Bike Gear Ratio Calculator, Explained
After this you can turn any chainring and cog pairing into a gear ratio, gear inches, meters of development and a road speed at your cadence, and compare gears across a whole cassette with confidence.
What a gear ratio actually measures
A bicycle gear ratio is the number of times the rear wheel turns for one full turn of the pedals. Divide the chainring teeth by the rear cog teeth and you have it. A 50-tooth chainring with a 17-tooth cog gives a ratio of 2.941, so every pedal stroke spins the rear wheel just under three times.
That single number is useful, but it hides the wheel. A ratio of 2.941 moves a 26" mountain bike a shorter distance than the same ratio on a 700c road wheel, because the tire that touches the ground is smaller. To compare gears fairly across bikes, you multiply the ratio by wheel diameter. That gives gear inches and development, the two numbers that let you say one gear is genuinely taller or shorter than another.
When to use it, and when not to
Reach for this when you are choosing a cassette, planning a chainring swap, or deciding whether a single-ring setup covers your terrain. It answers concrete questions: will 34×32 spin fast enough up a 12 percent grade, and does my top gear run out of road on a fast descent?
Do not use it to predict how hard a gear feels. Effort depends on grade, wind, weight and your power, none of which live in a gear ratio. A tall gear on the flat can be easy; the same gear uphill can stall you. For the physics of speed and effort, use the Cycling Speed & Power Calculator. Gearing tells you the geometry, not the work.
Gear inches survive from the penny-farthing era, when the pedals bolted straight to the front wheel and a "60 inch" machine had a 60 inch wheel. A modern derailleur gear of 60 inches feels like riding that old wheel, without the height.
The formulas and the intuition behind them
Start with the raw ratio.
Here C is chainring teeth and S is rear cog (sprocket) teeth. Bigger chainring or smaller cog means a larger R, a taller gear, more distance per stroke and more force at the pedal.
Gear inches scale that ratio by the wheel's rolling diameter in inches.
D_{in} is the diameter of the wheel and tire together. A 700x25c wheel rolls at about 26.4 inches across. Development is the same idea in meters, the distance you travel per pedal revolution.
D_m is the rolling diameter in meters and L is meters of development. Multiply development by cadence and you get speed.
N is cadence in revolutions per minute, and v is speed in kilometers per hour. The factor 60/1000 converts meters per minute into kilometers per hour.
Rolling diameter, not the nominal tire size, drives every result. A 700x25c and a 700x40c sit on the same rim but roll at different diameters (about 26.4 vs 28.0 inches), so the same gear ratio gives a taller gear on the fatter tire.
A worked example with the demo numbers
50×17 on a 700x25c wheel at 90 rpm
- Ratio: R = 50 / 17 = 2.941.
- Rolling diameter of 700x25c is about
0.670m, which is26.38inches. - Gear inches: G = 2.941 \times 26.38 = 77.6 inches.
- Development: L = 2.941 \times \pi \times 0.670 = 6.19 m per pedal stroke.
- Speed: v = 6.19 \times 90 \times 0.06 = 33.4 km/h.
So spinning 50×17 at a steady 90 rpm carries you at about 33.4 km/h on level ground, ignoring wind and losses. Each stroke covers 6.19 meters, a little over the length of a car.
Reading the cassette sweep
The real value comes from comparing one chainring against every cog. Hold the 50-tooth ring and the 700x25c wheel fixed, vary the cog, and watch speed at 90 rpm fall as the cog grows. Small cogs are your fast gears; large cogs are your climbing gears.
| Cog (teeth) | Ratio | Gear inches | Development (m) | Speed (km/h) |
|---|---|---|---|---|
| 11 | 4.545 | 119.9 | 9.568 | 51.67 |
| 13 | 3.846 | 101.5 | 8.096 | 43.72 |
| 15 | 3.333 | 87.94 | 7.016 | 37.89 |
| 17 | 2.941 | 77.60 | 6.191 | 33.43 |
| 21 | 2.381 | 62.81 | 5.011 | 27.06 |
| 28 | 1.786 | 47.11 | 3.758 | 20.29 |
Notice the spacing. Dropping from the 11 to the 13 loses about 7.95 km/h, but going from the 21 to the 28 loses only about 6.77 km/h across a bigger tooth jump. Percentage steps between cogs matter more than the raw tooth count, and they stay tighter at the small end.
Explore cadence and gearing yourself
The clearest way to feel gearing is to fix a target speed and see which gear and cadence deliver it. Slide cadence up and the same gear goes faster; move to a bigger cog and you spin faster for the same road speed.
Common mistakes
The errors below are the ones that make two calculators disagree or make a gear feel wrong on the road.
- Using nominal wheel size instead of rolling diameter
- A "29-inch" wheel does not roll at 29 inches. Tire casing, tread and pressure change the real circumference by a centimeter or more. Small differences shift speed by a few tenths of a km/h, which is fine for planning but not for a bike computer.
- Comparing ratios across different wheels
- A ratio of
2.0on a 26" wheel is a shorter gear than2.0on a 700c wheel. Convert to gear inches before you compare. On 700x25c that ratio is52.8inches; on a 26" wheel it is about52.3inches, close here but not equal. - Confusing taller with harder
- A taller gear covers more ground per stroke, but the force you feel depends on grade and power, not on the ratio alone.
- Ignoring cross-chain limits
- The extreme corners of a 2x drivetrain (big-big and small-small) run the chain at a steep angle. They appear in a full sweep but wear the chain and should be avoided in practice.
Speed at cadence assumes zero drivetrain loss and no slipping. Real chains lose 2 to 4 percent, and headwind or grade change the picture completely. Treat the speed figure as the ceiling for that gear and cadence, not a promise.
Related tools
Gearing sets the geometry; other calculators cover the forces and the fit. Once you know your gears, estimate real speed and effort with the Cycling Speed & Power Calculator, and see how you fare on a set climb with the Climb Time & VAM Calculator. To judge whether your climbing gears match your engine, check your Power-to-Weight (W/kg) Calculator. For the parts around the wheel, the Bike Tire Pressure Calculator and the Bike Frame Size Calculator cover pressure and fit. If your training crosses into indoor rowing, the Rowing Split ↔ Watts Converter handles that math.
Frequently asked questions
What gear ratio is good for climbing?
For steep loaded climbs many riders want a ratio near or below 1.0, meaning the cog has as many teeth as the chainring or more. A 34×34 gives 1.0, about 26.9 gear inches on 700x25c, low enough to spin up a 10 percent grade without grinding.
How do I compare a 1x setup to a 2x setup?
Compute gear inches for every gear in each drivetrain, then compare the highest and lowest values (range) and the size of the steps between them. A 1x usually gives a similar range with bigger jumps between gears.
Why does the same gear feel different on my two bikes?
Different wheel and tire sizes change rolling diameter, so the same tooth combination becomes a different gear in inches. A gravel bike on 700x40c runs taller gears than a road bike on 700x25c for identical chainring and cog.
Does cadence change the gear ratio?
No. Cadence changes how fast you cover the fixed distance the gear provides. The ratio, gear inches and development depend only on teeth and wheel size.
What is a normal top-gear speed?
A 50×11 on 700x25c at 90 rpm gives about 51.7 km/h. Most riders spin that out on descents rather than the flat, where power, not gearing, is the limit.
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