Rack and Pinion Calculator

Inputs

Module (m)

Gear module (mm). For DP, m = 25.4/DP.

Pinion teeth (z)

Number of teeth on the pinion.

teeth

Pinion speed (n)

Rotational speed of the pinion shaft.

rpm

Pinion torque (T)

Torque at the pinion shaft.

N·m

Default result

Travel per revolution(s)

125.66mm

= π · m · z

Also computed

Linear speed(v)209.4mm/s

Linear force(F)500N

0.5 kN

Ideal — no efficiency loss.

Pitch diameter(d)40mm

= m · z

Method notes 4 notes

Travel per revolution = the pinion pitch circumference, s = π · d = π · m · z. One pinion turn moves the rack by s.
Linear speed v = s · n / 60 (n in rpm → mm/s). Linear force F = T / r, with the pitch radius r = d/2 = m·z/2.
F is the ideal tangential force at the pitch line — it ignores mesh friction and drive efficiency, so the usable push is somewhat lower.
Pinion and rack must share the same module and pressure angle. Helical racks run quieter and carry more load but add an axial thrust.