Root Diameter

Root diameter, abbreviated as RD, is the diameter at the bottom of the tooth.  It is the diameter of the circle that passes through the bottom (or root) of the gear teeth.  This formula takes into account that the root diameter is located below the pitch diameter, and the subtraction of twice the addendum ensures that the root diameter includes the bottom of the gear teeth.  It's worth noting that for gears with special tooth forms, the calculation of the root diameter may involve additional parameters related to the specific tooth geometry.  The root diameter is used to ensuring proper gear tooth strength and clearance in the gear assembly.

 

Root Diameter formula
\( RD \;=\; PD + 2 \; D \)     (Root Diameter) \( PD \;=\; RD - 2 \; D \) \( D \;=\;  (RD - PD) \;/\; 2 \)
Symbol	English	Metric
\( RD \) = root diameter	\(in\)	\(mm\)
\( PD \) = pitch diameter	\(in\)	\(mm\)
\( D \) = dedendum	\(in\)	\(mm\)