You can do it with the depth guage of your vernier caliper, use the outer diameter of the rim as a datum then take depth soundings to the bead seat and the spoke bed. Since the bead seat is a known diameter (622mm for 700c), the rest is simple arithmetic. This method doesn't need to account for non-circularity of unbuilt rims, and the errors will be part of small measurement; where 1% error on a full rim diameter measurement will be wrong by enough to make the wheel unbuildable, 2% on the 10-30mm depth measurements will be of the same order as the granularity of spoke supply.
You can do it with the depth guage of your vernier caliper, use the outer diameter of the rim as a datum then take depth soundings to the bead seat and the spoke bed. Since the bead seat is a known diameter (622mm for 700c), the rest is simple arithmetic. This method doesn't need to account for non-circularity of unbuilt rims, and the errors will be part of small measurement; where 1% error on a full rim diameter measurement will be wrong by enough to make the wheel unbuildable, 2% on the 10-30mm depth measurements will be of the same order as the granularity of spoke supply.