There are several methods of determining body fat. Everything from height and circumference to dual energy X-ray absorptiometry can be used in determining body fat percentage- with varying accuracy. The more expensive methods (dual X-ray, Body Average Density Measurements) tend to yield more accurate results, yet require special equipment and professional supervision. Most home body-fat measurement kits use Biolectrical Impedance Analysis, which, while not the most accurate, is probably the most affordable and convenient method for a person to routinely measure their body fat percent. These monitors are sometimes sold with scales.
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There are a few ways you can do this but they all have their advantages and disadvantages. 1) Have skin-folds taken, see and exercise physiologist, or maybe a doctor or personal trainer to have this done
2) bio-electrical impedance - this is those scales that display your percentage body fat
3) underwater/hydrostatic weighing - not sure where you would go for this or how much it would cost (but this is the gold standard)
4) dual energy x-ray absorpiometry - extremely expensive, and I'm pretty sure you need a doctors referral just a quick thing about body fat percentage though, it's only an estimation as it is based on a calculation and it is unlikely to be entirely correct (could be out by something like 10-15% depending on accuracy of testers etc. so if for example your body fat percentage is 25% it really means that it could really be anywhere from 10-40%).
my point being do you necessarily want to know or spend money finding this out?
Go on line and search for a body mass calculator or BMI. The steps are very easy, just plug in your height and weight and the calculator will do all the work.