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I bought three belts downsized by 0.25 inches from OEM starting at 47.5", and the 1st one I tried worked.
OEM is 48 inches.. The belt that works after installing the Singer alt, is measured @ 47.5 inches. The other 2 that weren't used were 47.25 inches, and 47 inches.
All other pulleys are stock OEM size. Only the alternator had a different than OEM pulley size.
3 belts of your choice that will work are:
Part# Bando 6PK1205
Part# Dayco 5060475
Part# Goodyear Continental Elite 4060475 Poly-V (Gatorback design)
Tags for search: 2009 2010 2012 2013 Toyota Corolla 1.8 2ZR-FE, Singer High output alternator, serpentine belt