Spur gear calculator (standard and profile-shifted, center distance, contact ratio)
From module, number of teeth and profile shift coefficients: reference, tip, root and base diameters, working pressure angle, center distance and transverse contact ratio.
Mesh
Pinion (z1)
Gear (z2)
invαw = 2tanα(x1 + x2)/(z1 + z2) + invα (inv α = tanα − α)
y = (z1 + z2)/2 × (cosα/cosαw − 1) a = ((z1 + z2)/2 + y)m
d = zm db = d cosα df = d − 2(1.25 − x)m
Tip: keep clearance ha1 = (1 + y − x2)m / no shortening ha1 = (1 + x1)m
Left: an 18-tooth standard spur gear (no profile shift) drawn from the calculated involute. Right: the basic rack profile (pressure angle α = 20°) that sets tooth depth and pitch, enlarged. On profile-shifted gears the tip and root circles move by the amount of shift.
Printed from Kezuriba (kezuriba.net/en/gears/spur/)
✎Notes
- Sources differ on the tip of profile-shifted gears. One method shortens the tip to keep 0.25m tip clearance (KHK’s data), the other does not, and the contact ratio changes (e.g. m = 2, z12 with x0.5 against z40: 1.361 vs 1.399). Record on the drawing which one you used.
- Set the profile shift coefficients to 0 for a standard spur gear.
The formulas follow the published technical data listed below and have been checked against the worked examples in those sources. For design or inspection, confirm against your drawing and the standards.