Apple's web site says there are 38mm and 42mm versions. On the back of one in a photo, it says "42MM CASE".
If 38mm and 42mm are the case widths, not including the crown, and the side view is the same scale as the front view, then the thickness including the sensor is between 14mm and 15mm, not including the sensor bulge. Under 13mm thick for just the case, minus sensor bulge.
My slimmest automatic watch is 11mm, so the Apple Watch will be a couple or 3 mm thicker. But that's still thinner than my diving watch.