how to find the rpm of the redbot without using the encoder in the redbot, based on the given Pwm value from 0 to 255?
Hi,
What is redbot? please a link to it.
Why don't you want to use the encoder?
Tom.... 
Not sure what redbot is. But you can't find the precise RPM of a moving motor without some kind of a feedback i.e. encoder.
As you mentioned you can roughly calculate it by knowing your motor's RPM spec and PWM coming from your microcontroller. But that wouldn't be precise.
Good luck!