Rack Velocity Calculation In Rack And Pinion Gear Systems

There are various applications of spur gear systems such as internal gears, external gears, and idler gears according to the requirements of gear systems. One of these gear systems is the rack and pinion systems. Rack and pinion systems are generally used in automotive steering systems and door sliders.

Precise calculations of rack velocities are very important according to the rotational velocity of the pinion.

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One may think that the calculation of the rack is very easy. We just need to find the circumferential speed of pinion gear. This assumption can be correct in the basics. But it will not give the exact speed of the rack. Because there is a phenomenon called meshing between spur gear systems.

Precise Calculation Of Rack Velocity

In the calculation of rack velocity, it is very important that the consideration of diametral pitch or metric of gears. You can use the calculator below to calculate the exact velocity of the rack in the pinion rack system.

Rack Velocity Calculator

You need to enter the rotational velocity of the pinion which the unit must be rad/s. Then enter the pitch diameter value of the selected gear pair. If you enter the pitch diameter value as the unit of in., you will have the velocity as in/s. If you enter the pitch diameter value as mm, you will have the rack velocity as mm/s.

Click on the ‘Calculate!’ button to have rack velocity. If you want to do another calculation, you just need to click on the ‘Reset!’ button to make another calculation.

The pitch diameter of the pinion is the diameter that the diametral pitch is considered.

You can use the MB-Unit Converter tool to convert your units to other unit sets.


Precise calculation of rack velocity can be done by consideration of pitch diameter, instead of the usual diameter of the pinion.

Mechanicalland does not accept any responsibility for calculations made by the users of calculators. A good engineer must check the calculations again and again.

Do not forget to leave your comments and questions about the velocities of the rack and pinion below.

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