Bangle size is determined by the size of your hand and not your wrist. To find yours, simply tuck your thumb into the palm of your hand (as if about to put on a bangle), and using a measuring tape, measure your hand all the way around the set of knuckles closest to your wrist. Compare that measurement to the chart below. The standard size in US is 3 for round bangles, and 2 for oval bangles.
Ring size is determined by inner diameter, not circumference. To find yours, cut a thin piece of paper and wrap it around your finger, keeping it close to your bottom knuckle. Mark where the paper meets and measure its length with a ruler. US 7 is the standard ring size. Measurements below in millimeters.