A gear tooth caliper measures tooth thickness at the reference circle by setting its depth blade from the tooth tip. For a standard, unshifted external spur gear, the nominal chordal thickness is calculated from module and tooth count; it is not the same value as circular tooth thickness along the pitch arc. This table gives calculated examples for a 20° full-depth tooth system. Use the drawing’s tooth thickness and backlash allowance when setting an inspection limit.

Spur gear chordal tooth thickness reference

What the values represent

Module m is the pitch diameter divided by tooth count, so d = mz. The circular tooth thickness for an unshifted standard tooth is half the circular pitch, πm/2. A caliper does not measure that arc directly: it contacts the tooth flanks across a straight chord. The chordal tooth-thickness equation uses the half-angle ψ at the pitch circle, and the chordal height locates the caliper’s horizontal jaws relative to the tooth tip.

The table uses profile shift coefficient x = 0, pressure angle α = 20°, and addendum ha = m. For a module 2 mm gear with 20 teeth, the pitch diameter is 40 mm and the circular thickness is 3.1416 mm. The half-angle is 4.5°, giving a chordal thickness of about 3.1384 mm. The small difference between arc and chord is geometric; it is not an allowance for manufacturing error.

How to take the measurement

Clean the gear and caliper contacts, then verify the instrument zero and calibration. Set the depth blade to the calculated chordal height and place the measuring faces across one tooth at that depth. Keep the caliper aligned with the tooth’s transverse plane and avoid rocking it across a flank. Repeat on multiple teeth around the gear and compare the spread as well as the average with the applicable drawing requirement. A single reading can miss runout, pitch variation, or local tooth damage.

Before calculating, confirm whether the gear uses module or diametral pitch, its tooth count, pressure angle, profile shift, and standard addendum. If the tooth has a specified backlash reduction or modified profile, use the documented tooth thickness in the equations. The default zero shift in this reference cannot represent a shifted gear. For helical gears, the measurement plane and normal/transverse system also change the equations.

Worked example and limits

For m = 2 mm, z = 20, x = 0, and α = 20°, the pitch diameter is 2 × 20 = 40 mm. The chordal half-angle is 90°/20 = 4.5°. Substituting into ŝ = zm sin ψ gives 40 sin 4.5° = 3.1384 mm. With a standard addendum ha = 2 mm, the chordal height is 2 + 40/2 × (1 − cos 4.5°) = 2.0617 mm. These values are nominal geometry, rounded to four decimals for display.

To accept or reject a gear, obtain the drawing’s specified tooth-thickness or backlash range and inspection method. A nominal equation alone does not supply tolerance, calibration uncertainty, or allowable variation. A physical measurement may also depend on the instrument’s contact geometry and operator technique. If a measurement differs from the nominal value, investigate the actual design shift, tooth thinning, and setup before changing a gear.

Common mistakes

Do not set the caliper at the pitch circle without using the chordal height; the tooth narrows away from that circle. Do not compare a measured chord directly with the circular arc thickness. Also avoid applying this table to helical, internal, bevel, or profile-shifted gears without the appropriate equations. The publisher KHK distinguishes chordal-caliper measurement from span and over-pin/ball methods; those methods have different datums and are not interchangeable.

These calculations follow KHK-USA’s spur-gear chordal tooth-thickness equations. Use the gear drawing, applicable inspection standard, calibrated equipment, and the exact gear manufacturer’s data for production acceptance.