Bicycle Gear Ratio Calculator Formula
Understand the math behind the bicycle gear ratio calculator. Each variable explained with a worked example.
Formulas Used
Gear Ratio
ratio = gear_ratioDevelopment (per pedal turn)
development_m = gear_ratio * wheel_circumference_mSpeed at Cadence
speed_kmh = gear_ratio * wheel_circumference_m * cadence_rpm * 60 / 1000Variables
| Variable | Description | Default |
|---|---|---|
chainring_teeth | Front Chainring Teeth | 50 |
cog_teeth | Rear Cog Teeth | 17 |
wheel_circumference_m | Wheel Circumference(m) | 2.1 |
cadence_rpm | Pedaling Cadence(rpm) | 80 |
gear_ratio | Derived value= chainring_teeth / cog_teeth | calculated |
How It Works
Bicycle Gear Ratios
The gear ratio determines how far the bike travels per pedal revolution and directly affects speed and effort.
Formula
Gear Ratio = Front Teeth / Rear Teeth
Development = Gear Ratio x Wheel Circumference
Speed = Development x Cadence x 60 / 1000
Higher ratios (big front, small rear) mean higher speed but more effort. Lower ratios (small front, big rear) are easier for climbing.
Worked Example
50-tooth chainring, 17-tooth rear cog, 2.1 m wheel, 80 rpm cadence.
- 01Gear ratio = 50 / 17 = 2.94
- 02Development = 2.94 x 2.1 = 6.18 m per pedal turn
- 03Speed = 6.18 x 80 x 60 / 1000 = 29.6 km/h
Frequently Asked Questions
What gear ratio is good for climbing?
A ratio below 1.5 (like 34/28) is comfortable for steep hills. Mountain bikes may go as low as 0.85 (24/28) for extreme climbs.
What is gear inches?
Gear inches = Gear Ratio x Wheel Diameter (inches). This older system is still used by track cyclists and single-speed riders.
How does cadence affect speed?
In the same gear, higher cadence means higher speed. Most efficient cadence is 80-100 rpm. Elite cyclists may spin 100-120 rpm in races.
Ready to run the numbers?
Open Bicycle Gear Ratio Calculator