Skid Patch Calculator

Enter your bike’s chainring and cog teeth count to find out how many skid patches you have and optimize your tire life. A higher number of skid patches means more even tire wear when skidding.

What is a Skid Patch Calculator?

A skid patch calculator is a tool used primarily by fixed-gear bicycle riders to determine the number of distinct points on their rear tire that make contact with the ground when they perform a skid to slow down or stop. On a fixed-gear bike, the pedals are always in motion when the bike is moving, and the rider can resist the pedal motion to lock the rear wheel, causing a skid. The skid patch calculator helps riders understand how evenly their tire will wear if they frequently skid.

The number of skid patches depends on the gear ratio, specifically the number of teeth on the front chainring and the rear cog. Some gear ratios result in very few skid patches, leading to rapid wear in specific spots on the tire, while other ratios distribute the wear over many more points.

Anyone riding a fixed-gear or single-speed bike (if they skip-stop or skid) and wants to maximize their rear tire’s lifespan should use a skid patch calculator. It’s especially useful for urban riders and messengers who might skid frequently. A common misconception is that any gear ratio is fine, but using a skid patch calculator reveals that certain ratios are far superior for tire longevity if skidding is part of your riding style.

Skid Patch Calculator Formula and Mathematical Explanation

The number of skid patches is determined by simplifying the fraction formed by the number of teeth on the chainring (C) and the number of teeth on the cog (T). We find the Greatest Common Divisor (GCD) of C and T.

The formula is:

Number of Skid Patches (Single Foot) = T / GCD(C, T)

If you can skid with either foot forward (ambidextrous skidding), and the number of skid patches calculated above is not already equal to T (meaning C and T are not co-prime and both even), you might effectively double the number of wear points if the initial number of patches is less than T * 2 / GCD(C, T) and other conditions are met (specifically, if C and T are not both even and T/GCD(C,T) is odd, it doubles). More simply, if you skid with both feet, and C and T aren’t both even, you double the single-foot patches if T/GCD(C,T) is odd. If C and T are both even, the number of distinct points remains T/GCD(C,T) but is visited in half the revolution pattern, so effective single foot patches are T/(2*GCD(C,T)) if both even. Wait, if both are even, it’s T/GCD reduced. If T/GCD is odd, ambi doubles it. If T/GCD is even, ambi doesn’t double.

Let’s simplify:
1. Calculate `gcd_val = GCD(C, T)`.
2. `single_foot_patches = T / gcd_val`.
3. If C and T are both even, the true number of wear spots from one foot position is `T / (2 * gcd_val)`, but because the crank positions repeat twice as fast relative to tire rotation, it’s still effectively `T/gcd_val` for one foot, but visited more often. Wait, no. If both even, it’s `T/(2*gcd_val)` effective spots per foot position set. Let’s restart the formula logic.

Correct approach:
1. `gcd_val = GCD(Chainring, Cog)`
2. `reduced_cog = Cog / gcd_val`
3. `reduced_chainring = Chainring / gcd_val`
4. Number of skid points (single foot) = `reduced_cog`.
5. If `reduced_chainring` is NOT even (i.e., it’s odd), then ambidextrous skidding gives `reduced_cog * 2` skid points. If `reduced_chainring` is even, ambidextrous skidding gives `reduced_cog` skid points because the skid patches overlap for both foot positions.

So, Single Foot Skid Patches = Cog / GCD(Chainring, Cog).
If Chainring/GCD(Chainring, Cog) is odd, Ambidextrous Skid Patches = 2 * Cog / GCD(Chainring, Cog).
If Chainring/GCD(Chainring, Cog) is even, Ambidextrous Skid Patches = Cog / GCD(Chainring, Cog).

The skid patch calculator uses these relationships.

Variables Used

Variable	Meaning	Unit	Typical Range
C	Number of teeth on the chainring	Teeth	40 – 55
T	Number of teeth on the cog	Teeth	13 – 22
GCD(C, T)	Greatest Common Divisor of C and T	–	1 or more
Skid Patches	Number of distinct wear points on the tire	Patches	1 to T

The fixed gear guide explains more about gear ratios.

Practical Examples (Real-World Use Cases)

Example 1: Common Ratio

A rider has a 48-tooth chainring and a 16-tooth cog.

• Chainring (C) = 48
• Cog (T) = 16
• GCD(48, 16) = 16
• Single Foot Skid Patches = 16 / 16 = 1
• Reduced Chainring = 48 / 16 = 3 (odd)
• Ambidextrous Skid Patches = 2 * 1 = 2

With only 1 or 2 skid patches, the tire will wear out very quickly in those spots if the rider skids often. This is a poor ratio for skidding.

Example 2: Better Ratio

A rider changes their cog to a 17-tooth one, keeping the 48-tooth chainring.

• Chainring (C) = 48
• Cog (T) = 17
• GCD(48, 17) = 1 (48 and 17 are co-prime)
• Single Foot Skid Patches = 17 / 1 = 17
• Reduced Chainring = 48 / 1 = 48 (even)
• Ambidextrous Skid Patches = 17

With 17 skid patches, the wear is distributed over many more points, significantly increasing tire life even with frequent skidding. This is a much better ratio for a skidder. Check our tire selection guide for durable options.

How to Use This Skid Patch Calculator

1. Enter Chainring Teeth: Input the number of teeth on your bike’s front chainring into the “Chainring Teeth” field.
2. Enter Cog Teeth: Input the number of teeth on your rear cog into the “Cog Teeth” field.
3. Select Skidding Style: Choose whether you primarily skid with one foot forward or can comfortably skid with either foot forward.
4. View Results: The calculator will instantly update and show:
   • The primary result based on your selected skidding style.
   • Your gear ratio.
   • The number of skid patches for both single-foot and ambidextrous skidding.
5. Interpret Results: A higher number of skid patches is generally better for tire longevity if you skid. Ratios where the cog and chainring are co-prime (GCD=1) and the cog is prime often give the most patches.
6. Use the Table and Chart: The table below the calculator shows skid patches for common cog sizes with your current chainring, and the chart visualizes the wear points.

This skid patch calculator helps you choose a gear ratio that balances riding feel with tire wear. Our bike maintenance tips also cover tire care.

Key Factors That Affect Skid Patch Calculator Results

• Chainring Size: The number of teeth on the front ring. Larger chainrings paired with the same cog can change the GCD and thus the patches.
• Cog Size: The number of teeth on the rear cog. Prime numbered cogs (like 13, 17, 19) often result in more skid patches when paired with common chainring sizes because they are more likely to be co-prime.
• Gear Ratio (Chainring/Cog): The ratio itself isn’t directly used, but the individual numbers are. The key is how reducible the fraction C/T is.
• Greatest Common Divisor (GCD): The largest number that divides both the chainring and cog teeth count without leaving a remainder. A smaller GCD (ideally 1) means more skid patches (equal to the cog teeth count).
• Ambidextrous Skidding: Being able to skid with either foot forward can double the number of effective skid patches IF the reduced chainring number (Chainring/GCD) is odd. It offers no benefit if it’s even.
• Rider Technique: While not part of the calculation, how often and how hard a rider skids will determine how quickly even a large number of skid patches wear down. More skidding = faster wear, regardless of the number of patches from the skid patch calculator.

Understanding these factors, along with information from our drivetrain explained page, can help you make informed choices about your drivetrain components.

Frequently Asked Questions (FAQ)

What is the ideal number of skid patches?

The more, the better, up to the number of teeth on your cog (or twice that if you’re ambidextrous and the ratio allows). Ratios that give 13, 15, 17, 19 or more patches are excellent for tire life if you skid.

Does the skid patch calculator work for freewheel bikes?

No, this skid patch calculator is specifically for fixed-gear bikes where the rear wheel is directly tied to pedal movement, allowing skidding by resisting pedal motion. Freewheel bikes don’t allow this type of skidding.

If I have many skid patches, will my tire last forever?

No, but it will last significantly longer than if you had very few (like 1 or 2). All tires wear out eventually, but more patches distribute the wear more evenly.

Is it bad to have only a few skid patches?

If you skid frequently, yes. You’ll wear out your rear tire very quickly in specific spots, potentially leading to a flat or blowout. If you rarely or never skid, the number of skid patches is less important.

How do I find the GCD?

The calculator does it for you. Mathematically, you can use the Euclidean algorithm to find the Greatest Common Divisor of two numbers.

Does tire pressure affect skid patches?

Tire pressure doesn’t change the number of skid patches (which is determined by gearing), but it can affect how the tire wears during a skid and the size of the contact patch.

Can I increase skid patches without changing my gear ratio much?

Sometimes, changing your cog by just one tooth (e.g., from 16 to 17 with a 48 chainring) can dramatically increase skid patches while only slightly changing the gear ratio.

Why does ambidextrous skidding sometimes double the patches?

When you skid with the other foot forward, the crank arms are 180 degrees opposite. This means the tire contacts the ground at a different rotational position relative to the chainring/cog engagement if the reduced chainring number is odd, effectively giving new patches between the old ones.