How to use this calculator
- Enter teeth. Use pinion and driven gear tooth counts.
- Enter normal module. Use the normal tooth size from the drawing or cutter system.
- Set helix angle. Use the pitch-cylinder helix angle for the gear pair.
- Add speed and torque. Enter optional input RPM, torque and efficiency to estimate output values.
- Read layout dimensions. Use center distance, pitch diameters, axial pitch and lead for first-pass layout.
How it works
A normal-system helical gear starts with normal module mn and
helix angle beta. The transverse module used for pitch diameter is:
mt = mn / cos(beta)
Pitch diameters follow as d1 = z1 x mt and d2 = z2 x mt.
The standard external center distance is a = (d1 + d2) / 2. The
transverse pressure angle is atan(tan(alpha_n) / cos(beta)), axial
pitch is pi x mn / sin(beta), and lead on the pinion is
pi x d1 / tan(beta).
After the layout geometry is fixed, use the gear mesh force calculator to convert torque, pitch diameter, pressure angle and helix angle into tangential, radial and axial loads for shafts and bearings.
Worked example
Verified against the live calculator
A 20-tooth pinion driving a 40-tooth gear has ratio 2:1. With
normal module 2 mm and helix angle 20 degrees, transverse
module is 2 / cos20 = 2.1284 mm.
Pitch diameters are 42.57 mm and 85.13 mm, so center
distance is 63.85 mm. At 1200 rpm input and
98% efficiency, output is 600 rpm and
19.6 N*m.
Frequently asked questions
How do you calculate helical gear pitch diameter from normal module?
For a normal-module helical gear, first convert to transverse module: mt = mn / cos(beta). Pitch diameter is then d = z * mt, or d = z * mn / cos(beta).
How do you calculate helical gear center distance?
For a standard external parallel-shaft mesh, center distance is half the sum of pitch diameters: a = (d1 + d2) / 2. With normal module, d1 and d2 use mn / cos(beta).
What is the difference between normal and transverse module?
Normal module is measured perpendicular to the helical tooth direction. Transverse module is measured in the plane of gear rotation. The transverse module is larger by the factor 1 / cos(beta).
Does helix angle change gear ratio?
No. Ratio is still driven teeth divided by driver teeth, i = z2/z1. Helix angle changes pitch diameter, center distance and axial thrust, not the tooth-count ratio.
Does this calculator rate tooth strength?
No. This is layout geometry. Tooth bending strength, pitting/contact stress, profile shift, backlash, thrust bearing load and lubrication need a gear rating method or manufacturer data.
Can I use inches?
Yes. Toggle units to enter and read module-equivalent lengths, pitch diameters, center distance, axial pitch and lead in inches. Tooth counts and angles stay unitless.
Method & assumptions
- Parallel-shaft external helical gear pair with matching normal module, normal pressure angle and helix angle magnitude.
- Pitch diameter is calculated from the normal-module relation
d = z x mn / cos(beta). - Speed and torque use tooth-count ratio and an entered efficiency allowance.
- Tooth bending, contact stress, profile shift, backlash, axial thrust, bearing loads and lubrication are not rated.