Rack and Pinion Ratio Calculator
A rack and pinion does not have a driven gear tooth ratio. Its useful ratio is rotary-to-linear: one pinion turn moves the rack by the pinion pitch circumference.
Rotary-to-linear ratio
For rack drives, the conversion ratio is distance per pinion revolution. Pitch diameter sets that travel directly.
travel/rev = pi * d = pi * m * z
Rack speed
Multiply travel per revolution by pinion RPM and divide by 60 to get linear speed.
v = travel/rev * rpm / 60
Motor turns to rack travel
Once travel per revolution is known, commanded motor turns convert directly to rack displacement before gearbox ratio, backlash and compliance are considered.
rack travel = motor turns * gear reduction output turns * travel/rev
When to use gear ratio instead
If two round gears mesh, use the gear ratio calculator. If a pinion drives a straight rack, use travel per revolution as the ratio between rotation and linear motion.
Frequently asked questions
What is the rack and pinion ratio?
For a rack, ratio normally means travel per pinion revolution. The calculator computes travel/rev from module and pinion teeth.
Can I include gearbox reduction?
Yes. First calculate rack travel per pinion revolution, then multiply by the gearbox output revolutions. A 5:1 reducer gives one pinion turn for five motor turns.
Related pages
- Rack and pinion calculator - working travel, speed and force calculator.
- Gear module calculator - module, diametral pitch, circular pitch and tooth size.
- Pitch diameter calculator - pinion pitch diameter from module or DP.
- Lead screw torque calculator - compare screw-drive thrust and speed against a rack drive.
- Overhung load calculator - check shaft and bearing load from the pinion.