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I currently run Shimano SG-B-53/39 chain rings coupled to a 9 speed 13/23 cluster. If I was to change my cassette to a 9 speed 11/32 would I need to also change my derailleur?

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    It depends on which derailleur you have now. Look up derailleur capacity. – ojs Jan 20 '19 at 9:25
  • If you need lower gears, you should also probably change out the crankset to a compact 50/34. A 34-28 lowest gear is about the same as a 39-32, and you might not have to change your rear derailleur at all, depending on the exact model as most Shimano road rear derailleurs can handle a 28 without any problem. A 50-11 at 90 rpm gives you 31.6 mph - if you're strong enough to get there. A 53-11 at 90 rpm only gets you up to 33.5 mph - and that 2 mph is really hard as power is proportional to speed cubed. And you wouldn't have the huge jumps that a 9-speed 11-32 cassette had. – Andrew Henle Jan 20 '19 at 14:48
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As ojs says in comments - depends on the derailleur, but it's very likely that you would have to swap the derailleur to accommodate an 11-32 cassette. Older 9 speed groupsets were not designed for wider range cassettes, they had small gaps between ratios instead. You may be able to get away with a 12-28 though.

The derailleur specs you need to find are: max rear sprocket size and total capacity. Total capacity must be equal to or larger than (largest sprocket teeth - smallest sprocket teeth) + (large ring teeth - small ring teeth).

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