{
  "id": "thread-measurement",
  "version": "ce353725d0da",
  "status": "published",
  "name": "Thread Measurement Calculator",
  "question": "What is the thread measurement?",
  "summary": "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.",
  "category": "physics",
  "subcategory": "mechanics",
  "url": "https://www.acalculator.org/physics/thread-measurement-calculator",
  "markdown": "https://www.acalculator.org/physics/thread-measurement-calculator.md",
  "kind": "function",
  "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."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "find": {
        "title": "Find",
        "description": "Work out the reading over the wires, or the pitch diameter from a reading.",
        "type": "string",
        "enum": [
          "m",
          "e"
        ]
      },
      "form": {
        "title": "Thread form",
        "description": "The thread angle: 60° for Unified (UN) and ISO metric threads, or 29° Acme.",
        "type": "string",
        "enum": [
          "60",
          "acme"
        ]
      },
      "pb": {
        "title": "Pitch as",
        "description": "Give the pitch as threads per inch or as the distance between threads.",
        "type": "string",
        "enum": [
          "tpi",
          "pitch"
        ]
      },
      "n": {
        "title": "Threads per inch (n)",
        "description": "The number of threads in one inch of length.",
        "type": "number",
        "minimum": 0.5,
        "maximum": 400
      },
      "P": {
        "title": "Pitch (P)",
        "description": "The distance from one thread to the next.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "minimum": 0.000001,
        "maximum": 10
      },
      "sb": {
        "title": "Size from",
        "description": "Type the pitch diameter, or the major diameter to use the basic pitch diameter of a 60° thread.",
        "type": "string",
        "enum": [
          "major",
          "pd"
        ]
      },
      "D": {
        "title": "Major diameter (D)",
        "description": "The nominal size of the thread, such as 0.25 in for 1/4-20.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "minimum": 0.000001,
        "maximum": 10
      },
      "E": {
        "title": "Pitch diameter (E)",
        "description": "The pitch diameter to check, for example a limit from a thread table.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "minimum": 0.000001,
        "maximum": 10
      },
      "M": {
        "title": "Measurement over wires (M)",
        "description": "The micrometer reading over the three wires.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "minimum": 0.000001,
        "maximum": 10
      },
      "W": {
        "title": "Wire diameter (W)",
        "description": "Optional: the diameter of the wires you use. Empty uses the best wire size.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "minimum": 0.000001,
        "maximum": 10
      }
    }
  },
  "outputs": {
    "result": {
      "label": "Answer",
      "description": "The measurement over wires or the pitch diameter, in inches and millimetres.",
      "format": "text"
    },
    "mIn": {
      "label": "Measurement over wires M (in)",
      "description": "The reading over the wires, in inches.",
      "format": "number"
    },
    "mMm": {
      "label": "Measurement over wires M (mm)",
      "description": "The reading over the wires, in millimetres.",
      "format": "number"
    },
    "eIn": {
      "label": "Pitch diameter E (in)",
      "description": "The pitch diameter, in inches.",
      "format": "number"
    },
    "eMm": {
      "label": "Pitch diameter E (mm)",
      "description": "The pitch diameter, in millimetres.",
      "format": "number"
    },
    "wireIn": {
      "label": "Wire used (in)",
      "description": "The wire diameter in the formula, in inches.",
      "format": "number"
    },
    "bestIn": {
      "label": "Best wire size (in)",
      "description": "The wire that touches the flanks at the pitch diameter: (P ÷ 2) ÷ cos α.",
      "format": "number"
    },
    "bestMm": {
      "label": "Best wire size (mm)",
      "description": "The best wire size in millimetres.",
      "format": "number"
    },
    "wireRange": {
      "label": "Usable wire sizes",
      "description": "The smallest and largest wires for this pitch (H28 tables).",
      "format": "text"
    },
    "pitchIn": {
      "label": "Pitch P (in)",
      "description": "The pitch in inches: 1 ÷ threads per inch.",
      "format": "number"
    },
    "pitchMm": {
      "label": "Pitch P (mm)",
      "description": "The pitch in millimetres.",
      "format": "number"
    },
    "wireMm": {
      "label": "Wire used (mm)",
      "description": "The wire diameter in the formula, in millimetres.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "find": "m",
      "form": "60",
      "pb": "tpi",
      "n": 20,
      "P": 0.0015,
      "sb": "major",
      "D": 0.00635,
      "E": 0.0055245,
      "M": 0.0066243199999999995
    },
    "outputs": {
      "result": "M = 0.260825 in (6.62496 mm)",
      "mIn": 0.26082531754730554,
      "mMm": 6.62496306570156,
      "eIn": 0.21752404735808356,
      "eMm": 5.525110802895322,
      "wireIn": 0.02886751345948129,
      "bestIn": 0.02886751345948129,
      "bestMm": 0.7332348418708247,
      "wireRange": "0.0252591 in (0.641581 mm) to 0.0505182 in (1.28316 mm)",
      "pitchIn": 0.05,
      "pitchMm": 1.27,
      "wireMm": 0.7332348418708247
    },
    "text": "For P = 0.05 in and a 0.0288675 in wire: M = 0.260825 in (6.62496 mm)."
  },
  "examples": [
    {
      "given": {
        "find": "m",
        "form": "60",
        "pb": "tpi",
        "n": 20,
        "sb": "major",
        "D": 0.00635
      },
      "expect": {
        "eIn": 0.21752404735808356,
        "bestIn": 0.028867513459481287,
        "mIn": 0.2608253175473055,
        "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); hand calculation in content.mdx: E = 0.25 − 0.649519 × 0.05 = 0.217524 in, M = E − 0.866025 × 0.05 + 3 × 0.0288675 = 0.260825 in",
      "tolerance": 1e-12
    },
    {
      "given": {
        "find": "m",
        "form": "60",
        "pb": "pitch",
        "P": 0.0015,
        "sb": "major",
        "D": 0.01
      },
      "expect": {
        "eMm": 9.025721420742506,
        "bestMm": 0.8660254037844386,
        "mMm": 10.324759526419165
      },
      "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); hand calculation in content.mdx",
      "tolerance": 1e-12
    },
    {
      "given": {
        "find": "e",
        "form": "60",
        "pb": "tpi",
        "n": 20,
        "M": 0.0066294,
        "W": 0.0007340599999999999
      },
      "expect": {
        "eIn": 0.21760127018922193
      },
      "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); hand calculation in content.mdx: E = 0.2610 + 0.866025 × 0.05 − 3 × 0.0289 = 0.217601 in",
      "tolerance": 1e-12
    },
    {
      "given": {
        "find": "m",
        "form": "acme",
        "pb": "tpi",
        "n": 5,
        "E": 0.02286
      },
      "expect": {
        "bestIn": 0.10329003121976855,
        "mIn": 1.0291517896553577
      },
      "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); hand calculation in content.mdx: best wire 0.516450 × 0.2 = 0.103290 in, M = 0.9 − 1.933357 × 0.2 + 4.993929 × 0.103290 = 1.02915 in",
      "tolerance": 1e-12
    }
  ],
  "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"
  ],
  "related": [
    "true-position",
    "speeds-and-feeds",
    "gear-ratio"
  ],
  "changelog": []
}