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Weight or fat? Weight would be dehydration or lopping off body parts.
For fat, it's the 'Rule of 30'. For every lbs of body fat you have, multiply it by 30. That's the maximum number of calories your body can extract from stored body fat per day (it's actually close to 32 but 30 covers variations in individuals and adds a small safety margin).
The above number is the maximum calorie deficit you can be in each day before your body does things you don't want, like breaking down muscle or slowing your metabolism. This is based on data from the Minnesota Starvation Experiment and might only be valid for fighting age white males.
For example, if you weight 180lbs and have 33.3% body fat, you have 60lbs of fat. You can have a calorie deficit of about 1800 calories with your body fat making up the difference. This comes out to about 1/2 lbs of fat loss in a single day.
Keep in mind that a 1800 calorie deficit is the max and your brain is going to fuck with you keep you from making that happen because it's in our nature to want to hold on to fat unless we have no choice. Also realize that as you lose lbs of fat, your maximum calorie deficit will get smaller, making the maximum possible amount of fat loss per day shrink.
If you were to do this, it would be important to get an accurate measure of your body fat. Home scales aren't great at this though they are ok for identifying trends. I recommend springing for a DEXA Scan and compare that to the number from your home body fat scale to get a error margin. The home body fat scale that you both step on and hold a sensor in your hands will give better results than step on or hold on their own. (pic related)
One last note: I believe the above will spike your cholesterol because even though dietary cholesterol has a dubious connection to blood cholesterol, the burning of body fat likely frees up stored cholesterol at a rate faster than your body can clear. When I used the above, I developed a small xanthelasma under each eye.
