Symbols with the subscript “G” or “P” are for the gear or the pinion respectively
Number of Teeth: N is a given value
Diametral Pitch: Pd is a given value
Shaft Angle: Σ is a given value
Pressure Angle: φ is a given value (usually 20 degrees)
Ratio: mG=NG/NP
Pitch Diameter: D = N/P
Pitch Angle: Pinion: ϒ = tan-1(NG/NP); Gear: Γ = Σ-ϒ
Outer Cone Distance: Ao=1/2(DP2+DG2)1/2
Face Width: F = Ao/3 or F = 10/Pd (use the smaller value)
Equivalent 90° Ratio: m90=mG
Working Depth: hk = 1.7/Pd
Addendum (at heel of tooth): Gear: aoG=(.46/Pd)+(.390/Pd*m902); Pinion: aoP=hk-aoG
Whole Depth: ht=1.888/Pd
Dedendum (at heel of tooth): Gear: boG=ht-aoG; Pinion: boP=ht-aoP
Dedendum Angle: Gear: δG=tan-1(boG/Ao); Pinion: δP=tan-1(boP/Ao)
Face Angle: Gear: Γo=Γ+δG; Pinion: ϒo=ϒ+δP
Outside Diameter: Gear: DoG=DG+2aoG*cos(Γ); Pinion: DoP=DP+2aoP*cos(ϒ)
Pitch Cone Apex to Crown: Gear: XoG=DP/2-aoG*sin(Γ); Pinion: XoP=DG/2-aoP*sin(ϒ)
Circular Pitch: p=π/Pd
Root Angle: Gear: ΓR=Γ-δG; Pinion: ϒR=ϒ-δP
Back-Angle Distance = Ao