How to use this calculator
- Choose the diameter basis. Enter module, diametral pitch, circular pitch or direct pitch diameter.
- Enter tooth count. Use the gear tooth count so pitch diameter and equivalent pitch values are consistent.
- Set pressure angle. Use the pressure angle from the drawing or gear standard, commonly 20 degrees.
- Read base geometry. Read base diameter, base radius, base pitch and the pitch-to-base radial difference.
How it works
An involute tooth flank unwinds from the base circle. Once the
gear pitch diameter d and pressure angle alpha are known,
the base circle diameter is:
d_b = d x cos alpha
If pitch diameter is not entered directly, this calculator derives it first: d = m x z m = 25.4 / DP d = z x p_c / pi Base pitch follows the same projection: p_b = p_c x cos alpha
Use this page when you only need base-circle geometry. For the full tooth profile, undercut warning and DXF export, use the involute gear calculator or gear generator. For mesh overlap, continue with the gear contact ratio calculator.
Worked example
Verified against the live calculator
A module 2 mm, 20-tooth spur gear has pitch diameter
d = 2 x 20 = 40 mm. With a 20 deg pressure angle,
base diameter is d_b = 40 x cos(20 deg) = 37.59 mm. Circular
pitch is pi x 2 = 6.283 mm, so base pitch is
6.283 x cos(20 deg) = 5.904 mm.
Reference data
This is a geometric projection, not a material or strength rating. The same formulas apply to standard involute spur-gear geometry as long as the pitch diameter and pressure angle are from the same gear definition.
| Input | Role |
|---|---|
| Pitch diameter | Direct input, or derived from tooth pitch and tooth count. |
| Module | Metric tooth size. Pitch diameter is d = m*z. |
| Diametral pitch | Converted to module by m = 25.4/DP. |
| Circular pitch | Converted to module by m = p_c/pi. |
| Pressure angle | Projects the pitch circle to the involute base circle. |
Source: Involute spur-gear geometry: d_b = d*cos(alpha), p_b = p_c*cos(alpha).
Frequently asked questions
What is the base circle diameter of a gear?
The base circle is the circle from which an involute tooth flank is generated. For an involute spur gear, base circle diameter is pitch diameter times the cosine of the pressure angle: d_b = d*cos(alpha).
How do you calculate base circle diameter?
First find pitch diameter from module, diametral pitch, circular pitch or a direct pitch diameter. Then multiply by cos(alpha), where alpha is the gear pressure angle.
Can I calculate base circle from module?
Yes. For a module gear, pitch diameter is d = m*z. The calculator then applies d_b = d*cos(alpha) and also returns base pitch p_b = pi*m*cos(alpha).
Is base circle diameter the same as pitch diameter?
No. The base circle is smaller than the pitch circle for any positive pressure angle. A 20 degree pressure angle gives d_b about 94% of pitch diameter.
Does this generate the involute tooth profile?
No. This page isolates the base-circle and base-pitch math. Use the involute gear calculator or gear generator when you need the full tooth profile, undercut check or DXF export.
Method & assumptions
- Uses transverse spur-gear involute geometry.
- Pressure angle is entered in degrees and projected with cosine.
- For helical gears, use the transverse pressure angle before applying the base-circle relation.
- Does not rate tooth bending strength, pitting, backlash, profile shift, undercut, tolerances or manufacturing process.