Shipping companies like FedEx or UPS sometimes determine the shipping rate by calculating the dimensional weight, or dim weight, of the package. For example, FedEx instructs their American audience to calculate the size in cubic inches and then to divide by 139. Others may use a divisor of 166 or 194. The result is the dim weight in pounds.

139, 166 and 194 are not obvious at first sight—the imperial system rarely makes things obvious!—but the intent is to estimate, respectively, 1/5th, 1/6th, and 1/7th the density of water:

5 (lb) * 453.59237 (g/lb) / (2.54 (cm/in) ^ 3) = 138.39952

6 (lb) * 453.59237 (g/lb) / (2.54 (cm/in) ^ 3) = 166.07943

7 (lb) * 453.59237 (g/lb) / (2.54 (cm/in) ^ 3) = 193.75933

In plain words: 5 lb of water has a volume of 138.39952 cubic inches, and so on. And a package having a volume of 138.39952 cubic inches is assumed to have a dim weight of 1 lb, or 1/5th of water.

The funny thing is: all shipping companies round these figures correctly except 138.39952 which is rounded up to 139. My guess is they did the same math as above except they approximated the pound as 454 g instead of exactly 453.59237 g:

5 (lb) * 454 (g/lb) / (2.54 (cm/in) ^ 3) = 138.52390 …which rounds to 139.

Therefore all the shipping companies who use a divisor of 139 instead of 138, such as FedEx, actually underestimate the intended dim weight by 0.7%, and correspondingly undercharge customers. Who wants to tell them?