Span measurement calculator (base tangent length over k teeth)
From module, pressure angle, teeth and profile shift (plus helix angle for helical gears): the number of teeth to span and the span measurement W. For checking tooth thickness.
Result
W = m·cosα × {π(k − 0.5) + z·invαt} + 2x·m·sinα (spur: αt = α)
k is the integer closest to the theoretical span number kth
W is measured with flat anvils on the two outer flanks, spanning k teeth. The measuring direction is tangent to the base circle and the anvils touch the flanks near the reference circle (drawn to scale for a standard spur gear, z = 24, k = 3).
Printed from Kezuriba (kezuriba.net/en/gears/span/)
✎Notes
- Sources differ on the span number and the face width needed for helical gears (KHK’s formulas are used here).
- For tooth-thickness control, apply the thickness tolerance (the reduction for backlash) to the W given here.
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.