07 December 2018

Calculating Gear Ratios with Rohloff Hubs


New Rohloff users often find themselves wondering which size front or rear sprockets to use with a SPEEDHUB 500/14 or how to compare different Rohloff gearing setups with a derailleur bike. Rohloff gearing can be easily compared to external gearing using the internal gear ratios for the SPEEDHUB and the size of the front and rear sprockets.

Here is what you need to do:

Multiply the external (primary) gear ratio (front sprocket tooth count divided by rear sprocket tooth count) by the internal gear ratio (from the chart below) to get the overall ratio for a given gear selection. This overall gear ratio can then be compared directly with a specific derailleur or single speed gear combination, assuming the same wheel size and crank length are being used. If those factors also differ between the two bikes you are comparing, see below for additional resources offering more in depth drivetrain comparisons.

In practice, comparing the high and low gears is usually sufficient to determine whether a given set up will provide the climbing and descending gears you desire. Note that this calculation is the same whether you are running a chain or a belt.

If you are not familiar with the concept of gear ratios, the articles below provide helpful background information:

https://adventure.howstuffworks.com/outdoor-activities/biking/bicycle4.htm

https://cyclingtips.com/2017/11/understanding-bicycle-gear-ratios-why-they-matter/

This chart shows the internal ratio for each of the 14 gears on a SPEEDHUB:

Gear #
Internal Ratio
1
0.279
2
0.316
3
0.360
4
0.409
5
0.464
6
0.528
7
0.600
8
0.682
9
0.774
10
0.881
11
1.000
12
1.135
13
1.292
14
1.467



The overall gear range of the SPEEDHUB is 526% (1.467/0.279), which is quite wide, and wider than most current derailleur systems. This means that there is a larger difference between the easiest and hardest gears when using a Rohloff hub compared to most derailleur-equipped bikes. You can choose weather the additional range is on the high end, low end, or split the difference based on the choice of front and rear sprocket sizes.

Calculating High and Low Ratios on your Rohloff


As an example, let's assume you have set up your new Rohloff-equipped bike with a 40T front sprocket and a 16T rear sprocket. Your external (primary) gear ratio with such a setup would be 2.5 (40/16=2.5). Looking at the chart above, we can see that the internal ratio is 0.279 for gear #1 and 1.467 for gear #14. If you multiply the primary gear ratio by the internal ratios for the highest and lowest gears, you get the following high and low ratios:

Highest ratio: 2.5 * 1.467 = 3.668
Lowest ratio: 2.5 * 0.279 = 0.698

These numbers can now be compared directly to the ratios of derailleur gear combinations to compare the hardest and easiest gears.

Calculating Ratios with Derailleur Systems: 1x11 Example

Assume you have a 1x system with a 30T front sprocket and a 10-42T cassette. This setup provides 420% overall gear range range (42/10), which is less than Rohloff's 526%. To calculate the high and low ratios with a derailleur system, simply divide the front sprocket tooth count by that of the largest and smallest cassette sprockets. In this case, we get the following high and low ratios:

Highest ratio: 30/10 = 3.000
Lowest ratio: 30/42 = 0.714

Comparing these numbers against the Rohloff Example above, the Rohloff setup offers both a harder/faster gear (3.668 vs 3.0) and an easier/slower gear (0.698 vs 0.714) than the derailleur system.

So, how do all of these numbers affect your choice of sprockets with the Rohloff?

If you felt the high gear on the derailleur setup was fast enough (3.000) and wanted an easier climbing gear, decreasing the front sprocket size on the Rohloff system from 40T to 33T (2.063 primary ratio) would match the high ratio of the derailleur setup and decrease the low ratio to 0.575. If the low gear on the derailleur setup was easy enough (0.714 ratio) and you wanted more top end gearing, increasing the front sprocket size on the Rohloff system to 41T (2.563 primary ratio) would match the low ratio of the derailleur setup and increase the high ratio to 3.759.

Another Example: Comparing Rohloff to 1x12 Derailleur System

Assume you have a 1x system with a 30T front sprocket and a 10-50T cassette. This gives you 500% overall gear range (50/10)—still less than Rohloff's 526%. Using the method outlined above, we reach the following high and low ratios:

Highest ratio: 30/10 = 3.000
Lowest ratio: 30/50 = 0.6

Comparing these numbers against the Rohloff example above, the Rohloff setup offers a harder/faster gear (3.668 vs 3.0) but not as low of an easiest/slowest gear (0.698 vs 0.6) compared to the derailleur system.

If the high gear on the derailleur setup was fast enough (3.000) and you wanted an easier climbing gear, decreasing the front sprocket size on the Rohloff system to 33T (2.063 primary ratio) would match the 3:1 high ratio of the derailleur setup while also decreasing the low ratio of the Rohloff system to 0.575 (vs the 0.6 ratio of the 30/50T derailleur combination).

If the low gear on the derailleur setup was too low and you wanted more top end gearing, increasing the front sprocket size on the derailleur system to 35T would match the low ratio of the Rohloff setup (0.698) and increase the high ratio of the derailleur system to 3.5.

One More Example:

Assume you have a 3x system with 24/34/48T front sprockets and an 11-32T cassette. This gives you a 582% overall gear range ([48/24] * [32/11]), which is wider than the range of the Rohloff hub, and results in the following high and low ratios:

Highest ratio: 48/11 = 4.364
Lowest ratio: 24/32 = 0.75

In this example, the derailleur system offers a harder/faster gear (4.364 vs 3.668) and the Rohloff system offers an easier/slower gear (0.698 vs 0.75). If the low gear on the derailleur setup was easy enough (0.75 ratio) and you wanted more top end gearing, you could increase the front sprocket size on the Rohloff system to 43T (2.688 primary ratio) to match the low ratio of the derailleur setup and increase the high ratio to 3.943. If you wanted to match the high gear of the derailleur system (4.364), you would need to increase the front sprocket size to 48T (3.000 primary ratio) to match the high gear on the derailleur system, which would also increase the low ratio to 0.837.

In practice, you are often limited by available sprocket sizes and will need to adjust slightly (maybe 43T is not available so you have to choose 42T or 44T), but there are generally enough sprocket sizes available to achieve just about any combination that is practical for cycling.

General Recommendations


If you are not sure where to start, here is a general reference list based on primary gear ratio. You may want to adjust these recommendations for rider strength/fitness, terrain, and cargo load, but they are a good starting point for those new to using a Rohloff SPEEDHUB 500/14.

1.9-2.3*: Mountain biking, fat biking, more heavily-loaded off-road touring
2.1-2.5*: Off-road bikepacking
2.4-2.6: On-road touring
2.5-2.75: On-road bike packing, commuting, gravel riding
2.75-3: Road, faster/more fit gravel rider
>3-3.4: Faster/more fit road rider

* Note that Rohloff stipulates that riders over 100kg (221lbs) must use a 2.5 primary ratio to maintain their warranty. All tandems and e-bikes also fall into this category.

Online Tools

Online gear ratio calculators are useful for determining which size sprockets to use with the Rohloff SPEEDHUB 500/14. They are programmed to provide gearing information for Rohloff, derailleurs, and other internal systems (gear hubs and gearboxes), and can also be used to compare gearing between bikes with different size wheels and/or crank arms in case you are considering a new bike with an entirely new configuration. Here are a couple that we recommend:

http://www.sheldonbrown.com/gear-calc.html
http://ritzelrechner.de/

We are Here to Help


At Cycle Monkey, we love to help riders gain a better understanding of the components and equipment they are riding on, empowering them to experiment and tinker with their riding setups like we love to. If you have any questions about gearing, sprocket selection, or a custom bike build, drop us a line. If this guide was helpful, we also want to hear from you! Let us know on our Facebook page.

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