According to the USPS website: Rectangular envelopes are able to be processed via a sorting machine. The envelope is grabbed by on one of it’s longer sides. The machine then locates the stamp which will be either on the upper right corner or, if the envelope is upside down, on the lower left corner. The machine will then rearrange the letter (takes up to 2 motions) to read the address and route the envelope properly.
With a square envelope, there is no long side for the envelope to automatically land on. The machine would have to take more steps to get it adjusted properly in order for the machine to read it. Since the Post Office sorts so much mail, it is easier for the machine to simply remove the square envelope from the sorter. At that stage, it is necessary for a human to manually enter the address into the system so that it may be routed to the appropriate Post Office. A human dealing with entering an envelope manually costs the Post Office ten times more than what it would cost if the envelope was machinable. Thus, the additional cost for square envelopes. The surcharge for non-machinable envelopes is .20 cents for the first ounce.
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