# 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 module mn mm Pressure angle αn ° Helix angle β ° Number of teeth z Profile shift coefficient x Normal tooth thickness allowance Esn mm Addendum gear basic rack haP Addendum tool basic rack haP0 Tip radius factor of tool ρaP0 Diameter of measurement ball (input) DM mm Spanned teeth for measurement (input) k
 Number of teeth z 20 Normal module mn 1 mm Transverse module mt 1 mm Normal pressure angle αn 20 ° Transverse pressure angle αt 20 ° Helix angle β 0 ° Base helix angle βb 0 ° Reference diameter d 20 mm Base diameter db 18.7939 mm Tip diameter da 22 mm Root diameter df 17.5 mm Root form diameter dFf 18.8003 mm Normal tooth thickness on reference circle sn 1.5708 mm Normal tooth thickness on tip circle san 0.6949 mm Generating profile shift coefficient xE 0 Generating profile shift coefficient at untercut limit xEmin -0.0843 Measurement ball diameter DM 1.7 mm Radial single-ball dimension MrK 11.1471 mm Dimensions over balls MdK 22.2941 mm Diameter of measuring circle (balls) dMBall 19.9594 mm Number of teeth for span measurement k 2 Base tangent length Wk 4.7083 mm Diameter of measuring circle (span) dMSpan 19.3746 mm