Calculation of geometry for helical gear

The main geometrical dimensions are calculated for a helical gear. This includes the measurements over balls and the base tangent length or span. If the diameter of measurement balls or the number of teeth to span are given to zero, they are set by the calculation. The sign convention is used as by ISO 21771. So a negative sign is used for the number of teeth for internal gears but all diameters are always positive.
These online calculations are provided free of charge by MESYS AG. The software is tested and no errors are known, but there is no warranty for the correctness of the results and for the availability of the calculations. The usage is at own risk.

Normal modulemnmm
Pressure angleαn°
Helix angleβ°
Number of teethz
Profile shift coefficientx
Normal tooth thickness allowanceEsnmm
Addendum gear basic rackhaP
Addendum tool basic rackhaP0
Tip radius factor of toolρaP0
Diameter of measurement ball (input)DMmm
Spanned teeth for measurement (input)k
Number of teethz 20.0000
Normal modulemn 1.0000mm
Transverse modulemt 1.0000mm
Normal pressure angleαn 20.0000°
Transverse pressure angleαt 20.0000°
Helix angleβ 0.0000°
Base helix angleβb 0.0000°
Reference diameterd 20.0000mm
Base diameterdb 18.7939mm
Tip diameterda 22.0000mm
Root diameterdf 17.5000mm
Root form diameterdFf 18.8003mm
Normal tooth thickness on reference circlesn 1.5708mm
Normal tooth thickness on tip circlesan 0.6949mm
Generating profile shift coefficientxE 0.0000
Generating profile shift coefficient at untercut limitxEmin -0.0843
Measurement ball diameterDM 1.7000mm
Radial single-ball dimensionMrK 11.1471mm
Dimensions over ballsMdK 22.2941mm
Diameter of measuring circle (balls)dMBall 19.9594mm
Number of teeth for span measurementk 2
Base tangent lengthWk 4.7083mm
Diameter of measuring circle (span)dMSpan 19.3746mm