Mechanical ratio
Divide front chainring teeth by rear-cog teeth. A 50/25 combination is 2.0, meaning the rear wheel turns about twice per crank revolution on a conventional direct chain drive. A lower ratio provides more leverage and less distance per pedal turn; a higher ratio does the opposite.
Why ratio alone can mislead across bikes
Two bicycles can use the same 50/25 tooth combination but have different wheel diameters. The tooth ratio is identical, yet the larger wheel travels farther per revolution. Mechanical ratio is therefore excellent for comparing cassette or chainring choices on the same bike but incomplete for cross-bike comparisons.
Gear inches
Gear inches multiply effective wheel diameter by the chainring/cog ratio. A 27.5-inch effective wheel with 42/21 gearing is 55 gear inches, while a 29-inch wheel with the same tooth counts is 58. Lower gear inches represent easier effective gearing; higher values represent more distance per crank revolution.
Cadence turns gearing into road speed
Cadence is crank RPM. Multiply cadence by the tooth ratio to obtain wheel RPM, then multiply by wheel circumference for theoretical road speed. For example, a 50/17 ratio at 90 rpm cadence on a 27.5-inch effective wheel is roughly 21.7 mph in the ideal no-slip model.
A practical low-gear comparison
A 34-tooth chainring with a 34-tooth rear cog is a 1.00 ratio. Changing only the rear cog to 40 teeth lowers the ratio to 0.85, so the rear wheel turns 15% fewer revolutions per crank turn. At the same cadence that means 15% less theoretical road speed, but greater mechanical leverage for climbing.
Why tire size still matters
Actual outside tire diameter varies with nominal wheel size, tire width and construction. Two bicycles both described as 700c or 29-inch can have meaningfully different rollout if one uses a narrow road tire and the other a large-volume off-road tire. Use actual or measured outside diameter when precision matters.
Gearing does not predict rider performance
A calculator cannot know the rider's sustainable power, gradient, wind, surface or aerodynamic position. A gear can be mathematically available yet unusable at the desired cadence on a steep climb or into a headwind. Use gearing metrics to compare mechanical options, not to promise performance.
Choosing the right GIIRR metric
Use simple gear ratio when comparing tooth combinations on one bike, gear inches when wheel size differs, and cadence-to-speed when you want a road-speed estimate at a chosen pedaling rate. Looking at all three prevents a single number from being given more meaning than it has.
GIIRR is a calculation aid, not a substitute for manufacturer fitment limits, service data or professional engineering review.