For an ideal roller-chain drive with matching pitch and synchronized engagement, selected tooth counts N1 and N2 determine the tooth-count ratio N2/N1 and ideal driven revolutions per driver revolution N1/N2. These relationships do not size or rate a real drive.
Sprocket and Chain Drive · Selected Tooth-Count Ledger
Explore selected tooth-count ratio, ideal driven revolutions and ideal lossless torque factor.
Equation Used
- N1 and N2 are selected integer tooth counts.
- Both sprockets are assumed to use one matching but unspecified chain pitch and tooth system.
- The speed relationship assumes synchronized engagement with no shaft or coupling slip.
- The torque factor additionally assumes lossless power transmission.
- Pitch, dimensions, centre distance, wrap, chain length, load, lubrication, wear, efficiency, life and safety are excluded.
The secondary figure uses normalized common-pitch polygons only; centre distance, chain path and tooth form are not determined.
Selected tooth-count ledger
Each complete driver revolution advances an ideal engaged chain by N1 pitches. The driven sprocket therefore turns N1/N2 revolution. Under an additional lossless-power assumption, the ideal driven/input torque factor is N2/N1.
The visual uses independent normalized common-pitch polygons. It does not claim a centre distance, chain length, tangent chain path, wrap angle or tooth form.
What the calculator determines
Use it to compare selected tooth-count ratios, ideal driven revolutions and the lossless torque factor. A real drive additionally requires an identified chain series, pitch, width, tooth form, centre distance, wrap, chain length, load, speed, service factor, alignment and lubrication method.
Exact selected relationships
Selected tooth-count ratio R=N2/N1; ideal driven revolutions per driver revolution=N1/N2; ideal lossless torque factor=N2/N1; signed tooth-count difference=N2-N1.
Selected-input example
At N1=13 and N2=26, the selected tooth-count ratio is 2.00, the ideal driven shaft turns 0.50 revolution per driver revolution, the ideal lossless torque factor is 2.00 and the signed tooth-count difference is 13.
Not a chain-drive design
The model excludes actual pitch and dimensions, tooth form, roller diameter, chain width, centre distance, wrap, chordal speed variation, chain length, tension, lubrication, wear, alignment, power capacity, efficiency, life and safety. Manufacturer engineering data is required for those decisions.
Questions
Is N2/N1 always a reduction?
No. It is a selected tooth-count ratio and may be below, equal to or above one.
Does the torque factor predict real output torque?
No. It is only the ideal lossless ratio. Real torque requires input torque and losses.
Can the drawing determine chain length?
No. Centre distance and an identified chain pitch are not inputs.
Manufacturer technical references
- Renold, Transmission Chain Installation, Maintenance & Designer Guide — sprocket geometry, selection and maintenance context.
- iwis, Handbook for Chain Engineering — chain-drive geometry, design and calculation context.
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