in swelling and inflammation - both of which cause more water retention. And, of course, a reduction in both of those improves our health (which is our major goal).
A so-called ideal of a body fat percentage for women is 20 to 21% and for men is 13 to 17%. Don't stop until you get to those levels!
THE FORMULA, "THE MATH"
Weigh change = Pounds in - pounds out. (Duh!)
Expended energy (burns weight)
Eliminate waste (not used for energy) - Includes net excreted water
Note that expended energy includes the cost in calories of energy needed to digest one's food. It also, of course, includes just basal resting metabolism (where calories are used just to maintain the body) plus of course energy expended for exercise and other movement. If one eats protein, about 20-30% of the calories in the protein are used up in digestion, whereas fat uses about 3% and carbs 6-8% generally. If one eats refined foods hardly any energy is needed to digest it.
Also, certain foods and practices will raise your metabolism, so that you actually burn more calories. Spicy foods, exercise earlier in the day, build more muscle, etc.
RAPID WEIGHT LOSS
I can lose 10 lbs in a week if I simply dehydrate myself and/or get rid of fecal matter and other waste in the body. If I cut down on carbs, which retain water, I will lose water weight.
Of course, that is not at all the same as losing fat, as a pure loss rather than those temporary or situational ones.
I lose water by:
Excreting more (diuretics, sweating)
Retaining less (reducing retention by reducing sodium, etc.; reducing inflammation of muscles such as by taking anti-inflammatories)
Losing muscle mass (which is 75% water; fat water % is 10%)
THE ONLY WAY TO LOSE FAT
Remember, our goal was to lose fat, not just weight.
Fat loss formula (not "weight" loss):
Fat loss = Fat burned - calories converted to fat (Calories out - calories in) (Duh!)
I lose fat by burning fat or flushing out fat. If I never eat more calories than I expend in a day, I will not gain fat. So, the rule must always be to never eat more calories than the accurately computed calories burned!
Flushing out fat somehow trapped in the body is, of course, positive, but it is also temporary and one-time - and due to the correction of a malfunctioning of the body.
The reason the authorities say that a pound of fat equals 3500 calories is simply that if we burn (use up) one pound of fat it creates 3500 calories of energy/heat. (If we store fat, we have eaten 3500 calories more than we've used up. We store fat the most rapidly when we spike our blood sugar and the insulin goes into emergency storage mode to prevent tissue damage. See Why We Get Fat.)
If we make it a rule to never eat more calories than expended, we will never gain weight (and will probably lose weight because one will have some times where one eats less).
DON'T BE FOOLED
The point of the above discussion is to prevent you from making incorrect conclusions, so that you can focus on what actually works for losing fat and not go off into appealing but less effectual side trips.