Rack and Pinion Force Calculator
Rack push force comes from pinion torque divided by pitch radius. Use the working rack and pinion calculator to solve pitch diameter, travel per revolution, rack speed and ideal linear force from one set of inputs.
Force formula
Ideal rack force is the tangential force at the pinion pitch radius. Use pinion torque in N*m and pitch radius in metres.
F = T / r
Pitch radius from module
For a metric rack and pinion, pitch diameter is module times pinion tooth count. The pitch radius is half of that diameter.
r = (m * z) / 2
Worked example
A module-2, 20-tooth pinion has d = 40 mm and r = 0.020 m. With 10 N*m at the pinion, ideal rack force is F = 10 / 0.020 = 500 N before efficiency and service factors.
What the calculator adds
The working calculator also returns travel per pinion revolution and rack linear speed, so the same inputs cover actuator sizing, motor RPM selection and first-pass force checks.
Frequently asked questions
Does the rack and pinion force calculator include efficiency?
The force shown by the working calculator is ideal pitch-line force. Apply mesh efficiency, bearing losses, acceleration load and a service factor before selecting a motor or gearbox.
Does a smaller pinion increase force?
Yes. Smaller pitch radius gives more force for the same torque, but it also reduces rack travel per revolution and rack speed at a fixed RPM.
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.