Bike Gear Ratio Calculator
Calculate gear inches from chainring, rear cog, and wheel diameter to compare drivetrain ratios.
What this tool does
This calculator computes gear inches, a dimensionless measure of bicycle gearing, using the standard cycling mechanics formula: (chainring teeth ÷ rear cog teeth) × wheel diameter. It requires three inputs (chainring tooth count, rear cog tooth count, and wheel diameter in inches), and outputs the gear inches value, which represents the effective diameter of a directly driven wheel that would produce the same mechanical advantage. The gear ratio metric originated in the penny-farthing era and remains the standard method for comparing drivetrain configurations across different bicycles and wheelsets.
Formula Used
Disclaimer
This calculator is for educational and informational purposes only. It does not provide medical, nutritional, or training advice. Results are mathematical estimates and may not reflect individual circumstances. Consult a qualified coach, registered dietitian, medical professional, or physiotherapist for personal guidance.
How Bike Gear Ratio Calculator works
This calculator computes gear inches, the effective diameter of a directly driven wheel that would give the same mechanical advantage as your drivetrain: the measure inherited from the penny-farthing, whose gearing really was its wheel diameter. It multiplies the ratio of front chainring teeth to rear cog teeth by the wheel diameter. To get the distance travelled per pedal revolution, multiply gear inches by π: continental Europe states gearing this way, as development or rollout in metres. A higher gear-inch value indicates a harder gear (more resistance, greater distance per pedal stroke), while a lower value indicates an easier gear. The tool accepts chainring and cog tooth counts plus wheel diameter in inches, then returns the gear-inch measurement and the numeric ratio.
The formula
The calculation follows the classic gear-inch formula:
Gear inches = (Chainring teeth ÷ Rear cog teeth) × Wheel diameter (inches)
For example, a 50-tooth chainring paired with a 16-tooth cog on a 27-inch wheel yields (50 ÷ 16) × 27 = 84.4 gear inches. The intermediate ratio of 3.125 means the rear wheel rotates 3.125 times for every pedal revolution. Multiplying by wheel diameter converts this ratio into the effective diameter of the imaginary directly driven wheel that would produce the same mechanical advantage; multiplying that by π gives the development, 84.4 × π ≈ 265 inches, about 6.73 metres of road per pedal revolution. The definitions and their history are set out in Sheldon Brown's cycling glossary and treated rigorously in Wilson's Bicycling Science (MIT Press).
Where this method is most accurate
Gear inches provide a consistent comparison standard across different wheel sizes and drivetrain setups. The calculation assumes a perfectly circular wheel with the stated diameter; actual rolling radius varies slightly with tyre width, pressure, and rim design. The method does not account for chainline efficiency, drivetrain friction, or pedalling cadence effects on power delivery. Gear inches serve best as a relative comparison tool rather than an absolute predictor of cycling speed or effort, since rider power output, aerodynamics, terrain, and wind conditions all influence actual performance.
What this tool does not do
This calculator computes a mechanical ratio and does not recommend specific gearing choices for training, racing, or terrain. It does not estimate cycling speed, power output, caloric expenditure, or optimal cadence ranges. The tool does not diagnose mechanical issues, predict component wear rates, or advise on drivetrain compatibility. It performs a single arithmetic operation using the values entered and returns the resulting gear-inch measurement.
Disclaimer
This tool is provided for educational and informational purposes only. It is not a substitute for professional coaching, bicycle fitting services, or mechanical advice from qualified technicians. Every cyclist's physiology, experience level, and riding conditions differ. Numbers generated by this calculator represent mathematical estimates based on the formula shown; they do not constitute training guidance or performance guarantees.
Questions
- What are gear inches?
- Gear inches express the effective diameter of a directly driven wheel that would produce the same mechanical advantage as the actual drivetrain. A higher gear-inch value means a harder gear (more distance per pedal stroke), while a lower value indicates an easier gear. The measurement allows comparison across different wheel sizes and component combinations.
- How does wheel diameter affect the calculation?
- Wheel diameter scales the gear-inch result proportionally: larger wheels cover more ground per rotation. Enter the actual outside diameter, not the marketing name. A 700c road wheel is nominally a "28-inch" wheel in European sizing, but with a 25 mm tyre its true diameter is about 26.5 inches (672 mm), and the traditional 27-inch figure is close enough for most comparisons. Mountain bikes typically measure 26, 27.5, or 29 inches depending on tyre.
- Why does a smaller rear cog produce a higher gear?
- A smaller rear cog has fewer teeth, so the chain wraps around it fewer times per revolution. This increases the ratio of chainring teeth to cog teeth, causing the rear wheel to spin faster relative to pedal cadence. The result is a higher gear-inch value, meaning more resistance and greater distance travelled per pedal stroke.
- Can this calculator compare gearing across different bikes?
- Yes. Gear inches normalise comparisons by accounting for both drivetrain ratios and wheel size. A road bike with 50/16 gearing on 700c wheels can be directly compared to a mountain bike with 32/11 gearing on 29-inch wheels by calculating the gear inches for each setup. The tool does not account for tyre width or actual rolling radius variations.
- What is the difference between gear inches and gear ratio?
- Gear ratio is the simple division of chainring teeth by rear cog teeth (e.g., 50 ÷ 16 = 3.125). Gear inches multiply this ratio by wheel diameter, folding wheel size into the comparison. Neither is itself a distance: multiply gear inches by π to get the development, the actual road covered per pedal revolution, which is how continental Europe and track gearing rules state the same quantity.
Sources & Methodology
Gear inches = (chainring teeth / rear cog teeth) × wheel diameter (inches). This formula, standardised in cycling mechanics literature, converts drivetrain gearing into an equivalent directly driven wheel diameter. The method originated in the penny-farthing era when wheel size directly determined gear ratio.
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