Fixed Gear Calculator

What is a Fixed Gear Calculator?

A fixed gear calculator is an essential tool for any single-speed or track cyclist. It helps you understand and optimize the relationship between your bike’s components and your physical output. Unlike geared bikes, a fixed-gear bicycle has a single, direct drivetrain, meaning your gearing choice is critical and permanent for a given ride. This calculator allows you to input key variables—such as chainring teeth, cog teeth, and wheel size—to compute crucial metrics like gear ratio, skid patches, gain ratio, and potential speed at a specific cadence. Using a fixed gear calculator ensures you select a setup that matches your riding style, terrain, and fitness level, preventing you from being “over-geared” on hills or “under-geared” on flats.

Fixed Gear Calculator Formulas and Explanation

The core of this fixed gear calculator lies in a few key formulas that translate component sizes into performance metrics. Understanding them can help you make more informed decisions.

1. Gear Ratio

This is the most fundamental metric. It represents how many times the rear wheel rotates for one full rotation of the pedals. A higher number means a “harder” gear.

Formula: Gear Ratio = (Number of Chainring Teeth) / (Number of Cog Teeth)

2. Skid Patches

Skid patches are the number of distinct points on your rear tire that will make contact with the ground when you perform a skid with your cranks in a fixed horizontal position. More skid patches mean more evenly distributed tire wear, extending the life of your tire. This is a critical metric for urban fixed-gear riders. It’s calculated by reducing the gear ratio fraction to its simplest form; the denominator is the number of skid patches. For more detail, check out this skid patch calculator.

Formula: Skid Patches = Denominator of the simplified fraction (Cog Teeth / GCD(Chainring Teeth, Cog Teeth))

3. Gain Ratio

Gain Ratio is a more comprehensive metric than gear ratio because it accounts for crank arm length and wheel size. It represents the ratio of the distance the bike travels to the distance the pedal travels in one revolution. It provides a universal value to compare gearing across different bikes.

Formula: Gain Ratio = (Wheel Radius / Crank Arm Length) * Gear Ratio

4. Speed at Cadence

This formula calculates your potential speed based on your gearing and how fast you are pedaling (your cadence).

Formula: Speed (km/h) = Cadence (RPM) * Gear Ratio * Wheel Circumference (m) * 60 / 1000

Variable Explanations

Variable	Meaning	Unit	Typical Range
Chainring Teeth	Number of teeth on the front sprocket.	Teeth (integer)	42 – 55
Cog Teeth	Number of teeth on the rear sprocket.	Teeth (integer)	13 – 22
Wheel Circumference	Total distance the wheel travels in one rotation.	Millimeters (mm)	2070 – 2145 (for 700c)
Crank Arm Length	Length of the pedal crank arm.	Millimeters (mm)	165 – 175
Cadence	The rate of pedaling.	Revolutions Per Minute (RPM)	60 – 110

Practical Examples

Let’s see how the fixed gear calculator works with some real-world scenarios.

Example 1: The City Commuter

A rider wants a versatile setup for city riding with a mix of flats and small hills. They need a good number of skid patches to save their tires.

• Inputs: Chainring = 47t, Cog = 17t, Wheel Size = 700c x 28mm, Crank Length = 170mm, Cadence = 85 RPM.
• Results:
  • Gear Ratio: 2.76
  • Skid Patches: 17 (Excellent for tire life)
  • Gain Ratio: 5.2
  • Speed: 30.5 km/h
• Interpretation: This is a great all-around setup. The gear ratio is manageable for gentle climbs, and the 17 skid patches ensure the rear tire wears very slowly. For more on gearing, see our guide on fixed gear riding.

Example 2: The Track Racer

A track cyclist needs a high gear for maintaining top speed on a velodrome. Skid patches are not a concern.

• Inputs: Chainring = 51t, Cog = 15t, Wheel Size = 700c x 23mm, Crank Length = 165mm, Cadence = 110 RPM.
• Results:
  • Gear Ratio: 3.40
  • Skid Patches: 5 (Low, but not a priority)
  • Gain Ratio: 7.1
  • Speed: 49.3 km/h
• Interpretation: This is a powerful, high-speed gear. The gain ratio of 7.1 indicates a lot of distance covered per pedal stroke, ideal for racing but difficult to accelerate from a stop. To compare gear options, a gear ratio chart can be very helpful.

How to Use This Fixed Gear Calculator

1. Enter Drivetrain Details: Input the number of teeth on your front chainring and rear cog. These are the most critical values for the fixed gear calculator.
2. Select Wheel Size: Choose your wheel and tire size from the dropdown. This affects the speed and gain ratio calculations.
3. Specify Crank Length: Enter your crank arm length in millimeters. It’s usually printed on the inside of the crank arm.
4. Set Your Cadence: Input your typical or target pedaling cadence in RPM. 90 RPM is a common benchmark.
5. Choose Units: Select whether you want to see your speed in metric (km/h) or imperial (mph).
6. Analyze the Results: The calculator will instantly update your Gear Ratio, Skid Patches, Gain Ratio, and Speed. Use these metrics to decide if a gear combination is right for you.

Key Factors That Affect Fixed Gear Performance

Choosing the right setup with a fixed gear calculator involves balancing several factors:

• Terrain: Hilly areas require a lower gear ratio (e.g., 2.5-2.7), while flat areas allow for a higher ratio (e.g., 2.8-3.2).
• Rider Fitness: Stronger riders can push a higher gear ratio, generating more speed.
• Riding Style: Are you a spinner (high cadence) or a masher (low cadence, high power)? Your preferred cadence influences your ideal gearing. A bike gear calculator can explore this further.
• Tire Longevity (Skid Patches): For urban riders who skid to stop, a combination that yields many skid patches (ideally a prime number cog with a non-multiple chainring) is crucial for saving money on tires.
• Crank Length: Shorter cranks (165mm) are often preferred for track racing to improve cornering clearance, while longer cranks (170mm+) can provide more leverage.
• Wheel and Tire Size: A larger wheel circumference effectively increases your gear ratio, making the gear feel slightly harder.

Frequently Asked Questions (FAQ)

1. What is a good gear ratio for a beginner?

A good starting point for a beginner on a fixed gear calculator is a ratio between 2.7 and 2.8, such as 46/17 or 48/17. This provides a balance of acceleration and top speed without being too demanding on the knees.

2. Why are prime numbers important for cogs?

Cogs with a prime number of teeth (like 13, 17, 19) make it much harder for the chainring tooth count to be a direct multiple. This results in a gear ratio fraction that doesn’t simplify much, maximizing the number of skid patches. For instance, 48/16 gives 1 skid patch, but 48/17 gives 17.

3. How many skid patches is considered ‘good’?

Anything above 7 is generally considered good. Ratios that result in 1, 2, or 3 skid patches will wear out your rear tire very quickly in specific spots.

4. Can I use this calculator for a single-speed bike with a freewheel?

Yes. While the “Skid Patches” metric is only relevant for fixed-gear bikes, the Gear Ratio, Gain Ratio, and Speed calculations are perfectly valid for any single-speed bicycle.

5. What’s the difference between Gear Ratio and Gain Ratio?

Gear Ratio only compares the front and rear sprockets. Gain Ratio is a more complete metric that also includes wheel radius and crank length, giving a true measure of the distance traveled for the effort put in. It’s better for comparing gearing between bikes with different wheel sizes or crank lengths.

6. Why does my speed on the road not match the fixed gear calculator?

The calculator provides a theoretical speed in perfect conditions. Real-world factors like wind resistance, road gradient, tire pressure, and friction in the drivetrain will affect your actual speed.

7. Does an ambidextrous skidder get more skid patches?

Yes. If you can skid with either your left or right foot forward, you can sometimes double your skid patches. This calculator shows the single-foot-forward number, which is the guaranteed minimum.

8. How do I find my crank arm length?

The length in millimeters (e.g., “165”, “170”) is almost always stamped or engraved on the inside face of the crank arm, near the pedal hole.