Measuring over wires or pins is a shop-floor method for checking gear tooth thickness. The right wire diameter matters because the contact point should fall near the useful part of the tooth flank. This compact reference calculates a common standard starting diameter for selected diametral pitches on 20-degree external involute spur gears.

Apply the relation within its scope

The listed diameter uses d = 1.728/DP, where DP is diametral pitch in teeth per inch and d is the wire diameter in inches. This gives a starting wire size for the standard 20-degree external spur gear convention. For a gear at 10 DP, the standard relation gives 0.1728 inch, or about 4.389 mm. The values are calculated and rounded for display; choose an available precision wire or pin set and use its actual certified diameter in the measurement calculation.

Place the wires in opposing tooth spaces and measure over them with suitable measuring equipment. For odd tooth counts, placement is not exactly diametrically opposite, so the measurement geometry differs. The measurement over wires is a tooth-thickness measurement and should not be mislabeled as a direct pitch-diameter measurement. Record the actual wire diameter, gear tooth count, pressure angle, tooth thickness basis, and measurement arrangement with the inspection result.

Geometry changes the measurement

Profile shift, backlash allowance, tooth thinning, pressure-angle deviation, tooth modifications, and nonstandard addendum affect the expected reading. A custom wire size can be used, but the target measurement must be recalculated for that exact diameter and gear specification. A listed “best” wire does not by itself define the tolerance or the acceptance limit.

The table is limited to external involute spur gears using the stated 20-degree basis. Helical gears introduce helix angle and normal-versus-transverse geometry; use an appropriate gear inspection method and the relevant normal or transverse pitch data. Internal gears, bevel gears, worms, splines, non-involute forms, and nonstandard pressure angles require their own equations or controlled reference.

Make an inspection plan, not just a reading

Before inspection, confirm the drawing’s datum scheme, gear quality requirements, temperature condition, measuring instrument calibration, pin or wire condition, and operator method. The gear should be clean and free from burrs. Use repeatable contact force and take readings at the specified locations. A single measurement may miss runout, lead error, profile error, or local damage; the required inspection plan can include additional gear metrology checks.

Use the selected diameter as a planning aid, then verify the exact over-wire value using an authoritative gear calculation or inspection standard for the actual tooth geometry and tolerances. Do not use this quick table to accept a gear whose drawing or customer specification requires a formal method. The source material recommends consulting current AGMA standards and information sheets for gear data and tolerances.

Dimensional traceability matters when comparing readings between operators or production lots. Record whether the wires are calibrated pins or flexible wires, the instrument resolution, measurement temperature, and the number and location of readings. If the drawing gives an over-pin tolerance, use its specified pin diameter and calculation basis rather than replacing it with the nearest value in this table. A suitable wire can improve contact geometry, but the inspection plan and tolerance still come from the gear definition.

The conversion shown in both units is d(mm)=25.4×d(in). For example, at 10 diametral pitch the starting wire is 0.1728 inch, or approximately 4.389 mm. The conversion does not add precision: select the actual wire from the available calibrated set, record its measured diameter, and calculate the expected over-wire dimension using the specified gear geometry. If the required pin size falls between available wires, use the inspection method and calculation authorized by the drawing or quality plan.

Sources: Rush Gears’ measurement-over-wires instructions for the standard 1.728/DP pin relation and Gear Technology’s overview of measurement over pins for the distinction between tooth-thickness measurement and pitch diameter.