Skid Patch Calculator

Optimize tire longevity on your fixed-gear bike by calculating your skid patches.

Visual representation of your gear ratio.

What is a Skid Patch?

A “skid patch” is a term used by fixed-gear cyclists to describe the specific points on a rear tire that make contact with the ground during a skid. When a rider on a fixed-gear bike (a bike with no freewheel mechanism) locks their legs to stop the pedal rotation, the rear wheel stops turning and skids along the pavement. Because the crank arms are always in a fixed position relative to the rear wheel, you tend to skid with your feet in the same position (e.g., right foot forward). This means the same spot on the tire hits the ground repeatedly, causing it to wear out much faster than the rest of the tire. The goal is to maximize the number of skid patches to distribute this wear over as many points on the tire as possible, significantly extending its life. A higher number of skid patches is always better.

The Skid Patch Calculator Formula

The calculation for skid patches relies on basic number theory, specifically finding the greatest common divisor (GCD) of your chainring and cog teeth count. The formula is straightforward.

Skid Patches = Cog Teeth / GCD(Chainring Teeth, Cog Teeth)

Where:

• Cog Teeth is the number of teeth on your rear cog.
• Chainring Teeth is the number of teeth on your front chainring.
• GCD(…) is the Greatest Common Divisor, which is the largest positive integer that divides both numbers without leaving a remainder.

For example, a 48/16 ratio has a GCD of 16. The calculation is 16 / 16 = 1. This means you have only one skid patch, which will wear out your tire extremely quickly. In contrast, a 47/17 ratio (two prime numbers) has a GCD of 1. The calculation is 17 / 1 = 17, giving you 17 distinct patches and much more even tire wear.

Formula Variables

Variables used in the skid patch calculator.

Variable	Meaning	Unit	Typical Range
Chainring Teeth	Number of teeth on the front sprocket.	Teeth (unitless)	42 – 55
Cog Teeth	Number of teeth on the rear sprocket.	Teeth (unitless)	13 – 22
GCD	Greatest Common Divisor of the two inputs.	(unitless)	1+

Practical Examples

Let’s look at two common scenarios to see how the choice of gearing dramatically affects tire life.

Example 1: The “Bad” Ratio

• Inputs: Chainring = 48t, Cog = 16t
• GCD(48, 16): 16
• Result: 16 / 16 = 1 Skid Patch

This setup, often found on stock bikes, is terrible for tire wear. Every time you skid, the same single point on the tire grinds against the pavement. You’ll develop a flat spot and need a new tire very quickly. Check out our guide on fixed-gear maintenance to learn more.

Example 2: The “Good” Ratio

• Inputs: Chainring = 49t, Cog = 17t
• GCD(49, 17): 1
• Result: 17 / 1 = 17 Skid Patches

By slightly changing the gearing to use numbers that are relatively prime (their GCD is 1), the number of skid patches equals the number of teeth on the cog. This spreads the wear across 17 different points, meaning your tire will last much longer. Choosing the right components is key, as explained in our article on choosing the right cog.

How to Use This Skid Patch Calculator

Using this tool is simple:

1. Enter Chainring Teeth: Input the number of teeth on your front chainring into the first field.
2. Enter Cog Teeth: Input the number of teeth on your rear cog into the second field.
3. Read the Results: The calculator will instantly update. The large green number is your primary skid patch count. You can also see intermediate values like the gear ratio and the GCD, which are used in the calculation.
4. Interpret the Results: A higher skid patch count is better. If your number is low (e.g., 1-4), consider changing your gearing to a more optimal ratio.

Key Factors That Affect Skid Patches

• The Ratio, Not the Size: The absolute size of your chainring or cog doesn’t determine the patches, but their ratio does. A 48/16 (3.0 ratio) has 1 patch, while a 39/13 (3.0 ratio) also has 1 patch.
• Prime Numbers are Your Friend: Using a prime number for your cog (like 13, 17, 19) or chainring (like 43, 47, 53) often results in a high number of skid patches, as they are less likely to share a common divisor with their partner.
• Relative Primes: The best combinations are “relatively prime”—meaning their only common divisor is 1. For example, 48 and 17 are relatively prime. 49 (7×7) and 16 (2x2x2x2) are also relatively prime.
• Ambidextrous Skidding: If you are skilled enough to skid with either your left or right foot forward, you can sometimes double your skid patches. This calculator shows this potential as “Ambidextrous Patches.” This typically works unless the simplified gear ratio numerator is even.
• Even vs. Odd Numbers: Ratios with two even numbers (like 44/16) are easily simplified and often lead to few patches. Mixing odd and even can improve the outcome.
• Small Changes Matter: As shown in the examples, changing your cog by just one tooth (from 16 to 17) can increase your skid patches from 1 to 17. Our guide to gear ratio basics can help you decide.

Frequently Asked Questions (FAQ)

Why are more skid patches better?

More patches mean wear is distributed more evenly around the tire, leading to a longer lifespan and saving you money.

What is a good number of skid patches?

Anything above 7 is considered decent. Ratios that provide 13, 15, 17 or more patches are excellent.

Does this apply if I have brakes?

Technically, yes, but the concept is most important for brakeless fixed-gear riders who rely on skidding to slow down. However, even with brakes, your drivetrain causes wear patterns, so more patches are still beneficial for even wear.

How do I find the number of teeth on my gears?

The tooth count is usually stamped directly onto the side of the chainring and cog.

What does “ambidextrous skidding” mean?

It means you are comfortable and able to initiate a skid with either your left foot or your right foot in the forward pedal position. This can double your available skid patches in many gear ratios.

Why does my 48/16 ratio only have 1 patch?

Because 48 is a direct multiple of 16 (48 = 3 x 16). This creates a 3/1 simplified ratio. The denominator is 1, so you only have one patch. For every 3 revolutions of the pedals, the wheel revolves exactly once, always landing on the same spot. You can learn more about this effect in our advanced gearing theory article.

Is a higher gear ratio better?

Not necessarily for skid patches. A high ratio like 52/13 (4.0) has only 1 patch. A lower ratio like 47/17 (~2.76) has 17 patches. The patch count is determined by the divisibility of the numbers, not the resulting ratio value.

How can I change my number of skid patches?

The easiest and cheapest way is to buy a new rear cog with a different number of teeth. Changing a cog is a simple maintenance task. Our guide to component swapping can walk you through it.

Related Tools and Internal Resources

If you found this calculator useful, check out our other resources:

• Gear Ratio Calculator: Calculate your gear inches and development.
• Complete Bike Fit Guide: Ensure your bike is set up for comfort and efficiency.
• Fixed-Gear Maintenance Essentials: Learn how to care for your ride.