The scales that have this ability have a few electrodes that contact your skin. Bone, muscle and fat have different electrical properties. By sending various small currents through your body the scale is able to measure these properties. So it can roughly tell how much fat there is compared to muscles and bones. It is not accurate enough to be used in any medical sense since there are so many different variables that affect the measurement. But if you follow the user guide exactly and happens to be a upper middle class white man in your 20s or 30s living in California the results are surprisingly accurate.
Scales typically do this by sending a weak electric current through your body between two metal contacts, one for each of your feet. Different kinds of tissue have different levels of resistance so by comparing the resistance of your body and your weight it can estimate your body fat percentage.
This estimate is not particularly accurate, having a typical error of around 3-4% higher or lower. It may be better than nothing but that kind of accuracy can probably be obtained just by looking at the person.
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