# What is the thread measurement?

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.

- Page: https://www.acalculator.org/physics/thread-measurement-calculator
- JSON spec: https://www.acalculator.org/physics/thread-measurement-calculator.json
- Version: ce353725d0da

## Default answer

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).

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| find | Find | Work out the reading over the wires, or the pitch diameter from a reading. |
| form | Thread form | The thread angle: 60° for Unified (UN) and ISO metric threads, or 29° Acme. |
| pb | Pitch as | Give the pitch as threads per inch or as the distance between threads. |
| n | Threads per inch (n) | The number of threads in one inch of length. |
| P | Pitch (P) | The distance from one thread to the next. |
| sb | Size from | Type the pitch diameter, or the major diameter to use the basic pitch diameter of a 60° thread. |
| D | Major diameter (D) | The nominal size of the thread, such as 0.25 in for 1/4-20. |
| E | Pitch diameter (E) | The pitch diameter to check, for example a limit from a thread table. |
| M | Measurement over wires (M) | The micrometer reading over the three wires. |
| W | Wire diameter (W) | Optional: the diameter of the wires you use. Empty uses the best wire size. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| result | Answer | The measurement over wires or the pitch diameter, in inches and millimetres. |
| mIn | Measurement over wires M (in) | The reading over the wires, in inches. |
| mMm | Measurement over wires M (mm) | The reading over the wires, in millimetres. |
| eIn | Pitch diameter E (in) | The pitch diameter, in inches. |
| eMm | Pitch diameter E (mm) | The pitch diameter, in millimetres. |
| wireIn | Wire used (in) | The wire diameter in the formula, in inches. |
| bestIn | Best wire size (in) | The wire that touches the flanks at the pitch diameter: (P ÷ 2) ÷ cos α. |
| bestMm | Best wire size (mm) | The best wire size in millimetres. |
| wireRange | Usable wire sizes | The smallest and largest wires for this pitch (H28 tables). |
| pitchIn | Pitch P (in) | The pitch in inches: 1 ÷ threads per inch. |
| pitchMm | Pitch P (mm) | The pitch in millimetres. |
| wireMm | Wire used (mm) | The wire diameter in the formula, in millimetres. |

## 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.

## Assumptions

- 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.

## Worked examples

1. find = m, form = 60, pb = tpi, n = 20, sb = major, D = 0.00635 gives eIn = 0.217524, bestIn = 0.028868, mIn = 0.260825, result = 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 = m, form = 60, pb = pitch, P = 0.0015, sb = major, D = 0.01 gives eMm = 9.025721, bestMm = 0.866025, mMm = 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 = e, form = 60, pb = tpi, n = 20, M = 0.006629, W = 0.000734 gives eIn = 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 = m, form = acme, pb = tpi, n = 5, E = 0.02286 gives bestIn = 0.10329, mIn = 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).

## FAQ

### 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.

## Sources

- NBS Handbook H28 (1942), Screw-Thread Standards for Federal Services, Appendix 2, Wire Methods of Measurement of Pitch Diameter: the general formula; for 60° threads E = M + 0.86603p − 3G; best wire G = 0.57735p; Table 117 (best 0.577350p, maximum 1.010363p, minimum 0.505182p); the helix term left out for standard fastening screws (public domain scan), retrieved 2026-10-18. https://archive.org/details/screwthreadstand2819unit
- 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) and E = M − (4.993929w − 1.933357p), retrieved 2026-10-18. https://archive.org/details/screwthreadstan2819unit_3
- Pratt & Whitney Measurement Systems, Thread Measuring Wires (60-degree threads), Calibration: best 0.57735 ÷ TPI, minimum 0.505182 ÷ TPI, maximum 1.010363 ÷ TPI, after ASME B1.2 and B1.16M, retrieved 2026-10-18. https://www.prattandwhitney.com/Calibrating_Thread_Measuring_Wires_60_degree_threads_/
- Bureau of Indian Standards, IS 4218-1 (identical with ISO 68-1) and IS 4218-3 (identical with ISO 724): H = (√3 ÷ 2)P, D2 = D − 2 × (3/8)H = D − 0.6495P, retrieved 2026-10-18. https://archive.org/details/gov.in.is.4218.3.1999