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Rack And Pinion Travel Calculator

Work out rack and pinion travel instantly with clear inputs, formula shown and shareable results.

About Rack And Pinion Travel Calculator

A pinion of module m with N teeth has pitch diameter m x N, so one revolution advances the rack by pi x m x N. That is also the resolution denominator: with a 2 mm module 20-tooth pinion, one motor revolution through a 10:1 gearbox moves 12.57 mm.

Formula

Rack and pinion

pitch diameter = module x teeth; travel per revolution = pi x pitch diameter

Worked example

With the default values below, Rack And Pinion Travel Calculator returns Linear travel of 439.82. Change any input above and every figure here is recalculated in your browser.

Inputs used

Gear module
2 mm
Pinion teeth
20 teeth
Pinion revolutions
3.5 rev
Gearbox ratio
10 :1

Results

Linear travel
439.82 mm
Travel per pinion revolution
125.66 mm
Motor revolutions required
35.00 rev
Pinion pitch diameter
40.00 mm

Step by step

  1. 1Values used
  2. 2Rack and pinion
  3. 3Linear travel= 439.82 mm
  4. 4Travel per pinion revolution= 125.66 mm
  5. 5Motor revolutions required= 35.00 rev
  6. 6Pinion pitch diameter= 40.00 mm

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 2 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why use rack and pinion over a ball screw?

Unlimited stroke length and high speed. The trade is lower stiffness, more backlash and the need for a preloaded or twin-pinion arrangement for precision.

How do I improve resolution?

Use a smaller module or fewer pinion teeth, or increase the gearbox ratio — but all three reduce speed and increase reflected inertia.

Related Calculators

Rack And Pinion Travel Calculator – Calculate Linear travel