# Chain Length Calculator

By Avram Aruh
Last updated: Sep 23, 2021

This chain length calculator will help you determine the required chain length for your bicycle. We all know that there are many ways to calculate bicycle chain length, such as measuring a reference chain. But, what if you do not have a reference at hand? Well then, we're sure that this bike chain length calculator will come in handy! In this article, you will also learn about bike chain sizes.

## Why is bicycle chain length significant? 🚴

The bike chain is the most vital part in propelling a bike, and it consists of inner and outer plates that are held together with bolts. Many standard bicycle chain sizes have been developed over time, with some being specially designed for mountain bikes or road bikes with different stabilities and weights. Also, bike chain width is essential for deciding the number of derailleurs. If the number of derailleurs increases from 9 to 11 speeds, the bike chain's width must also increases.

Bike chains aren't all good news, however. If the bike chain is damaged, it will instantly damage the chain rings and sprocket set. If you calculate the bicycle chain length to be longer than it should be, it will hang, and gear shifting will be very hard. On the other hand, if you calculate the chain length to be shorter, it will damage the derailleur hanger.

## What size bike chain do I need?

Unfortunately, there isn't a universal bike chain that fits all types of bikes. Bike chain sizes vary based on several factors, and it is as important as bicycle chain length. If you are asking the question like "What size bike chain do I need?", the table below shows the most commonly used bike chain sizes:

CSV To HTML using codebeautify.org
# of rear sprockets External width (in) Internal width (in)
5-6-7-8 speed 9/32" 3/32"
9 speed 1/4" - 9/32" 11/128"
10 speed 1/4" - 9/32" 11/128"
10 speed narrow 7/32" 11/128"
11 speed 7/32" 11/128"
12 speed 13/64" 11/128"

You don't need to think about the external width of the chain if you are using a single-speed bike.

## How to measure a bike chain length?

There are three ways to measure the chain length of a bike:

1. You can use your original chain as a reference to find the required bike chain size.

2. Buy a very long chain and use the largest front chainring and largest cog to find the maximum required chain length for your bike.

3. You can calculate the bike chain length with a chain length calculator.

While calculating the bicycle's chain length, it is important to know the names of the chain related parts of a bicycle. Basically, the following parts of a bike are important for a chain length calculator: 1. Chain stay - the length between the center of the back wheel and the center of the pedal;

2. Front chainring - located in the middle of a bicycle, where the pedal is placed; and

3. Rear cog - the place with multiple sprockets in the middle of the rear wheel. The bicycle chain is also connected from the rear cog to the derailleur, which the rider uses to change the gear ratios being used.

## How do we calculate bicycle chain length? Bike chain size formula

In our chain length calculator, we use two different equations for calculating bike chain length. One of them is called the simple equation, and is valid for chain stay length (C) greater than 15 inches and for bikes with standard front chainring or rear cog size, which is the following formula:

`L = 2*(C) + (F/4 + R/4 + 1) `

Where,

• L - the bike chain length in inches;
• C - the chain stay length in inches;
• F - the number of teeth on the largest front chainring; and
• R - the number of teeth on the largest rear cog.

We also have another formula for calculating chain length, the rigorous equation. This equation is more accurate for bikes with a chain stay length (C) less than 15 inches. We can also use the rigorous equation for bikes with a large front chainring and a smaller rear cog. If you have a bicycle like this, you should calculate your chain length with the following equation:

`TSPCL = 0.25*(F+R)+2√(C*C)+(0.0796*(F-R))²`
.

Where,

• TSPCL - the theoretical shortest possible chain length in inches;
• C - the chain stay length in inches;
• F - the number of teeth on the largest front chainring; and
• R - the number of teeth on the largest rear cog.

Our chain length calculator gives you the result of both the simple and the rigorous equations (in the `advance mode`).

## How chain size calculator works? Tips and tricks

When we want to calculate bicycle chain length, we should firstly convert fractional inches to decimal inches.. We generally use this conversion for the chain stay length (C) part of the chain size formula. The table below gives the decimal of each fractional inch measurement:

 Fractional Inches Decimal Inches 1/8" 0.125" 1/4" 0.250" 3/8" 0.375" 1/2" 0.500" 5/8" 0.625" 3/4" 0.750" 7/8" 0.875"
 💡 Example: Let's calculate the chain length of a bike with a 42-32-22 front chainring using the simple equation. The rear cog set has 32 teeth on the largest cog and the chain stay length is 16-3/8".

1. Looking at the table above, we should convert the chains stay length from a fraction to a decimal. 16-3/8" equals 16.375" in decimal.

2. We have 42-32-22 front chainring. We should always consider the largest one, so we will take 42 into account.

3. We know the largest amount of teeth on the rear cog, which is 32.

4. Apply these values into the bicycle chain length formula.

`L = 2*(16.375) + (42/4 + 32/4 + 1)`

5.Our chain length becomes 52.25 inches. Since it is hard to find a chain length like this, we will round up to 52 inches.

 💡 If the decimal of our bicycle chain length is equal to or greater than 0.5, we will round up to the largest possible number. For example, if our chain length equals 52.5 inches, we will round up to 53 inches.

• If we use the rigorous equation for this case, the chain length calculator outputs 51 inches!

Now that you have learned how our chain length calculator works and how to measure a bike chain length, it means that you are ready for a bike trip! Check our other calculators for cyclists, such as the biking life gain, calories burned biking, and biking life gain calculators.

Avram Aruh
Chain stay length
in
Largest front chainring
teeth
Largest rear cog
teeth
Chain length
in
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