How this calculation works
Gear torque creates a tangential tooth force, while tooth geometry also creates separating and axial components. This page resolves those magnitudes for an external parallel-axis helical gear. It does not replace torque ratio or speed calculations.
Ft = 2T/d; Fr = Ft tanαn/cosβ; Fa = Ft tanβA worked example
At 100 N m and 100 mm pitch diameter, tangential force is 2000 N. A normal pressure angle of twenty degrees and helix angle of twenty-five degrees give about 803.2 N radial force and 932.6 N axial force.
Good to know
Only ideal static magnitudes are reported. Rotation direction, tooth handedness and which gear is driving determine force directions. Dynamic factors, tooth stress, contact fatigue and bearing reaction distribution require further analysis.
Reference: Illinois mechanics reference — machine dynamics (opens in a new tab) ↗
What this model answers
Gear torque creates a tangential tooth force, while tooth geometry also creates separating and axial components.
This page resolves those magnitudes for an external parallel-axis helical gear. It does not replace torque ratio or speed calculations.
The Bearing variable duty cycle L10 life calculator needs equivalent bearing loads derived from a shaft-load analysis; raw gear force magnitudes are not automatically those loads.
Keep the input conventions consistent
Use pitch diameter rather than outside tooth-tip diameter.
The pressure-angle entry is the normal pressure angle; using a transverse angle in that same formula would double-apply the helix conversion. Enter the magnitude of helix angle and torque.
Read the result carefully
The tangential component follows torque divided by pitch radius.
Axial force vanishes in the zero-helix spur-gear limit, while radial force remains. The resultant force is a vector magnitude, not the arithmetic sum of all three components.
Check whether the pressure angle is specified in the normal or transverse plane before comparing a gear drawing with the input labels. A helical mesh also introduces an axial force component. Tangential force alone therefore does not describe the complete bearing-loading question, even when transmitted torque is known.
Work through the numbers
At 100 N m and 100 mm pitch diameter, tangential force is 2000 N.
A normal pressure angle of twenty degrees and helix angle of twenty-five degrees give about 803.2 N radial force and 932.6 N axial force.
Where the calculation stops
Only ideal static magnitudes are reported.
Rotation direction, tooth handedness and which gear is driving determine force directions. Dynamic factors, tooth stress, contact fatigue and bearing reaction distribution require further analysis.
A few questions, answered
Why is axial force zero at zero helix?
The ideal spur-gear limit has no helical component to create axial thrust.
What should I change in the comparison?
Inspect the spur-gear limit while holding torque, pitch diameter and pressure angle fixed.