Gear Inches Calculator
Convert chainring, sprocket, and wheel size into gear inches, rollout, and speed.
What it does
Gear inches describe how far a bicycle travels for one turn of the cranks in a way that lets you compare bikes with different wheel sizes. The number is the diameter of an imaginary penny-farthing wheel that would move the same distance per pedal revolution. A 77 inch gear feels long and fast on flat ground; a 28 inch gear feels short and easy on a climb.
The calculation has two parts. The gear ratio is the chainring tooth count divided by the rear sprocket tooth count. Gear inches multiply that ratio by the wheel diameter measured in inches, including the tire. A 50 tooth chainring with a 17 tooth sprocket on a 26.3 inch wheel gives 50 / 17 = 2.94, and 2.94 x 26.3 = 77.4 gear inches.
Development converts the same idea into distance. Multiply gear inches by pi to get the circumference of that imaginary wheel, then convert to meters or feet. The 77.4 inch gear rolls about 6.17 meters per crank turn. Speed then follows from cadence: development times cadence times 60 minutes, converted to km/h or mph.
Wheel size is the input people get wrong most often. A 700c rim with a 25 mm tire measures about 26.3 inches across, while the same rim with a 32 mm tire is closer to 26.7 inches. Use the mounted diameter, tire included, because that is what actually rolls on the road.
The calculator accepts metric wheel diameter in centimeters and reports development in meters and speed in km/h, or imperial diameter in inches with development in feet and speed in mph. Gear inches and the gear ratio are the same in both modes, since the underlying definition does not change.
How to use
- Pick metric or imperial units.
- Enter the mounted wheel diameter, tire included.
- Enter the chainring tooth count.
- Enter the rear sprocket tooth count.
- Enter the cadence you expect to hold.
- Read gear inches for comparison, development for distance, and speed for pace.
Formula
- Wheel diameter
- Mounted diameter of the wheel and tire, in inches for the gear inch formula.
- Chainring
- Number of teeth on the front chainring.
- Sprocket
- Number of teeth on the rear sprocket or cog.
- Cadence
- Pedal revolutions per minute, used only for the speed output.
Gear inches are traditionally expressed in inches, so a metric wheel is converted to inches before the ratio is applied. Development uses pi times the gear inch diameter and a 0.0254 conversion to meters. The speed output assumes a constant cadence and no wheel slip, and it does not account for tire deformation under load.
Worked example
Example: 50 x 17 on a 66.8 cm wheel at 90 rpm
A bike with a 66.8 cm mounted wheel diameter, a 50 tooth chainring, a 17 tooth rear sprocket, and a cadence of 90 rpm.
- Convert the wheel: 66.8 cm / 2.54 = 26.299 inches.
- Gear ratio: 50 / 17 = 2.941.
- Gear inches: 26.299 x 2.941 = 77.4 inches.
- Development: 77.4 x pi x 0.0254 = 6.17 meters per crank turn.
- Speed: 6.17 x 90 x 60 / 1000 = 33.3 km/h.
- In imperial mode the same wheel is 26.3 inches, development is 20.25 feet, and speed is 20.7 mph.
Reference table
| Chainring | Sprocket | Gear inches | Development | Speed |
|---|---|---|---|---|
| 34 | 32 | 27.9 in | 7.32 ft | 7.5 mph |
| 50 | 17 | 77.4 in | 20.25 ft | 20.7 mph |
| 52 | 12 | 114.0 in | 29.84 ft | 30.5 mph |
| 50 | 28 | 47.0 in | 12.3 ft | 12.6 mph |
Limits
- Assumes the wheel diameter is measured accurately with the tire mounted and inflated.
- Ignores drivetrain losses, tire slip, and aerodynamic drag.
- Speed is a cadence estimate, not a prediction of real riding speed.
- Does not model internal gear hubs, which have their own ratio steps.
Common mistakes
- Using the rim diameter instead of the mounted wheel diameter with the tire.
- Swapping chainring and sprocket in the ratio.
- Mixing centimeters and inches in the same calculation.
- Treating gear inches as distance traveled; the distance is the development figure.
- Comparing gear inches across very different wheel sizes without checking development.
Try it yourself
Quick checks. Answers sit tucked under each question.
50 tooth chainring, 17 tooth sprocket, 66.8 cm wheel. What are the gear inches?
77.4 inches, with a ratio of 2.94:1.
34 tooth chainring, 32 tooth sprocket, 26.3 inch wheel at 80 rpm. What is the speed?
6.7 mph, with 27.9 gear inches.
52 tooth chainring, 12 tooth sprocket, 66.8 cm wheel at 100 rpm. What is the speed?
54.6 km/h, with 114.0 gear inches.
Questions
What are gear inches?
A way to express gearing as the diameter of an equivalent penny-farthing wheel, equal to wheel diameter times the chainring to sprocket ratio.
Why are gear inches still in inches?
The measure was defined that way historically and is still used for comparison, even in countries that ride metric wheels.
What is the difference between gear inches and development?
Gear inches describe an equivalent wheel diameter, while development states the actual distance traveled per crank turn.
Does wheel size really change the gear?
Yes. A larger mounted diameter covers more ground per turn, so the same chainring and sprocket produce a longer gear.
How do I measure my wheel diameter?
Measure from the ground to the top of the inflated tire and double it, or use the tire's published rolling diameter.
Is a higher gear inch number always better?
No. Higher gears suit flat roads and speed, while lower gears suit climbing and easier spinning. The right number depends on terrain and fitness.