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Bike Gear Calculator
Enter your chainrings, cassette and wheel size to get a gear chart with ratio, metres per pedal turn, gear inches and speed at your cadence. Climb mode shows the cadence you would turn in each gear on a grade. Example: 50×11 at 90 rpm is about 51.8 km/h on a 2,110 mm wheel.
Your gears
Climb mode: cadence in each gear
Colours follow our gearing guide: 70 rpm or more comfortable, 60–70 OK, 50–60 heavy, under 50 grinding. Which gears do I need for the Alps? Read the guide.
The formulas
Ratio = chainring teeth ÷ sprocket teeth. Metres per pedal turn (development) = ratio × wheel circumference. Gear inches = ratio × wheel diameter in inches (circumference ÷ π). Speed (km/h) = cadence × development × 60 ÷ 1000. In climb mode, speed comes from the power model below and cadence = speed in metres per minute ÷ development.
Tyre circumferences in the list are from Garmin's "Wheel Size and Circumference" chart (Edge 820 manual). The site default of 2,110 mm is the value used in our gearing guide; measure your own wheel for the most exact numbers.
Questions
How fast is 50×11 at 90 rpm?
On a 2,110 mm wheel: 50 ÷ 11 × 2.11 m × 90 × 60 ÷ 1000 ≈ 51.8 km/h.
What cadence will I turn on a steep climb?
By our model, an 80 kg rider and bike at 180 W climbs a 13% grade at about 6.1 km/h, which is about 48 rpm in a 34×34 gear on a 2,110 mm wheel.
How we calculate
Speed comes from a steady power balance on a constant grade: power × drivetrain efficiency = v × m × g × (sin θ + Crr × cos θ) + ½ × ρ × CdA × v³, where v is speed, m is rider + bike + kit, g = 9.80665 m/s², θ is the angle of the average grade, Crr is rolling resistance, ρ is air density and CdA is the drag area. We solve it for v, and time = distance ÷ v. No wind, no stops, steady power.
Our defaults are Crr 0.005, CdA 0.40 m², air density 1.15 kg/m³ and no drivetrain loss: the same assumptions as our gearing guide and the Angliru page, so the numbers on the site agree. You can change them under "Assumptions".
The model has the same structure as the road-cycling power model of Martin, Milliken, Cobb, McFadden and Coggan, "Validation of a mathematical model for road cycling power", Journal of Applied Biomechanics 14(3): 276–291 (1998). In that study, modelled and measured power agreed closely (R² = 0.97, standard error 2.7 W). Their test bike used Crr 0.0032 and a drivetrain efficiency of 97.698%, so their rider was faster than our more cautious defaults would predict. Leave efficiency at 1 to match the rest of this site.
More tools: Climb time calculator · Power-to-weight calculator