E500/501S WiFi Coverage vs Client/Smartphone connectivity

What is the capability of the client/smartphones to connect to the AP in terms of distance? we need to consider this when setting up a hotspot and not just the AP maximum coverage.  A client device might detect the SSID but might not be able to connect to AP or transfer data depending on its in built radio( transmit power and antenna gain) which is much lower than for the AP

It's going to be very difficult to give you an answer as clients will have wildly different antenna and radio characteristics.

That being said, on the spec sheets at least, Cambium claims the max range for the 500 and 501s is "Client: 213 m (700 Ft); Actual range will vary based on local RF conditions & client capability"

The 501s has a 90/120deg sector antenna with a much higher gain antenna (10/13dBi vs 5dBi) then the 500's omni. Although Cambium says that the max distance is the same for both products, I'd wager that you'd be able to get better long range LOS and near/NON-LOS performance out of the 501s.

As far as the problem you've mentioned, where a client can see an SSID, but the signal is too weak to connect, or performance is poor if it's allowed to connect, these issues can be reduced by setting an 'Enhanced Roaming' threshold on the AP.

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Specific numbers, as stated earlier, depend on specific characteristics of the client device.

It is ultimately the client's decision to roam.

Keeping both of those conditions in mind, a good rule of thumb is that mobile devices (smart phones, tablets, etc) will see about half the WiFi signal strength that a laptop will perceive.  So cut your modeled coverage in half.  I highly recommend getting heat mapping software and using it in your designs.  Acrylic WiFi is a good option, one of the less expensive options (though none of them are truly cheap).