Calculate geometry and contact ratios for external spur and helical gear pairs with parallel axes.
Start with the standard values or adjust the inputs.
Calculate pitch diameters, center distance and ratio for an involute cylindrical gear pair.
Normal module mₙ, tooth counts z₁/z₂, normal pressure angle αₙ, helix angle β and profile shifts x₁/x₂ define geometry; addendum and dedendum factors refine dimensions.
Tooth count and module set pitch diameter and tooth size. Helix angle improves overlap but creates axial force; profile shift changes addendum clearance and center distance, so it is not just a correction factor.
Normal module and helix angle give transverse module. Pitch diameter is d = mₜ·z, center distance a = (d₁+d₂)/2 and ratio i = z₂/z₁. Profile shift changes center distance and addendum.
m = 2 mm, z₁ = 20 and z₂ = 40 at β = 0° give d₁ = 40 mm, d₂ = 80 mm, a = 60 mm and i = 2.
Sources and limits: ISO 21771-1 defines cylindrical-gear geometry and terms. Tooth flank and root load capacity require a separate ISO 6336 assessment.
Calculate pitch diameters, center distance and ratio for an involute cylindrical gear pair.
Mechanical calculators translate geometry and load into a response such as torque, stress, deflection, spring force or bearing life. The position of the load relative to the effective axis is often decisive.
Normal module and helix angle give transverse module. Pitch diameter is d = mₜ·z, center distance a = (d₁+d₂)/2 and ratio i = z₂/z₁. Profile shift changes center distance and addendum.
Normal module mₙ, tooth counts z₁/z₂, normal pressure angle αₙ, helix angle β and profile shifts x₁/x₂ define geometry; addendum and dedendum factors refine dimensions. Tooth count and module set pitch diameter and tooth size. Helix angle improves overlap but creates axial force; profile shift changes addendum clearance and center distance, so it is not just a correction factor.
Enter normal module, both gears' tooth counts, pressure angle, helix angle and profile shift factors if used. The calculator returns pitch diameters, center distance and ratio of the gear pair.
m = 2 mm, z₁ = 20 and z₂ = 40 at β = 0° give d₁ = 40 mm, d₂ = 80 mm, a = 60 mm and i = 2.
Tooth count and module set pitch diameter and tooth size. Helix angle improves overlap but creates axial force; profile shift changes addendum clearance and center distance, so it is not just a correction factor. The result shows the idealized component response for the selected load case. A small change in diameter, height, length or load can have a large effect because of power laws.
Module in millimetres, angles in degrees, diameter and center distance in millimetres, ratio dimensionless.
Setting the basic geometry of a new gear pair, or checking whether two existing gears with given module and tooth count actually produce the planned center distance. For tooth thickness inspection in production, continue with the gear span measurement Wk over k teeth.
ISO 21771-1 defines cylindrical-gear geometry and terms. Tooth flank and root load capacity require a separate ISO 6336 assessment.
Common mistake: Don't confuse normal and transverse module – with helical gearing they differ, and only the transverse module directly sets pitch diameter and center distance. Don't ignore profile shift as a mere correction value; it genuinely changes center distance and addendum height and must be compatible between both gears.
Normal module is measured perpendicular to the tooth flank; the helix angle enlarges the module measured in the transverse plane by a factor of 1/cos β.
It allows fine-tuning center distance, avoiding undercut at low tooth counts, or improving tooth strength, while changing addendum and dedendum circle diameters.
No, it provides only dimensions. Tooth-root and flank load capacity are verified separately with the ISO 6336 capacity calculator.
Tooth counts, module, pressure angle, and profile shifts produce diameters, centre distance, and mesh indicators.
ISO 21771-1 provides the common geometry language. The calculator supports diameters, centre distance, and contact ratios; it does not size material or gear accuracy.
Check low tooth counts and profile shifts for manufacturability and unobstructed meshing.
Nominal geometry does not yet define production flank tolerances or backlash.
Torque, material, lubrication, and duty cycle are outside this geometry model.
Load-capacity rating for pitting and tooth-root breakage.
Accuracy system and deviations for cylindrical gears.
Extended geometry for internal and crossed-axis arrangements.