CNC / machinist calculator
Three-Wire Thread Measurement Calculator
The three-wire method is how you check the pitch diameter of a thread with an ordinary micrometer: seat three wires of a known size in the thread grooves and measure across them. This calculator turns a target pitch diameter into the dimension you should read over the wires, or works backward from a measured reading to the actual pitch diameter, and tells you the best wire size to use. It handles 60 degree Unified and metric threads, 55 degree Whitworth, and 29 degree ACME and Brown & Sharpe worm threads. Worms with other included angles (many are 30 or 40 degrees) are out of scope.
How it works
A wire resting in the groove touches both flanks, so the distance over three wires is fixed by the pitch diameter, the wire size, the pitch and the thread angle. The relationship is the measurement equals the pitch diameter plus the wire diameter times one plus the cosecant of the half angle, minus half the pitch times the cotangent of the half angle. For a 60 degree thread this simplifies to the pitch diameter plus three wire diameters minus 0.86603 times the pitch.
The best wire is the one that contacts the flanks right at the pitch line, which is the pitch divided by twice the cosine of the half angle, or 0.57735 times the pitch for a 60 degree thread. Using the best wire makes the reading least sensitive to small errors. The calculator suggests it, but you can enter whatever wire you actually own and it recomputes.
For a 60 degree thread the basic pitch diameter is the major diameter minus 0.649519 times the pitch, which is how you get the target to aim for. The formulas and constants here are drawn from Machinery's Handbook and the NBS Handbook H28 three-wire method and cross-checked against published pitch diameters for a Unified and a metric example.
Worked example
A 1/2-13 UNC thread (pitch diameter 0.4500 in) with best wires of 0.0444 in should measure 0.5167 in over three wires. Read less than that and the pitch diameter is undersize; more, and it is oversize.
Frequently asked questions
What is the three-wire method?
It is a way to measure the pitch diameter of a thread using three wires of a known diameter placed in the thread grooves and a micrometer read across them. It is more accurate than a thread micrometer and needs only ordinary wires and a mic.
What is the best wire size?
The best wire contacts the flanks exactly at the pitch line, which makes the reading least sensitive to errors. It is the pitch divided by twice the cosine of the half thread angle, and for a 60 degree thread that is 0.57735 times the pitch.
How do I get the target pitch diameter?
For a 60 degree Unified or metric thread the basic pitch diameter is the major diameter minus 0.649519 times the pitch. Look up or compute that, enter it as the pitch diameter, and the calculator gives the over-wires reading to aim for.
Does it work for ACME and Whitworth threads?
Yes. Select 29 degrees for ACME and 29-degree Brown & Sharpe worm threads, or 55 degrees for Whitworth. The general formula uses the half thread angle, so the wire coefficient and best wire size adjust automatically for each form.
Can I use a wire I already have instead of the best size?
Yes. Enter your actual wire diameter and the calculator recomputes the measurement. Any wire that seats on the flanks works; the best size just minimizes sensitivity to error, but a nearby standard wire is fine in practice.
Related calculators
Sources
- Thread measuring wire formulas (Osborn Products, Machinery's Handbook table)
- Measurement of threads by the three-wire method (Van Keuren, NBS Handbook H28)
- Three-wire screw measurement calculator (CGTK)
Every formula on this page is shown and sourced. See how we verify.
These calculators are for planning and as a starting point. Recommended speeds and feeds are published starting values that vary with your specific tool, coating, machine rigidity, workholding and coolant. Always start conservative, listen to the cut, and follow your tool maker data sheet.