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Sprocket and pulley change calculator

What a front or rear sprocket (or belt pulley) change does to final drive, speed and rpm.

Units
km/hAny speed you know, e.g. at 5,000 rpm in top gear.

Result

Change in final drive (positive = shorter, more acceleration)7.14 %
Speed at the same rpm93.3 km/h

How it is calculated, with your numbers
  1. Current final drivefd1 = r1 / f145 / 15 = 3.000
  2. New final drivefd2 = r2 / f245 / 14 = 3.214
  3. Change in final drive (positive = shorter, more acceleration)change = (fd2 / fd1 − 1) × 100(3.21429 / 3 − 1) × 100 = 7.14 %
  4. Speed at the same rpmv2 = v1 × fd1 / fd2100 × 3 / 3.21429 = 93.3 km/h

Working uses the metric units the formula is written in.

  • f1 Current front teeth
  • r1 Current rear teeth
  • f2 New front teeth
  • r2 New rear teeth
  • v1 Speed at an rpm with current gearing (km/h)
  • fd1 Current final drive
  • fd2 New final drive
  • change Change in final drive (positive = shorter, more acceleration)
  • v2 Speed at the same rpm

What it means

The final drive ratio is rear teeth divided by front teeth. A smaller front or bigger rear sprocket raises it ("shorter" gearing): quicker acceleration and more rpm at any speed, lower top speed in each gear. One tooth at the front changes the ratio far more than one tooth at the rear.

A different final drive also makes the speedometer read differently on bikes that take speed from the gearbox output, and it changes the chain length needed.

Assumptions and limits

  • Same tyre and rpm before and after.

Sources

  • Foale, T., Motorcycle Handling and Chassis Design: The Art and Science, 2002.