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What is the widest range (in gear-inch ratio) available on an Internal Gear Hub (IGH) without the use of a supplemental derailleur or internally geared crank (aka mountain drive)?

And how does this ratio compare with what is possible with a standard 3x9 or 1x11 derailleur setup (standard as in what would be available in a mainline, non-modified, off the shelf bicycle).

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The Rohloff "500/14 Speedplay" has 14 gears and a difference of 526%, so the fast/high/hard gear is 5.26 larger than the slow/low/easy gear.

https://www.rohloff.de/fileadmin/_processed_/f/7/csm_uebersetzungsvergleich.en_01_c2544f4fb2.jpg

So this is roughly equal to a MTB 24/34/44 triple and a 12-34 rear cassette, which would have a range of gears of 519%

An advantage of the IGH generally is that the gears are sequential so there's only one action to move through the range.

An advantage of the derailleur bike is that the gears are closer together in broad swathes so you have smaller jumps between gears.

Neither MTB nor Rohloff bike has the high gears of a fast road bike, like a gear of 52front/11rear but there are not a lot of times when such gears are needed outside of racing and fast downhills.

Much more reading at https://www.rohloff.de/en/experience/technology-in-detail/gear-range-comparison/ and https://en.wikipedia.org/wiki/Rohloff_Speedhub

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    If that range isn't enough, explore Saint Sheldon's 63 speed at: sheldonbrown.com/org/otb.html – Criggie Jun 24 '17 at 22:41
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    You can use a different chainring to get a bigger high gear than 52/11. Usually there are limitations on the lowest ratio (so you don't tear the hub internals apart). The answer would be complete with a comparison of gear ratios for 3x9, 2x10 and 1x11 or 1x12 – Rider_X Jun 25 '17 at 1:10
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    @Rider_X yes, but anything too much larger than 52~53 teeth is going to be uncommon and more expensive. I'll give it a go using "commonly available" sizings, – Criggie Jun 25 '17 at 2:29

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