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The power rating of woofers provided by the manufacturer is most often the thermal power limit and is determined by the materials of construction, including the adhesives used.
There are two additional power ratings that have to be calculated based on the enclosure and lowest frequency of response; these are Par which is the acoustical power output as limited by the displacement of the speaker; and Per which is the maximum electrical power input to acheive Par.
Since the calculation for Par is based on the enclosure, it will change with different enclosures and for different enclosure types (sealed versus vented). I refer you to Vance Dickason's Loudspeaker Design Cookbook for further understanding and for the formulas needed to calculate these.
If Per is less than the thermal rating provided by the manufacturer, it is safest to use the Per number.