This  signal to noise ratio is known  as Shannon's limit.  Assuming all computers, modems, telephone lines etc are working flawlessly,  Shannon's limit for computers communicating with each other over a dial up network is 56k.

 Prior to 2002 the modem speed limit in the united states was 53k.  Also, there is still alot of  information on the internet suggesting that the limit still remains at 53k. Here is a link explaining modem speed limit was officially raised to 56k since 2002.  Current dial up speed limit

 Regardless if the speed limit is 53k or 56k, the maximum speed is always unattainable. To reach a  connection speed close to 56k,  you'd really have to be at your internet service provider and get the telephone lines out of the loop entirely. If you're only connecting at 33.6k or less, your residential  telephone line could be emanating from a  repeater
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How fast is dial up?



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So how fast is dial up anyway? Thats easy, 56k. Here's the reason why. There is a limit as to how much electric power can be used to transmit analog signals over conventional  telephone lines. The federal communications commission imposed a power limit to prevent a  phenomenon known as "cross talk".

 If you've ever talked on the phone and heard someone else  faintly talking or a fax tone in the background, thats cross talk. If too much  power were used  during data transmission, "cross talk" would increase between adjacent  phone lines. As a result  additional erroneous data would be created during  transmission and  defeat the purpose of  increasing signal strength to achieve a higher dial up connection speed.