How to use this calculator
- Choose module or diametral pitch. Pick the gear size system and enter the module in mm or DP in 1/in.
- Enter teeth and pressure angle. Enter the gear tooth count, mating tooth count and pressure angle.
- Set profile shift if needed. Use profile shift to adjust tooth thickness and reduce undercut risk on small gears.
- Read geometry and export. Read diameters, pitch and center distance, inspect the preview and export DXF if needed.
How it works
A standard spur gear is usually defined by module m, tooth count
z and pressure angle alpha. The main diameters are:
d = m · z d_b = d · cos alpha d_a = d + 2m, d_f = d - 2.5m
where d is pitch diameter, d_b base diameter,
d_a outside diameter and d_f root diameter.
The preview and DXF are generated from the involute curve on the base circle.
Mating gears must share the same module or DP and pressure angle. The center
distance for an unshifted pair is a = m(z1 + z2)/2.
Worked example
Verified against the live calculator
A 20-tooth, module 2 spur gear at 20 degrees has pitch diameter
d = 2 × 20 = 40 mm, outside diameter 44 mm,
root diameter 35 mm and base diameter about 37.6 mm.
With a 40-tooth mate, the standard center distance is 60 mm.
Frequently asked questions
What does the spur gear calculator return?
It returns pitch, base, outside and root diameters, addendum, dedendum, whole depth, circular pitch, tooth thickness, center distance with a mating gear, recommended backlash, undercut warning, live profile preview and DXF export.
Is this an involute spur gear calculator?
Yes. The tooth flanks are generated as involutes of the base circle, using the module or diametral pitch, tooth count and pressure angle you enter.
Can I use diametral pitch instead of module?
Yes. Choose diametral pitch in the size-system selector. Internally the calculator converts DP to module with m = 25.4 / DP, so metric and imperial inputs drive the same geometry.
What pressure angle should I use?
20 degrees is the common modern default for spur gears. Use 14.5 degrees for legacy gears that require it, and 25 degrees when a stronger tooth and higher radial load are acceptable.
Why does the calculator warn about undercut?
Low tooth-count spur gears can have their involute flank cut away near the root. Positive profile shift or more teeth can avoid undercut.
Method & assumptions
- External involute spur gears only; bevel, helical and internal gears are not modelled here.
- Standard full-depth teeth: addendum = m, dedendum = 1.25m, clearance = 0.25m.
- The DXF is a generated tooth outline for CAD/CAM layout; verify tool compensation, backlash and load capacity before production.