Span Measurement Over Teeth Calculator

Inputs

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Specify gear size by metric module (mm) or imperial diametral pitch (teeth per inch).
Module in mm (metric) or diametral pitch in 1/in (imperial), per the size system above.
mm
Number of teeth on the measured gear.
teeth
Standard pressure angle of the gear (20° is the modern default, 14.5° on legacy imperial gears).
°
Addendum modification coefficient. Positive shift widens the span by 2·x·m·sin(α).
Auto picks the span count that puts caliper contact near the pitch circle.

Results

Default result
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Span measurement(W)
15.321mm
Pass

Measured with a vernier/disc micrometer flat across the flanks; the anvils must clear the root and tip.

Base tangent length over k teeth — the caliper/micrometer reading.

Also computed

Teeth in span(k)3

Base pitch(p_b)5.904mm

Adding one tooth to the span adds exactly one base pitch to W.

Contact diameter(d_c)Pass40.59mm

Caliper contact lands near the pitch circle — the intended measuring zone.

Pitch diameter(d)40.00mm

Base diameter(d_b)37.59mm

Tip diameter (est.)(d_a)44.00mm

Estimated as m·(z + 2 + 2x); use the drawing tip diameter when available.

Method notes 4 notes
  • Spur gears only. Helical gears use the normal module and virtual tooth count in the normal plane — not this page.
  • W assumes an unmodified involute flank. Tip/root relief, crowning and heavy undercut shrink the usable contact window.
  • The reading is independent of runout (it references the base circle), which is why span measurement is preferred over a tooth-depth check.
  • Tolerance: drawings usually specify W with an upper/lower allowance to control backlash; this page returns the theoretical (zero-backlash) value.

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