acalculator

What is the thread measurement?

Pick the thread form and the pitch, then type the thread size or your micrometer reading. The thread measurement calculator gives the measurement over three wires, or the pitch diameter, with the best wire size and the range of wires that fit.

Your numbers

Units
Find
Thread form
Pitch as
Leave empty to use the best wire size.
Answer
M = 0.260825 in (6.62496 mm)

For P = 0.05 in and a 0.0288675 in wire: M = 0.260825 in (6.62496 mm).

Measurement over wires M (in)
0.260825
Measurement over wires M (mm)
6.62496
Pitch diameter E (in)
0.217524
Pitch diameter E (mm)
5.52511
Wire used (in)
0.0288675
Best wire size (in)
0.0288675
Best wire size (mm)
0.733235
Usable wire sizes
0.0252591 in (0.641581 mm) to 0.0505182 in (1.28316 mm)
Pitch P (in)
0.05
Pitch P (mm)
1.27
Wire used (mm)
0.733235

Answer: M = 0.260825 in (6.62496 mm). For P = 0.05 in and a 0.0288675 in wire: M = 0.260825 in (6.62496 mm).

How to calculate

Thread measurement calculator for the three-wire method: the measurement over wires for a pitch diameter, or the pitch diameter from a reading, with the best wire size, for 60° and 29° Acme threads.

Example with the default inputs (Find Measurement over wires, Thread form 60° (UN, metric), Pitch as Threads per inch, Threads per inch (n) 20, Size from Major diameter, Major diameter (D) 0.25 in): For P = 0.05 in and a 0.0288675 in wire: M = 0.260825 in (6.62496 mm).

Method: M = E − (P ÷ 2) × cot α + W × (1 + csc α), α = half the thread angle: 60° threads M = E − 0.866025P + 3W, 29° Acme M = E − 1.933357P + 4.993929W; E = M + (P ÷ 2) × cot α − W × (1 + csc α); best wire (P ÷ 2) ÷ cos α; basic 60° pitch diameter E = D − 0.649519P.

  • The lead (helix) angle is neglected, as H28 does for standard fastening screws (the error is under 0.00015 in with the best wire).
  • Three wires of the same diameter, a perfect thread form, and a micrometer reading taken square to the axis.

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. Find Measurement over wires, Thread form 60° (UN, metric), Pitch as Threads per inch, Threads per inch (n) 20, Size from Major diameter, Major diameter (D) 0.25 in gives Pitch diameter E (in) 0.217524, Best wire size (in) 0.028868, Measurement over wires M (in) 0.260825, Answer M = 0.260825 in (6.62496 mm).Source: NBS Handbook H28 (1942), Screw-Thread Standards for Federal Services, Appendix 2, Wire Methods of Measurement of Pitch Diameter (general formula; 60° form E = M + 0.86603p − 3G; best wire G = 0.57735p; Table 117: best 0.577350p, maximum 1.010363p, minimum 0.505182p; the helix term is neglected), https://archive.org/details/screwthreadstand2819unit (retrieved 2026-10-18); IS 4218-3 (identical with ISO 724:1993), basic dimensions: D2 = D − 2 × (3/8)H = D − 0.6495P with H = (√3/2)P (IS 4218-1, identical with ISO 68-1), https://archive.org/details/gov.in.is.4218.3.1999 (retrieved 2026-10-18)
  2. Find Measurement over wires, Thread form 60° (UN, metric), Pitch as Pitch, Pitch (P) 0.05906 in, Size from Major diameter, Major diameter (D) 0.3937 in gives Pitch diameter E (mm) 9.025721, Best wire size (mm) 0.866025, Measurement over wires M (mm) 10.32476.Source: IS 4218-3 (identical with ISO 724:1993), basic dimensions: D2 = D − 2 × (3/8)H = D − 0.6495P with H = (√3/2)P (IS 4218-1, identical with ISO 68-1), https://archive.org/details/gov.in.is.4218.3.1999 (retrieved 2026-10-18) (M10 × 1.5: D2 = 9.026 mm); NBS Handbook H28 (1942), Screw-Thread Standards for Federal Services, Appendix 2, Wire Methods of Measurement of Pitch Diameter (general formula; 60° form E = M + 0.86603p − 3G; best wire G = 0.57735p; Table 117: best 0.577350p, maximum 1.010363p, minimum 0.505182p; the helix term is neglected), https://archive.org/details/screwthreadstand2819unit (retrieved 2026-10-18)
  3. Find Pitch diameter, Thread form 60° (UN, metric), Pitch as Threads per inch, Threads per inch (n) 20, Measurement over wires (M) 0.261 in, Wire diameter (W) 0.0289 in gives Pitch diameter E (in) 0.217601.Source: NBS Handbook H28 (1942), Screw-Thread Standards for Federal Services, Appendix 2, Wire Methods of Measurement of Pitch Diameter (general formula; 60° form E = M + 0.86603p − 3G; best wire G = 0.57735p; Table 117: best 0.577350p, maximum 1.010363p, minimum 0.505182p; the helix term is neglected), https://archive.org/details/screwthreadstand2819unit (retrieved 2026-10-18)
  4. Find Measurement over wires, Thread form 29° Acme, Pitch as Threads per inch, Threads per inch (n) 5, Pitch diameter (E) 0.9 in gives Best wire size (in) 0.10329, Measurement over wires M (in) 1.029152.Source: NBS Handbook H28 (1957), Part III, Appendix 13, Three-Wire Method of Measurement of Pitch Diameter of 29° Acme threads (Table 13.1: best 0.516450p, maximum 0.650013p, minimum 0.487263p; E = M − (4.993929w − 1.933357p)), https://archive.org/details/screwthreadstan2819unit_3 (retrieved 2026-10-18)

How it works

With α half the thread angle (30° for 60° threads, 14.5° for 29° Acme), P the pitch, W the wire diameter, E the pitch diameter and M the measurement over the wires (NBS Handbook H28, the lead angle left out):

  • Measurement over wires: M = E − (P ÷ 2) × cot α + W × (1 + csc α).
    • 60° threads: cot 30° ÷ 2 = 0.866025 and 1 + csc 30° = 3, so M = E − 0.866025P + 3W.
    • 29° Acme: cot 14.5° ÷ 2 = 1.933357 and 1 + csc 14.5° = 4.993929, so M = E − 1.933357P + 4.993929W.
  • Pitch diameter from a reading: E = M + (P ÷ 2) × cot α − W × (1 + csc α).
  • Best wire size = (P ÷ 2) ÷ cos α: 0.577350P for 60° and 0.516450P for 29° Acme. An empty wire box uses it.
  • Usable wires (H28 tables): 0.505182P to 1.010363P for 60°, and 0.487263P to 0.650013P for 29° Acme. A typed wire outside the range has no answer. The page compares the typed wire and pitch exactly, so a wire at a limit fits: 1.010363 × 0.05 in = 0.05051815 in at 20 threads per inch.
  • Basic pitch diameter of a 60° thread from its major diameter D: E = D − (3√3 ÷ 8)P = D − 0.649519P (the basic profile of ISO 68-1 and of the Unified thread).
  • Pitch: P = 1 ÷ n inch for n threads per inch, or the pitch you type.

The cot, csc and cos are computed in full, not from the rounded constants above.

Rules

  • Threads per inch from 0.5 to 400; pitch, diameters, reading and wire from 0.000001 m to 10 m.
  • A pitch diameter or reading of 0 or less has no answer.

Output format

The headline reads M = a in (b mm) (or E = … when finding the pitch diameter), and the usable wires read a in (b mm) to c in (d mm), each number to 6 significant figures with thousands commas. The usable wire limits are exact, rounded half up once (0.05051815 in shows as 0.0505182 in). M, E, the wire sizes and the pitch also show as numbers in inches and millimetres (1 in = 25.4 mm) to 6 significant figures. All the other results are 64-bit floats, because of the trigonometry.

Worked examples by hand

1/4-20 UNC. P = 1 ÷ 20 = 0.05 in. Basic E = 0.25 − 0.649519 × 0.05 = 0.2175240 in. Best wire = 0.05 ÷ √3 = 0.0288675 in. M = 0.2175240 − 0.866025 × 0.05 + 3 × 0.0288675 = 0.2608253 in = 6.62496 mm.

M10 × 1.5. E = 10 − 0.649519 × 1.5 = 9.025721 mm (ISO 724 lists 9.026 mm). Best wire = 1.5 ÷ √3 = 0.866025 mm. M = 9.025721 − 1.299038 + 2.598076 = 10.324760 mm.

A reading. 1/4-20 with 0.0289 in wires reads 0.2610 in: E = 0.2610 + 0.866025 × 0.05 − 3 × 0.0289 = 0.2176013 in.

29° Acme. 5 threads per inch (P = 0.2 in), E = 0.9 in. Best wire = 0.516450 × 0.2 = 0.1032900 in. M = 0.9 − 1.933357 × 0.2 + 4.993929 × 0.1032900 = 1.0291518 in.

Other questions people ask

How do you measure a thread with three wires?

Lay one wire in a thread groove on one side and two in neighbouring grooves on the other side, then measure across them with a micrometer. For a 60° thread the reading is M = E − 0.866025P + 3W, with E the pitch diameter, P the pitch and W the wire diameter.

What is the best wire size for a thread?

The wire that touches the thread flanks at the pitch diameter: W = (P ÷ 2) ÷ cos α, with α half the thread angle. For 60° threads that is 0.57735P, so 0.0288675 in for 20 threads per inch. For 29° Acme threads it is 0.516450P.

How do you find the pitch diameter from the measurement over wires?

Rearrange the formula: E = M + 0.866025P − 3W for 60° threads. A 1/4-20 screw reading 0.2610 in over 0.0289 in wires has E = 0.2610 + 0.866025 × 0.05 − 3 × 0.0289 = 0.21760 in.

What is the measurement over wires for a 1/4-20 thread?

At the basic pitch diameter, 0.25 − 0.649519 × 0.05 = 0.217524 in, with best wires (0.0288675 in): M = 0.217524 − 0.0433013 + 0.0866025 = 0.260825 in.

Can I use any wire size?

Only wires that touch the flanks: for 60° threads from 0.505182P to 1.010363P (NBS Handbook H28). A smaller wire sinks below the crests, and a larger one rides on the corners of the thread.

Does the lead angle matter?

A little. H28 leaves out the lead (helix) angle for standard fastening screws, because with the best wire the error is under 0.00015 in. Fine threads on large or multi-start screws need a correction.