Gear range versus gear steps: why the percentage and cadence need a denominator
Compare endpoints, the complete tooth sequence, overlapping combinations and inverse cadence changes without treating gear count or range as a riding recommendation.
Published 11 October 2026 · OpenBikeFit
Same endpoints do not define the steps
- Fictional F = 36; rear sequence 12, 15, 18, 24.
- Ratios in low-to-high order: 1.500, 2.000, 2.400, 3.000.
- Adjacent increases: 33.3%, 20.0%, 25.0%. Ratio-style range: 200%.
- Same-speed rear 15 → 18: cadence 80 → 96 rpm; ratio decreases 16.7%.
Original schematic, not to scale. Percentages need a denominator. No cadence target, shift sequence, terrain result or drivetrain choice.
On this page
- 01Name the endpoints and the percentage convention
- 02One chainring shifts the whole set
- 03The complete sequence owns the steps
- 04Reversing a shift changes the denominator
- 05Same-speed cadence is an inverse relationship
- 06Multiple rings create combinations, not unique steps
- 07An internal hub is a different inventory
- 08Keep the whole comparison and unresolved questions
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Compare complete gearing declarations
Retain every numerical tooth pairing, optional wheel quantities, source-specific constraints and unknowns. No ranking, chain-length instruction or compatibility verdict.
Open toolName the endpoints and the percentage convention
A range figure summarizes the highest and lowest declared ratios. It does not show where intermediate gears lie. Write q_low and q_high with their front/rear tooth pairs and any internal transmission stages before calculating. The ratio-style range is 100 × q_high/q_low. The increase above the low endpoint is 100 × (q_high/q_low − 1). Those two descriptions differ by 100 percentage points, not by a mechanical property of the bicycle.
For fictional 1.000 to 4.000, the ratio-style range is 400% and the increase is 300%. A single numerical ratio has a ratio-style range of 100% and an increase of zero. Neither means a wheel has zero rotation. Keep the convention visible whenever a chart, product description or spreadsheet uses the word range.
One chainring shifts the whole set
With one fixed chainring F and a derailleur cassette running from R_small to R_large, the highest ratio is F/R_small and the lowest is F/R_large. Their quotient is R_large/R_small: F cancels. Fictional 11–44 therefore gives 400% ratio-style range whether the front ring is 36 or 42 teeth. Nevertheless every absolute ratio changes when the chainring changes.
With F = 36, the endpoint ratios are approximately 0.818 and 3.273. With F = 42 they are approximately 0.955 and 3.818. The unchanged 400% does not mean unchanged low gearing, development or same-speed cadence. Compare both endpoints and the full sequence, not just the impressive-looking percentage. No ring size is chosen or recommended by these examples.
The complete sequence owns the steps
Write every rear tooth count in declared physical order and keep the exact cassette identity. The fictional sequence 12, 15, 18, 24 is an arithmetic teaching set, not a product specification. With F = 36 its ratios are 3.000, 2.400, 2.000 and 1.500. Ordered from lower to higher numerical ratio, the increases are 33.3%, 20.0% and 25.0%. Four positions and a 200% range do not make those steps equal.
Another fictional sequence 12, 14, 20, 24 has the same endpoint range and position count, yet its adjacent gaps differ. A label such as 12–24 cannot choose between those inventories. Do not fill missing middle teeth by interpolation or borrow a familiar sequence from another variant. Keep an unknown middle step unknown even when both endpoints are known.
Reversing a shift changes the denominator
Compare a lower ratio a and higher ratio b using (b/a − 1) × 100 for the increase from a. Moving back from b to a uses (a/b − 1) × 100. Fictional 2.000 to 2.400 is a 20% increase; 2.400 to 2.000 is a 16.7% decrease. These are the same two endpoints, but the reference value changed. A signed subtraction in ratio units is a third quantity.
Retain the direction and base in each comparison. Saying the jump is 20% without naming which endpoint is the denominator can mislead a later reader. Do not add a forward and reverse percentage and expect zero, or convert a ratio-unit difference into percent without a base. Display rounding is not evidence that two unequal ratios are identical.
Same-speed cadence is an inverse relationship
Under the same steady engaged rolling condition and circumference, cadence_old × q_old = cadence_new × q_new. Thus cadence_new = cadence_old × q_old/q_new. With a fixed front ring, moving from a fictional 15-tooth rear sprocket to 18 teeth gives 80 × 18/15 = 96 rpm at the same modelled speed. The engaged ratio falls by 16.7% while cadence rises by 20%.
The assumption of unchanged speed is essential. If instead cadence stays 80 rpm, the modelled speed falls with the ratio. A real shift is transient and a rider may change speed and cadence together; this calculation does not describe the shift event or establish a desired rpm. Coasting, hub multipliers, slipping and changing rolling conditions require their own declaration.
Multiple rings create combinations, not unique steps
A two-ring system with four rear sprockets has eight nominal combinations, not necessarily eight distinct ratios or an eight-step shift sequence. Fictional rings 36 and 48 with rear 12, 16, 24 and 32 include both 36/24 = 1.500 and 48/32 = 1.500. Equal ratios remain different hardware paths. Their numerical overlap does not prove equivalent chain alignment or permission to use either combination.
Sorting the calculated ratios can reveal duplicates and overlap, but a sorted list is not an instruction for operating front and rear controls. Retain the pair that generated each value and the source-defined usable combinations. This guide gives no cross-chaining rule or universal shift pattern. If the manufacturer excludes a combination, numerical availability cannot override that restriction.
An internal hub is a different inventory
For an internal hub, the gear-specific multiplier table rather than a cassette tooth sequence determines the internal steps. The external chainring/sprocket ratio scales the absolute output while internal ratios determine the range if all other conditions are unchanged. Rohloff separately publishes range and gear-increase terminology for its named hub. Those figures are not copied into a derailleur cassette or another hub.
Do not infer an unknown internal table from the number of gears or a marketing range. Many different inventories can share two endpoints. Source limits on the primary chain ratio, transmission identity and permitted configuration also remain separate from the arithmetic. The example denominator rules here can compare declared numerical ratios; they cannot certify a complete assembly or its operation.
Keep the whole comparison and unresolved questions
A useful note includes all rings, the complete cassette sequence or internal table, exact model and variant, the percentage convention, each tooth pair, wheel reference and the fixed-speed or fixed-cadence assumption. Mark which values were observed and which were calculated. If one source omits a middle sprocket or an internal multiplier, stop that dependent calculation without deleting the available endpoints.
Next identify the cassette/freehub interface and read independent derailleur constraints. The existing crank shortlist does not calculate these gearing inventories; it remains a separate pedal-axis geometry discussion. The free blank worksheet can hold supplementary technical references and questions on paper, but has no dedicated gear-range fields. This path does not select a drivetrain, promise faster climbing or assess comfort, fitness, power or physical compatibility.
Practical questions
Frequently asked questions
Is 400% range a 400% increase?
Not under the stated ratio-style convention. A high/low ratio of four is 400% range and a 300% increase above the low endpoint. State the denominator and convention.
Does changing a single chainring change cassette range?
The ratio-style range from the same cassette endpoints is unchanged because the ring count cancels. Every absolute ratio and development changes; the low and high endpoints must still be recorded.
Does a 20% ratio increase mean cadence rises 20%?
At fixed speed and circumference cadence changes inversely. A 20% ratio increase produces a 16.7% cadence decrease. If speed changes, the fixed-speed statement no longer describes that observation.
Are two rings and twelve sprockets twenty-four unique gears?
They provide twenty-four nominal combinations, not necessarily unique ratios or a permitted shift sequence. Overlap and manufacturer restrictions must remain visible.