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# The Impact of Crank Length on Gear Ratio Earlier I wrote about endurance gearing where I explained that although the standard gearing formula produces a convenient number for standardising gear ratios, it leaves out the impact of crank length on the final ratio at the pedal.

To recap, standard gear inch formula is defined as: This gives a quick way to compare ratios and for riders to express their gearing setup. It’s a simplified model that works.

However, this model is only partially correct as it does not take into consideration how crank length impacts the real ratio between how far the pedals move in order to turn the wheel. Let’s take a brief quantitative look at the real impact of crank length on the standard gear chart.

### Crank Length Changes Everything

As Victorian Institute of Sport sprint coach Carl Brewer explained, “crank length is part of a system of leverage that covers everything from wheel circumference, gear ratio (chainring & sprocket) and crank length. The distance the pedal moves as a ratio of how far the bike moves is the true gear, and it’s called a gain ratio.  Riders get very confused when they change crank length because they’re not factoring in the change in this ratio. If you put on longer cranks you are reducing the gain, so it feels easier – it’s not the longer lever doing this, it’s the change in gain ratio and you can get exactly the same effect from using smaller tyres or changing gears. A ratio is a ratio.”

What Carl was saying is that the gear inch model is only partially correct as it does not take crank length into account. What is important is the distance traveled by the bike divided by the distance traveled by the pedals during one turn of the crank. The fact is that a first bike with a 50×14 (93.1 inches) has the same gear as a second bike with a 50×14 only if they have the same length cranks. If the first bike has 175’s and the second bike 170’s, the gear on the first bike is approximately 3% lower. To achieve the equivalent gear ratio you will now need 3% more gear inches. It’s a zero sum game. As Carl put it, there is “no free lunch” provided by crank length.

As an example, let’s take two almost identical bikes both running a 50×14 (93.1 inches) gear. The only difference is that the first bike has 175mm cranks and the second bike 170mm cranks. How does this impact the gearing?

The best way to explain it is with numbers. Firstly, think of the crank diameter of the two bikes as a ratio of the wheel radius. That is:

• 170mm Cranks & 175mm cranks
• 700c wheel with a constant radius of 340mm. (lets assume a wheel diameter of 680mm to keep it simple – reality will probably differ)

This will give a constant “radius ratio” for the 170mm cranks of 2. (340 ÷ 170 = 2). For 175mm cranks the radius ratio will be 1.943 (340 ÷ 175 =1.943). Once known, we don’t need to calculate these ratios for the two bikes again.

From here we can calculate out “gain ratio” This is the standard gear inch forma with the radius ratio factored in.

Gain Ratio = Radius ratio × Chainring teeth ÷ Rear Sprocket Teet

In relation to our example a above the actual relative gearing is:

Gain Ratio for 170mm cranks = 2 × 50 ÷ 14 = 7.143

Gain Ratio for 175mm cranks = 1.943 × 50 ÷ 14 = 6.939

The difference here expressed as a percentage is simply:

(7.143 ÷ 6.939)-1 = 3%

Note that this will be further complicated when we factor in different tyre heights across bikes because changes here will impact the radius ratio.

What this demonstrates is that exactly the same gear inches, yet with 5mm longer cranks, produces a 3% lower gear at the pedal.