Helical Gear Calculator

Inputs

Pinion teeth (z1)

Tooth count on the driving helical pinion.

Gear teeth (z2)

Tooth count on the driven helical gear.

Normal module (mn)

Tooth size measured normal to the helix. Pitch diameters use mt = mn/cos(beta).

Helix angle (beta)

Helix angle at the pitch cylinder.

Normal pressure angle (alpha_n)

Pressure angle in the normal plane. 20 degrees is common.

Input speed (n1)

Pinion input speed.

rpm

Input torque (T1)

Pinion input torque.

N·m

Efficiency (eta)

Torque multiplier efficiency allowance.

Default result

Center distance(a)

63.85mm

Pass

Computed from pitch diameters using transverse module.

a = (d1 + d2)/2 for standard parallel-shaft mesh.

Also computed

Gear ratio(i)2

Driven teeth / pinion teeth.

Transverse module(mt)2.128mm

mt = mn / cos(beta).

Transverse pressure angle(alpha_t)21.17°

Pinion pitch diameter(d1)42.57mm

Gear pitch diameter(d2)85.13mm

Axial pitch(px)18.37mm

px = pi*mn/sin(beta).

Method notes 3 notes

Normal-system helical gears use mt = mn/cos(beta), so d = z*mn/cos(beta) and a = (d1+d2)/2.
Transverse pressure angle is alpha_t = atan(tan(alpha_n)/cos(beta)). Axial pitch is pi*mn/sin(beta).
This is layout geometry only. It does not rate tooth bending, pitting/contact stress, thrust bearing load, backlash, profile shift, lubrication or gearbox housing stiffness.