Threading and thread measuring
Threading calculators and thread formulas
Pitch diameter for a Unified thread is major diameter - 0.649519 x P; every threading tool on the site starts from that basic profile.
Technical review pending. Formulas and values are cited. This notice comes down after a machinist review.
Unified inch basic profile (ASME B1.1)
P = 1 / TPI; H = 0.866025 x P; E = D - 0.649519 x P; D1 = D - 1.082532 x P; d3 = D - 1.226869 x P; h = 0.613435 x P
| Symbol | Meaning | Unit |
|---|---|---|
| D | Basic major diameter (nominal size) | in |
| TPI | Threads per inch | 1/in |
| P | Pitch | in |
| H | Height of the sharp V thread | in |
| E | Basic pitch diameter | in |
| D1 | Basic minor diameter, internal thread | in |
| d3 | External minor diameter at a rounded (UNR) root | in |
| h | External thread depth to the rounded root, 17/24 of H | in |
ISO metric basic profile (ISO 68-1)
d2 = D2 = D - 0.649519 x P; D1 = D - 1.082532 x P; d3 = D - 1.226869 x P; h3 = 0.613435 x P
| Symbol | Meaning | Unit |
|---|---|---|
| D | Basic major diameter (nominal size) | mm |
| P | Pitch | mm |
| d2, D2 | Basic pitch diameter, external and internal | mm |
| D1 | Basic minor diameter, internal thread | mm |
| d3 | External minor diameter at the root | mm |
| h3 | External thread depth to the root | mm |
Source: ASME B1.1 (Unified inch screw threads); ISO 68-1 (metric basic profile); Machinery's Handbook
Basic dimensions are not limits. Class 2A and 6g (external) and class 2B and 6H (internal) limits come from ASME B1.1 and ISO 965.
Threading tools
- Thread depth, infeed per pass, number of passes and compound infeed for a CNC lathe are in the CNC threading formulas guide.
- Pitch diameter of a 60° Unified or ISO metric thread from a micrometer reading over wires comes from the 3-wire thread measuring calculator.
- Acme pitch, depth, pitch and minor diameter and best wire size come from the Acme thread calculator.
- Acme pitch diameter over three wires, with a best wire table, is on the Acme 3-wire measuring page.
- Metric trapezoidal (Tr, 30°) pitch diameter over wires comes from the trapezoidal 3-wire calculator.
- A full annotated threading program for 1/2-13 UNC-2A on a Fanuc lathe is in the G92 threading cycle example.
- Metric trapezoidal thread dimensions by size: major, minor and pitch diameter. Coming
Which tool to use
- Three wires and a standard micrometer give pitch diameter on any thread you can reach, with no special gauge.
- A thread micrometer suits repeat checks of one thread form.
- Ring and plug gauges give go or no-go only. They tell you the thread fits, not by how much.
- Match the class table to the thread: 2A or 6g for external threads, 2B or 6H for internal threads.
Worked example: 1/2-13 UNC basic dimensions
1/2-13 UNC: D = 0.5000 in, 13 TPI.
- Pitch: P = 1 / 13 = 0.076923 in (0.0769 in).
- Pitch diameter: E = 0.5000 - 0.649519 x 0.076923 = 0.5000 - 0.0500 = 0.4500 in.
- Internal minor: D1 = 0.5000 - 1.082532 x 0.076923 = 0.5000 - 0.0833 = 0.4167 in.
- External minor, rounded root: d3 = 0.5000 - 1.226869 x 0.076923 = 0.5000 - 0.0944 = 0.4056 in.
- External thread depth: h = 0.613435 x 0.076923 = 0.0472 in.
Result: E 0.4500 in (11.43 mm), D1 0.4167 in (10.58 mm), d3 0.4056 in (10.30 mm), depth 0.0472 in (1.20 mm). The same depth drives the final X in the G92 example. Here, 0.5000 in basic major minus 2 x 0.0472 in gives 0.4056 in. The G92 example starts from the class 2A maximum major, 0.4985 in, so its final X is 0.4041 in.
Worked example: M10 x 1.5 basic dimensions
M10 x 1.5: D = 10 mm, P = 1.5 mm.
- Pitch diameter: d2 = 10 - 0.649519 x 1.5 = 10 - 0.974 = 9.03 mm.
- Internal minor: D1 = 10 - 1.082532 x 1.5 = 10 - 1.624 = 8.38 mm.
- External minor: d3 = 10 - 1.226869 x 1.5 = 10 - 1.840 = 8.16 mm.
- External thread depth: h3 = 0.613435 x 1.5 = 0.92 mm.
Result: d2 9.03 mm, D1 8.38 mm, d3 8.16 mm, depth 0.92 mm. Take the 6g (external) or 6H (internal) limits from ISO 965.
Common mistakes
- Sizing a part to basic pitch diameter. Class 2A external threads have an allowance below basic; size to the class limits.
- Reading an internal (2B, 6H) table for an external thread, or the other way around.
- Using 60° thread constants on Acme (29°) or trapezoidal (30°) threads. Each thread angle has its own wire size and constants.
- Cutting to the sharp V height (0.866025 x P). The thread is truncated at crest and root, so the depth is 0.613435 x P for an external thread.
FAQ
What is the pitch diameter of 1/2-13?
Basic pitch diameter is 0.4500 in: 0.5000 - 0.649519 x 0.076923 = 0.4500 in. The class 2A (external) and 2B (internal) limits are set from basic; take them from the ASME B1.1 table for 1/2-13 UNC.
What is the thread depth for M10 x 1.5?
External depth to the rounded root is h3 = 0.613435 x 1.5 = 0.92 mm, so the basic external minor diameter d3 is 8.16 mm.
How do you measure pitch diameter with three wires?
Use the best wire, 0.57735 x P, and measure over three wires with a micrometer. Then E = M - 3W + 0.86603 x P for a 60° thread. The 3-wire thread measuring calculator does the math.
How accurate does the micrometer need to be for 3-wire measuring?
A resolution of 0.0001 in (0.0025 mm) is the practical minimum for reading pitch diameter over wires.
What change gear cuts metric threads on an inch lathe?
A 127-tooth transposing gear. 5 in is 127 mm (5 x 25.4), so a 127-tooth gear in the train converts an inch leadscrew to metric pitches. Your lathe manual gives the full gear train for each pitch.
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