How to continue tracking weight loss from dieting when I start a strength training program that will add muscle weight

Weight can be confusing to track because you can experience variations in: fat weight, muscle weight, water weight, and food weight (the food in your digestive system).

The best way I know of to get a general idea of what's going on, if you want to be really thorough, is to do each of the following:
  • Weigh yourself only in the morning when you first get up, after going to the bathroom.
  • Use a scale that shows approximate % body fat (more about this below).
  • Measure your waist and hips with a measuring tape.
  • Book occasional body fat tests (more about this below). 

Many gyms offer group body fat testing at discounted rates, but you can also just find a body fat testing company and book directly with them for a more convenient schedule and location, usually as part of their trips to various gyms on various days.  It usually costs ~$40-70 for each test.

You can read up and decide which body fat testing method you prefer, most likely based on cost and convenience. 

Supposedly DXA scans are the most accurate, but from an engineer's perspective, I'm not convinced that they're better than hydrostatic tests.  (The latest isn't always the best, studies are provided by those who sell the service, and DXA scans are two dimensional, while hydrostatic tests are based on volume and density, which are three dimensional.)  There are other reasonably accurate testing methods/technologies as well.  Each method has its advantages and disadvantages. 

Each method tends to have certain errors, and different methods are inconsistent with each other.  So in order to track your progress, you need to stick with one method for personal consistency so that the errors will be consistent and you'll see your own progress relative to the last test, if that makes sense.

These tests are expensive enough that you probably will only get them done every few months or so. 

If you want something more frequent than that, a scale that estimates % fat can be useful.  They are less accurate than other tests because they only measure your lower body and make an estimate based on assumptions, but they are still useful in combination with the other measurements I described. 

Note that these scales can't distinguish between water weight and other lean weight.  So if you're on a low carb diet but you carb cycle and have a carb day, then when you suddenly gain 4 lbs overnight but see that your % fat also went down overnight, you can be pretty confident that it's water weight, not fat or muscle.  Our bodies tend to hold more water weight when we eat carbs.

However, if you want to keep it simple, a scale and a measuring tape should tell you everything you need to know.  Muscle is much denser than fat, so if you lose inches, you've lost fat, no matter what the scale says.  If you gain weight or stay the same but lose inches, then you've lost fat *and* gained muscle.  You can usually find flexible measuring tapes in your local pharmacy.
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