Gear geometry

Cylindrical Gear Geometry to ISO 21771-1

Calculate geometry and contact ratios for external spur and helical gear pairs with parallel axes.

ISO21771

Gear data

Normal module mn

Facewidth b

Pinion · teeth zWheel · teeth zNormal pressure angle αnHelix angle βPinion profile shift x1Wheel profile shift x2

Advanced tooth-depth data

Addendum coefficient haP*Dedendum coefficient hfP*Tip alteration coefficient k*

Calculation results

Start with the standard values or adjust the inputs.

Geometry before strength

What this calculator does

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.

Typical tasks

Balance centre distance and profile shift
Check contact ratio and tip clearance
Reconcile CAD and calculation geometry

Design notes and follow-up standards

Check before release

Undercut and interference

Check low tooth counts and profile shifts for manufacturability and unobstructed meshing.

Backlash and tolerances

Nominal geometry does not yet define production flank tolerances or backlash.

Load capacity

Torque, material, lubrication, and duty cycle are outside this geometry model.

Useful follow-up standards

ISO 6336

Load-capacity rating for pitting and tooth-root breakage.

ISO 1328

Accuracy system and deviations for cylindrical gears.

ISO 21771-2

Extended geometry for internal and crossed-axis arrangements.