Adding digital RPM to wood lathe

I've bought a sensor to detect the rotational speed of the machine. the sensor is triggered with several magnets attached to the spindle, this results in a higher resolution. Should I use an Arduino nano for registering the output of the sensor?

Yes, you could use a Nano.
You'll also need a display device.
Are you looking to indicate absolute values, or simply a traffic light "within limits"?

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