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That depends on your model. The Force and One both include an internal altimeter precisely for that purpose. Instead of measure actual stairs though, what they measure is a change in elevation. It credits one "floor" for each ten foot rise in elevation. That may or may not exactly coorelate to the number of flights in a building, depending on the height of the floors. Ten foot is typical of a commercial building, while residential tends to be a little less. Note that the elevation change can just as easily come from walking in hilly terrain or parking ramps; it does not have to be actual stairs.
The Flex and Zip do not include an altimeter. In the case of the Flex, it is what allows it to be more water resistant and worn in the shower. The models with an altimeter need an air hole to be able to measure changes in air pressure.