The present invention provides a polishing apparatus and a polishing method capable of calculating outside diameters of rolls of a polishing tape on a polishing-tape supply reel and a polishing-tape recovery reel and capable of calculating a remaining amount of the polishing tape and a consumption of the polishing tape from the outside diameters of the rolls. This polishing apparatus includes a polishing-tape supply reel (46), a polishing head (44), a polishing-tape drawing-out mechanism G1, and a polishing-tape supply and recovery mechanism (45) configured to recover the polishing tape (43) from the polishing-tape supply reel (46) via the polishing head (44). The polishing-tape supply and recovery mechanism (45) includes a motor Mb adapted to apply a torque to the polishing-tape supply reel (46) so as to exert a predetermined tension on the polishing tape (43) traveling through the polishing head (44), and a rotation angle detector REa adapted to detect a rotation angle of the polishing-tape supply reel (46).