In theory, what you do exactly is measure the voltage generated by the sensor, look it up in a table to find the experimentally determined and theoreticaly backed o2 concentration that corresponds to and then look that up in another table to find what the AFR would have been in the chamber to result in that residual o2 concentration in the exhaust. That o2 concentration to AFR table is also experimentally determined and theoretically backed. The experiments show that, consistently enough, for a given AFR in the chamber, o2 concentration in the exhaust will be constant regardless of other variables. For a narrow band sensor, its responses are only trustworthy in a narrow range either side of lambda=1 or stoichiometric AFR. Outside that it can only tell you lean or rich. A wideband sensor is accurate in a wider band of AF ratios, around 10:1 to 20:1. An odd first post I know.