If you know a bicycle’s gear ratio, cadence, and tire circumference, you can calculate its theoretical speed. This article breaks the equation into simple parts and works through numerical examples.
I am not a cycling professional or competitive racer. I am a beginner who enjoys cycling and studies questions that come up along the way. That is not an excuse for inaccuracy: the calculations below are checked as carefully as possible using public information, physical relationships, and explicit formulas.
The three numbers that determine theoretical speed
The basic inputs are gear ratio, cadence in crank revolutions per minute, and tire circumference, the distance traveled per wheel revolution.
Gear ratio = front chainring teeth / rear sprocket teeth
Wheel rpm = cadence × gear ratio
Speed (km/h) = cadence × gear ratio × tire circumference (m) × 60 / 1000Example: 40T × 11T with a 2.14 m circumference
40/11 = 3.636. At 90 rpm, 90 × 3.636 × 2.14 × 60 / 1000 ≈ 42.0 km/h.
| Cadence | Gear ratio | Theoretical speed |
|---|---|---|
| 60 rpm | 3.636 | about 28.0 km/h |
| 80 rpm | 3.636 | about 37.4 km/h |
| 90 rpm | 3.636 | about 42.0 km/h |
| 100 rpm | 3.636 | about 46.7 km/h |
What happens when chainring size changes?
Holding the rear sprocket at 11T, cadence at 90 rpm, and circumference at 2.14 m gives about 42.0 km/h with 40T, 48.3 km/h with 46T, and 52.5 km/h with 50T.
| Chainring | Gear ratio | Speed at 90 rpm |
|---|---|---|
| 40T | 3.636 | about 42.0 km/h |
| 46T | 4.182 | about 48.3 km/h |
| 50T | 4.545 | about 52.5 km/h |
Tire circumference matters too
With the same gearing and cadence, a larger circumference travels farther per wheel revolution. At 40T×11T and 90 rpm, 2.10 m gives about 41.2 km/h, 2.14 m about 42.0 km/h, and 2.20 m about 43.2 km/h.
These are drivetrain-based theoretical speeds, not a promise that a rider can sustain them. Aerodynamic drag rises rapidly with speed, so the power required to maintain high speed also rises sharply.
You can also calculate required cadence
Cadence (rpm) = speed (km/h) × 1000 / 60 / gear ratio / tire circumference (m)With 40T×11T and a 2.14 m circumference, the required cadence is roughly 64 rpm at 30 km/h, 86 rpm at 40 km/h, and 107 rpm at 50 km/h.
Theory versus real-world speed
This simplified calculation holds tire circumference constant and ignores tire deformation and drivetrain losses. Real riding also depends on rider power, aerodynamic drag and CdA, wind, road surface, tires and pressure, gradient, riding position, and drivetrain efficiency. At higher speeds, the question “what speed corresponds to this gear and cadence?” is different from “can I produce enough power to reach and hold that speed?”
Summary
The theoretical speed formula is cadence × gear ratio × tire circumference × 60 / 1000. A higher gear ratio, higher cadence, or larger circumference increases the calculated speed. Real maximum and cruising speeds, however, also require considering aerodynamic and rolling resistance, gradient, and available rider power.
