BMI
Quetelet, 1832
Weight in kilograms divided by height in metres squared. Adolphe Quetelet built it to describe populations and said in the same work that it did not apply to individuals, which is still the fairest summary of what it can and cannot do.
Energy
Mifflin-St Jeor, 1990
Predicts resting energy expenditure from weight, height, age and sex. Multiplying that figure by an activity factor gives total daily energy expenditure. The resting half lands within about 10 percent for most adults. The activity factor is the loose half, because you are grading your own week.
Body fat
US Navy circumference method
Reads neck, waist and, for women, hip against height. Ideal weight compares the Devine, Robinson, Miller and Hamwi formulas with the healthy BMI band. All four take height and sex and nothing else, so they return a reference figure rather than a target.
Hydration
Body weight plus exercise
No equation here measures you. Each one predicts the average of a study population, and two weeks of your own data will beat any of them.