Calculating Gear Ratios with Pinion Gearboxes

New Pinion users often find themselves wondering which size front or rear sprockets to use with their Pinion gearbox, or how to compare Pinion gearing setups with a derailleur bike. Pinion gearing can be easily compared to external gearing using the internal gear ratios for the gearbox and the size of the front and rear sprockets.

Here is what you need to do:

Multiply the external (secondary) 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 gear ratio for a given gear number. 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.

In practice, comparing the high and low gears is usually sufficient to determine whether a given set up will provide the climbing or descending gear 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 available gears in the various gearboxes:

	Internal Ratio
Gear Number	P1.18	P1.12/C1.12	P1.9 XR/C1.9XR	P1.9 CR	P1.6
1	0.55	0.55	0.55	0.77	1.05
2	0.61	0.64	0.68	0.90	1.32
3	0.68	0.76	0.84	1.05	1.61
4	0.76	0.89	1.05	1.23	2.04
5	0.84	1.05	1.32	1.45	2.50
6	0.94	1.23	1.61	1.69	3.13
7	1.05	1.45	2.04	2.04
8	1.18	1.72	2.50	2.38
9	1.32	2.04	3.13	2.78
10	1.45	2.38
11	1.61	2.78
12	1.82	3.33
13	2.04
14	2.27
15	2.50
16	2.78
17	3.13
18	3.45
Overall Range	628%	607%	569%	361%

Calculating High and Low Rations on your Gearbox: 12-Speed Pinion Example

As an example, assume you are running a 30T front sprocket and a 30T rear sprocket. This gives you a secondary gear ratio of 1 (30/30 = 1). Looking at the chart above, the internal ratio is 0.55 for gear #1 and 3.3 for gear #12. If you multiply the internal gearbox ratio by the secondary ratio for the highest and lowest gears, you get the following high and low ratios:

Highest ratio: 1 * 3.33 = 3.33
Lowest ratio: 1 * 0.55 = 0.55

These numbers can now be compared directly to the ratios of derailleur gear combinations.

Calculating High and Low Ratios with Derailleur Systems: 1x11 Example

Assume you have a 1x derailleur system with a 30T front sprocket and a 10-42T cassette.  This setup gives you 420% overall gear range range (42/10), which is less than the 600% range of the 12-speed Pinion gearbox.

To calculate the high and low ratios with a derailleur system, simply divide the front sprocket (chain ring) tooth count by that of the rear (cassette plate). In this case, we get the following high and low ratios:

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

So, how do these numbers help you select sprockets for your new Pinion setup? A simple comparison will go a long way.

Comparing these numbers against the Pinion example above, the Pinion setup will offer both a harder/faster gear (3.33 vs 3.0) and an easier/slower gear (0.55 vs 0.714) 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 gearbox to 27T (0.901 secondary ratio) would match the high ratio of the derailleur setup and decrease the low ratio to 0.495.  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 gearbox to 39T (1.30 secondary ratio) would match the low ratio of the derailleur setup and increase the high ratio to 4.33.

Another Example: Comparing Pinion to a 1x12 Derailleur System

Assume you have a 1x derailleur system with a 30T front sprocket and a 10-50T cassette.  This setup gives you 500% overall gear range (50/10), which is less than the 600% range of the 12-speed gearbox, and the following high and low ratios:

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

Comparing these numbers against the Pinion example above, the Pinion setup will offer both a harder/faster gear (3.33 vs 3.0) and an easier/slower gear (0.55 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 gearbox to 27T (0.901 secondary ratio) would match the high ratio of the derailleur setup and decrease the low ratio to 0.495.  If the low gear on the derailleur setup was easy enough (0.6 ratio) and you wanted more top end gearing, increasing the front sprocket size on the gearbox to 33T (1.09 secondary ratio) would match the low ratio of the derailleur setup and increase the high ratio to 3.633.

One more example: 

Assume you have a 3x system with 24/34/48T front sprockets and an 11-32T cassette.  This gives you 582% overall gear range ([48/24] * [32/11]), which is less than the 600% range of the 12-speed gearbox, and the following high and low ratios:

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

In this example, the derailleur system will offer a harder/faster gear (4.364 vs 3.33) and the gearbox will offer an easier/slower gear (0.55 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 gearbox to 41T (1.364 secondary ratio) to match the low ratio of the derailleur setup and increase the high ratio to 4.54.  If you wanted to match the high gear of the derailleur system (4.364), you would need to increase the front sprocket size to 39T (1.31 secondary ratio) to match the high gear on the derailleur system, which would also increase the low ratio to 0.721.

In practice, your choices may be limited by available sprocket sizes and you might need to adjust accordingly (maybe 43T is not available so you have to choose 42T or 44T). That said, 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, here is a general reference list based on secondary 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 internal gearing or singlespeed:

0.95-1.2: Mountain biking, fat biking, more heavily-loaded off-road touring
1.05-1.25: Off-road bikepacking
1.1-1.3: On-road touring
1.2-1.4: On-road bike packing, commuting, gravel riding
1.3-1.5: Road, faster/more fit gravel rider

Online Tools

Online gear ratio calculators are also 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 any 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 Facebook.