I have a caliper that reads in circumference! So the caliper measures the diameter like normal calipers but the scale is multiplied by Pie so it reads of the circumference. Took me quite some time to figure out what it was, as the inch side appears nearer to cm but it has fractions of an inch, while the metric side is in tenths, that was the clue.
I wondered if that could be what this is, or maybe the other way ie by wrapping the tape around the circumference it reads off in diameter? I could not read the markings in the photo so cannot tell.
Hadn't seen the last posts where you have figured it out. Decided to leave mine there as the caliper is interesting too.