Base Circle Diameter Calculator

Inputs

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Choose whether to enter pitch diameter directly or derive it from tooth size and count.
Metric module. Pitch diameter d = m*z.
mm
Gear tooth count used to derive pitch diameter and equivalent pitch values.
Standard spur gears are commonly 20 degrees; older gears may be 14.5 degrees and some stronger-tooth designs use 25 degrees.
deg

Results

Default result
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Base circle diameter (d_b)
37.588 mm
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Base circle that generates the involute tooth flank.

d_b = d*cos(alpha).

Also computed

Base circle radius (r_b) 18.794 mm

Pitch diameter used (d) 40 mm

Equivalent module (m) 2 mm

Equivalent diametral pitch (DP) 12.7 1/in

Circular pitch (p_c) 6.2832 mm

Base pitch (p_b) 5.9043 mm

Base pitch is circular pitch projected onto the base circle: p_b = p_c*cos(alpha).

Method notes 3 notes
  • Base circle diameter is d_b = d*cos(alpha), where d is pitch diameter and alpha is the pressure angle.
  • Pitch diameter is derived from d = m*z, m = 25.4/DP or d = z*p_c/pi when tooth pitch is entered.
  • This is involute geometry only. It does not rate bending strength, pitting, backlash, profile shift, undercut, tolerances or manufacturing method.

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