No offense, but reading your question, I did not get the impression, that you are sufficiently qualified to handle mains voltage.
You run a serious risk of killing yourself or someone else if you do!
That being said, you can actually measure the speed of your fan directly, which is much more safe and precise.
You could do that for example by either attaching a small magnet on the fan and using a hall effect sensor to detect, when the magnet passes by. Another way would be to use an reflective photoelectric sensor to detect the fan blades as they pass by the sensor.
In both cases you can calculate the exact speed of your fan by measuring the time between 2 pulses.