BIZOMAT MAKEOS · Threads
Three-Wire Thread Measurement
What should the measurement over three wires read for this thread, or what pitch diameter does a reading give?
Measurement over wires for 60°, 55° and 29° threads from the pitch diameter and wire size, the best wire size, and the pitch diameter from a measured reading.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Thread angle | choice | Included thread angle. |
| Pitch | mm or in | Thread pitch in the same unit as the diameters. |
| Pitch diameter (target) | mm or in | Target pitch diameter from the thread limits (e.g. mid-tolerance). |
| Wire diameter (0 = best size) | mm or in | Measured diameter of the wires you will use; 0 calculates with the best wire size. |
| Measured reading over wires (0 = none) | mm or in | Reading over the wires, to convert into a pitch diameter; 0 if not measured. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Thread angle
- What it is
- The included angle between the two flanks of the thread form being measured, which sets the best wire size and the wire constant.
- Units and format
- Choose one of 4 options from the list: 60° (metric, unified); 55° (Whitworth); 29° (Acme); 30° (metric trapezoidal).
- Example
- The form opens with “60° (metric, unified)” selected as a worked example. Choose the option that matches your case.
- Get it right
- Metric and unified are 60°; Acme is 29° and metric trapezoidal is 30°. Use the form on the drawing.
What this means: Pitch
- What it is
- The axial distance from one thread crest to the next, in the same unit as the diameters and wires.
- Units and format
- Enter a number in mm or in: millimetres or inches, as long as every length uses the same unit. The form accepts 0.000001 mm or in to 100 mm or in. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.75 mm or in as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Keep every length in one unit; for an inch thread the pitch is 1 ÷ TPI in inches.
What this means: Pitch diameter (target)
- What it is
- The pitch diameter the thread should have, from the thread limits for its class, often the middle of the tolerance. The tool adds the wire constant to it to give the expected reading.
- Units and format
- Enter a number in mm or in: millimetres or inches, as long as every length uses the same unit. The form accepts 0.000001 mm or in to 10000 mm or in. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10.863 mm or in as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The expected reading over wires changes one for one with the pitch diameter.
- Get it right
- Use the pitch diameter, not the major diameter, and the same unit as the pitch.
What this means: Wire diameter (0 = best size)
- What it is
- The measured diameter of the three wires you will actually use. 0 tells the tool to use the best wire size, which touches the flanks at the pitch line.
- Units and format
- Enter a number in mm or in: millimetres or inches, as long as every length uses the same unit. The form accepts 0 mm or in to 100 mm or in. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm or in as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measure the wires themselves; nominal sizes on the box may differ slightly.
What this means: Measured reading over wires (0 = none)
- What it is
- The micrometer reading taken across the three wires on the actual thread, which the tool converts back into a pitch diameter.
- Units and format
- Enter a number in mm or in: millimetres or inches, as long as every length uses the same unit. The form accepts 0 mm or in to 10000 mm or in. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm or in as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- 0 means no reading; the pitch diameter from reading is then not reported. Use the same wires as the wire diameter input.
Method and formulas
- Best wire W = (P ÷ 2) sec(α ÷ 2) (0.57735P for 60°).
- M = E − (P ÷ 2) cot(α ÷ 2) + W(1 + csc(α ÷ 2)); for 60° this is E − 0.866025P + 3W.
- From a reading: E = M + (P ÷ 2) cot(α ÷ 2) − W(1 + csc(α ÷ 2)).
- Example: pitch diameter 10.863 with 1.75 pitch and best wires (1.0104) reads 12.379 over the wires.
Limitations
- Lead-angle effect is ignored; it is small for single-start fastener threads but matters for multi-start and Acme threads.
- Measuring force and wire accuracy affect the reading; use calibrated wires.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Inspect external threads to their pitch diameter
- Choose wires for a thread
- Convert a wire reading to pitch diameter
Who it is for
- Quality inspectors
- Machinists
- Toolmakers
What you get
- Best wire size
- Expected measurement over wires
- Pitch diameter from the measured reading
Interpreting the result
- Compare the pitch diameter from the reading with the thread class limits.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 1990–2003. Topic reference; no source tables or recommended settings are reproduced.
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