How to use the three-wire pitch diameter calculator
The three-wire method seats three equal wires in the thread grooves and measures across them with a micrometer to get the pitch diameter. For the 60 degree Unified form of ASME B1.1 the reading follows M = pitch diameter + 3W โ 0.866025/n, where n is threads per inch, so the pitch diameter is recovered as M โ 3W + 0.866025/n.
Wires should ideally be the best wire size, 0.57735 รท n, which contacts the flank right at the pitch line; shop sets generally stay between 0.56 and 0.90 of the pitch. Worked check: a 1/2-13 UNC thread with 0.04441 in wires and a reading of 0.51662 in returns a pitch diameter of 0.45001 in, matching the 0.4500 in basic pitch diameter for that size.
For a precision acceptance decision, apply the corrections your procedure calls for: elastic compression of the wires and flanks under micrometer force, and the lead angle correction on coarse or multiple-lead threads. Pitch diameter limits depend on the class of fit called out on the drawing, such as 2A or 3A, so copy them from the ASME B1.1 tables rather than estimating, and cross-check any borderline part with a thread ring or setting gage.
Frequently asked questions
For a 60 degree Unified thread the measurement over wires is M = pitch diameter + 3W โ 0.866025/n, where n is threads per inch. Rearranged, pitch diameter = M โ 3W + 0.866025/n. A 1/2-13 UNC measured at 0.51662 in over 0.04441 in wires works out to 0.45001 in, matching the 0.4500 in basic pitch diameter.
That diameter makes the wire touch the thread flank exactly at the pitch line, which is 1/(2 cos 30 degrees) times the pitch. At the best wire size an error in the included thread angle has the least effect on the reading, and wires far from it need a separate correction.