Reconcile one completed conventional bicycle gear-pair record from whole tooth counts, measured loaded wheel rollout, and installed crank length.
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A quick decision brief for this specific tool
Inputs that matter
One de-identified completed owner, mechanic/fitter or reviewed-training conventional external-chain bicycle gear record; responsible record/revision/date/reviewer; exact bicycle and selected pair; direct-drive basis; installed chainring and rear-sprocket product/tooth evidence; exact wheel/rim/mounted-tire configuration; loaded rollout method/pressure/surface state; installed crank-length source; manufacturer compatibility; chain length/derailleur capacity/chainline/adjustment; wear/damage, installation/torque, intended-use/fit, safety/code, tolerance and review/retention records; whole front/rear tooth counts; supported measured circumference and crank-length units; completed reported ratio/development/gear-inches/gain-ratio source; and an optional same-setup independent report
Output to expect
Normalized measured circumference and crank length; reproduced direct drive ratio, development in mm/m/in/ft, measured rolling diameter, gear inches and gain ratio; signed completed same-basis differences; and optional independent same-basis differences
How it works
Validate every provenance field, exact choice, positive bounded value and whole tooth count; normalize measured rollout and crank length to millimeters; divide front teeth by rear teeth; multiply measured circumference by that ratio for development; divide development by pi and 25.4 for gear inches; divide development by two times pi times crank length for gain ratio; compare the completed and optional independent reports without clamping; require optional source and four reported values all-or-none; and normalize only mathematical zero
Confirm that bicycle, wheel/rim/tire state, selected installed tooth pair, direct-drive path, loaded rollout state, crank length, completed report and optional independent report all match. Another bicycle, gear pair, pressure/load state, crank, drive architecture or revision needs another run.
Use the result only for one completed conventional external-chain gear-pair geometry and transcription check. It does not model internal hubs, gearboxes, motors, belts or compound reductions; select compatible components; establish chain length, derailleur capacity, chainline or adjustment; assess condition, strength, installation or torque; recommend gearing; infer terrain, load, cadence, speed, rider fitness, fit or accessibility; set tolerance; or authorize purchase, modification, service, riding or compliance.
Choose your path
Built around the job you need to finish
Reconcile one completed conventional external-chain bicycle gear-pair record from whole installed tooth counts, one measured loaded wheel circumference and one installed crank length without selecting components or approving gearing, fit, service or use.
Bicycle owner checking one installed gear pair
Replace nominal wheel-size guesses and the legacy 25.4-times gear-inches error with a traceable same-bicycle calculation.
Freeze the exact bicycle and selected chainring/sprocket, measure one loaded wheel rollout at the recorded pressure, verify crank length and enter the completed reported values independently.
Receives reproducible drive ratio, development, gear inches and gain ratio with signed differences and no hill, cadence or purchase recommendation.
Mechanic or fitter reconciling a completed gearing report
Keep component identity, compatibility, chain/derailleur setup, condition and rider-fit decisions separate from arithmetic.
Retain exact manufacturer and service evidence, enter only the installed whole tooth counts, measured rollout and installed crank length, then compare the controlled report.
Can audit four gearing measures while capacity, chainline, adjustment, torque, fit and release stay with responsible records.
Instructor or reviewer checking independent same-setup evidence
Prevent a different wheel state, crank length, gear pair or drive architecture from being presented as corroboration.
Use the optional report only when bicycle, selected pair, loaded rollout state, crank length and output bases match exactly.
Gets deterministic all-or-none validation and separate independent differences without internal-hub, motor, belt or safety conclusions.
Authoritative checks for this tool
Outputs and checklists are planning aids. Review the linked current authorities and the records, terms, instructions, and requirements that apply to your exact situation before a consequential decision.
For one conventional direct chain path, divide the installed front chainring whole-tooth count by the selected rear sprocket whole-tooth count. Internal hubs, gearboxes, motor reductions, belts, and compound paths require different records.
drive ratio = front chainring teeth / rear sprocket teeth
Measured rollout and development
Use a completed straight one-revolution loaded rollout at the recorded riding pressure and configuration. Nominal tire width or bead-seat diameter alone does not reproduce actual mounted circumference.
development = measured wheel circumference × drive ratio
Gear inches
Divide measured circumference by pi to obtain the rolling diameter, convert that diameter to inches, and multiply by the tooth ratio. The previous implementation omitted the millimeter-to-inch conversion and overstated the example by 25.4 times.
gear inches = development (mm) / (pi × 25.4 mm/in)
Gain ratio
Gain ratio also includes installed crank length. It is a dimensionless wheel-travel-to-pedal-travel relationship, not another label for the front-to-rear tooth ratio.
gain ratio = development / (2 × pi × crank length)
Updated: August 2026
Example Scenarios
Reproduce one installed chainring and selected rear-sprocket record using a measured loaded rollout and checked crank length.
Compare a mechanic or fitter report with the same bicycle, selected tooth pair, rollout state, crank length, and output basis.
Verify the unit conversions and four gearing measures while keeping component compatibility, rider fit, terrain, cadence, and safe-use decisions external.
Common Mistakes to Avoid
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Labeling millimeters as gear inches
✓
Convert the measured rolling diameter from millimeters to inches before applying the tooth ratio.
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Calling tooth ratio a gain ratio
✓
Include measured rolling radius and installed crank length in the gain-ratio calculation.
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Treating arithmetic as component or riding approval
✓
Retain manufacturer compatibility, chain length and derailleur capacity, condition, installation, fit, intended use, safety, tolerance, and responsible release outside this record.
FAQ
Actual circumference changes with the rim, mounted tire, tread, pressure, and measurement state. A completed loaded rollout avoids assuming that tire height equals nominal width.
Drive ratio uses only front and rear tooth counts. Gear inches also includes the measured rolling diameter, expressed as an equivalent direct-drive wheel diameter.
Gain ratio includes wheel radius and installed crank length. It compares bicycle travel with pedal travel and is dimensionless.
No. Exact chain, chainring, cassette, freehub, derailleur, frame, capacity, chainline, and manufacturer rules remain separate evidence.
No. Terrain, load, cadence, speed, fitness, ability, biomechanics, accessibility, and intended use are responsible rider, fitter, coach, or clinician decisions.
No. It supports one conventional direct external-chain path only. Internal ratios, gearboxes, motor reductions, belts, and compound drives need their exact manufacturer-defined model.
About Reviewed Bicycle Gear Record
Check one exact external-chain gear pair against measured loaded wheel circumference and installed crank length. Reproduce drive ratio, development, gear inches, and gain ratio without turning arithmetic into component, fit, speed, cadence, or riding approval.
