Rack and Pinion Calculator
SI
Imp
Imperial
Inputs
View results
Module
(m)
Gear module (mm). For DP, m = 25.4/DP.
mm
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
Results
Default result
Edit inputs
Travel per revolution
(s)
125.66
mm
= π · m · z
Also computed
Linear speed
(v)
209.4
mm/s
Linear force
(F)
500
N
0.5 kN
Ideal — no efficiency loss.
Pitch diameter
(d)
40
mm
= 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.
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