Three-Wire Thread Measurement Calculator (Pitch Diameter)
The measurement you should read over three wires for a thread of known pitch diameter, the best wire size, and the pitch diameter from a measurement you took.
Results
What this tool does
Three equal wires are laid in the grooves — two on one side, one opposite — and the micrometer reads over them. The pitch diameter follows from M = d2 + w(1 + 1/sin(α/2)) − (p/2)cot(α/2), which for a 60° thread reduces to the machinist's rule M = d2 + 3w − 0.866 p. The best wire size, w = p ÷ (2 cos(α/2)) = 0.57735 p for 60°, is the one whose contact points lie on the pitch line, so small errors in the flank angle barely change the answer. Wires must be the same diameter and the thread clean; the result is for the pitch diameter only, not the lead or the flank angle.
Formula
M = d2 + w (1 + 1 ÷ sin(α/2)) − (p ÷ 2) cot(α/2) (60°: M = d2 + 3w − 0.866 p) · best wire w = p ÷ (2 cos(α/2))
Variables
| Symbol | Meaning | Unit |
|---|---|---|
d2 | Pitch diameter of the thread | mm |
p | Pitch | mm |
al | Thread angle (60° for metric and unified) | ° |
w | Diameter of the wires you use | mm |
ms | Measurement you took over the wires | mm |
M | Expected measurement over the wires | mm |
BW | Best wire size (touches the flanks at the pitch line) | mm |
PD | Pitch diameter from your measurement | mm |
Worked example
- Pitch diameter of the thread9.026 mm
- Pitch1.5 mm
- Thread angle (60° for metric and unified)60 °
- Diameter of the wires you use0.866 mm
- Measurement you took over the wires10.325 mm
- Expected measurement over the wires10.3250 mm
- Best wire size (touches the flanks at the pitch line)0.8660 mm
- Pitch diameter from your measurement9.0260 mm
Limitations
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.