Know how the carat measuring system works. Carats are a weight measure like ounces or grams. One carat equals 1/5 gram or 200 milligrams. If you convert to ounces, there are 142 carats in one ounce.
Obtain a small precision scale calibrated in grams. The type used in a high school science laboratory is perfect. Make sure the measuring pan is clean and dry. Due to the small quantities being weighed, even a tiny amount of dirt or water will cause an inaccurate measurement.
Weigh the Princess cut diamond carefully. Convert the weight in milligrams to grams by dividing by 100. For example, if you measure 150 milligrams, divide by 100 to get the weight of 0.15 grams.
Multiply the weight in grams by 5 to convert to carat measure. For instance, using a 0.15 gram Princess cut diamond, 0.15 gram * 5 is equal to 0.75 carats (3/4 carat).