{
 "version": "2026-10-20",
 "license": "Dimension sheets are written by Xem Studio from the cited sources and are free to use (CC BY 4.0, attribute 'Xem Studio'). Linked files belong to their publishers under the license shown; Xem Studio does not host them. 'license_verified: false' means the license shown is from memory or the publisher's page as last read and should be confirmed at the link before commercial use.",
 "slug": "springs",
 "name": "Compression, extension and torsion springs: sizes, rate formula, printed envelopes",
 "kind": "hardware",
 "category": "Hardware",
 "group": "Motion",
 "year": null,
 "question": "How do I calculate the rate of a compression spring?",
 "tags": [
  "spring",
  "compression spring",
  "extension spring",
  "torsion spring",
  "rate",
  "stirling",
  "long earth society"
 ],
 "aliases": [
  "compression spring rate formula",
  "spring sizes",
  "music wire spring calculator",
  "torsion spring design",
  "extension spring dimensions",
  "spring index"
 ],
 "overall_mm": {
  "length": null,
  "width": null,
  "height": null
 },
 "official_cad": false,
 "xem_status": "free-files",
 "les": true,
 "free_files": 8,
 "url": "https://xemstudio.com/objects/springs/",
 "sheet_txt": "https://xemstudio.com/objects/springs/sheet.txt",
 "sheet": {
  "basis": "Music-wire (ASTM A228) spring design: k = G·d⁴ / (8·D³·n) with G = 79.3 GPa, D = mean diameter, n = active coils; envelopes in common hobby sizes",
  "overall_mm": {
   "length": null,
   "width": null,
   "height": null
  },
  "notes": [
   "Rate k (N/mm) = G d⁴ / (8 D³ n): wire 1.0 mm, OD 10 (D = 9), 10 active coils → 79300 × 1 / (8 × 729 × 10) = 1.36 N/mm. Halve the coils, double the rate. Spring index D/d between 4 and 12 is makeable; 6–9 is comfortable.",
   "Compression: free length L, solid height ≈ (n + 2) × d, max deflection about 0.8 × (L − solid). Extension: same k, plus initial tension; hooks need D/2 of extra length each end. Torsion: rate in N·mm/deg = E d⁴ / (3667 D n) with E = 207 GPa.",
   "Printed TPU springs work for small forces (ratchet pawls, detents); PLA/PETG helices break. The files here are envelopes for fit and to check pocket clearance (pocket ID = OD + 0.5; guide rod = ID − 0.5).",
   "Where they go on the LES rigs: pawl return (torsion 0.8 × 8), diaphragm return and displacer-rod bias (compression 0.5 × 6 × 20), belt tensioner (extension 1.0 × 10 × 50)."
  ],
  "table": {
   "columns": [
    "type",
    "wire_mm",
    "od_mm",
    "length_mm",
    "coils",
    "rate_n_per_mm",
    "index_d_over_d"
   ],
   "rows": [
    [
     "compression",
     0.5,
     6,
     20,
     8,
     0.47,
     11
    ],
    [
     "compression",
     0.8,
     8,
     25,
     10,
     1.09,
     9
    ],
    [
     "compression",
     1,
     10,
     30,
     10,
     1.36,
     9
    ],
    [
     "compression",
     1.2,
     12,
     40,
     12,
     1.36,
     9
    ],
    [
     "compression",
     1.6,
     16,
     50,
     10,
     2.18,
     9
    ],
    [
     "extension",
     0.6,
     6,
     30,
     20,
     0.41,
     9
    ],
    [
     "extension",
     1,
     10,
     50,
     25,
     0.54,
     9
    ],
    [
     "torsion",
     0.8,
     8,
     10,
     6,
     "—",
     9
    ]
   ]
  }
 },
 "sheet_text": "Compression, extension and torsion springs: sizes, rate formula, printed envelopes — dimension sheet\nSource: Xem Studio, https://xemstudio.com/objects/springs/  (CC BY 4.0)\nBasis: Music-wire (ASTM A228) spring design: k = G·d⁴ / (8·D³·n) with G = 79.3 GPa, D = mean diameter, n = active coils; envelopes in common hobby sizes\nCatalog version: 2026-10-20\n\nSizes: see table below\n- Rate k (N/mm) = G d⁴ / (8 D³ n): wire 1.0 mm, OD 10 (D = 9), 10 active coils → 79300 × 1 / (8 × 729 × 10) = 1.36 N/mm. Halve the coils, double the rate. Spring index D/d between 4 and 12 is makeable; 6–9 is comfortable.\n- Compression: free length L, solid height ≈ (n + 2) × d, max deflection about 0.8 × (L − solid). Extension: same k, plus initial tension; hooks need D/2 of extra length each end. Torsion: rate in N·mm/deg = E d⁴ / (3667 D n) with E = 207 GPa.\n- Printed TPU springs work for small forces (ratchet pawls, detents); PLA/PETG helices break. The files here are envelopes for fit and to check pocket clearance (pocket ID = OD + 0.5; guide rod = ID − 0.5).\n- Where they go on the LES rigs: pawl return (torsion 0.8 × 8), diaphragm return and displacer-rod bias (compression 0.5 × 6 × 20), belt tensioner (extension 1.0 × 10 × 50).\n\ntype  wire_mm  od_mm  length_mm  coils  rate_n_per_mm  index_d_over_d\ncompression  0.5  6  20  8  0.47  11.0\ncompression  0.8  8  25  10  1.09  9.0\ncompression  1.0  10  30  10  1.36  9.0\ncompression  1.2  12  40  12  1.36  9.0\ncompression  1.6  16  50  10  2.18  9.0\nextension  0.6  6  30  20  0.41  9.0\nextension  1.0  10  50  25  0.54  9.0\ntorsion  0.8  8  10  6  —  9.0\n\nFiles elsewhere (not hosted by Xem Studio; license as stated by the publisher):\n- Wikipedia: Spring (device) — web — CC BY-SA 4.0 (text) — https://en.wikipedia.org/wiki/Spring_(device)\n- McMaster-Carr: Compression springs (free STEP per part, for your own design use; no redistribution) — STEP, PDF — McMaster-Carr site terms [verify license at link] — https://www.mcmaster.com/products/compression-springs/\n- Lee Spring: Spring design formulas — web — Lee Spring site [verify license at link] — https://www.leespring.com/learn-about-springs\n- Long Earth Society: Engine and rig builds — web, video — LES site — https://longearthsociety.com/engineering/\n\nFree files (CC BY 4.0, Xem Studio; STEP + STL, 8 parts): https://xemstudio.com/files/hardware/springs/index.json\nAPI: https://xemstudio.com/api/geometry?object=springs\n",
 "sources": [
  {
   "publisher": "Wikipedia",
   "title": "Spring (device)",
   "url": "https://en.wikipedia.org/wiki/Spring_(device)",
   "formats": [
    "web"
   ],
   "license": "CC BY-SA 4.0 (text)",
   "license_verified": true,
   "hosted": false
  },
  {
   "publisher": "McMaster-Carr",
   "title": "Compression springs (free STEP per part, for your own design use; no redistribution)",
   "url": "https://www.mcmaster.com/products/compression-springs/",
   "formats": [
    "STEP",
    "PDF"
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   "license": "McMaster-Carr site terms",
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   "publisher": "Lee Spring",
   "title": "Spring design formulas",
   "url": "https://www.leespring.com/learn-about-springs",
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    "web"
   ],
   "license": "Lee Spring site",
   "license_verified": false,
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  {
   "publisher": "Long Earth Society",
   "title": "Engine and rig builds",
   "url": "https://longearthsociety.com/engineering/",
   "formats": [
    "web",
    "video"
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   "license": "LES site",
   "license_verified": true,
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 ],
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 "related": [
  "ratchet-and-pawl",
  "pins-clevises-and-joints",
  "balloons-and-diaphragms",
  "shaft-collars-clips-and-shafts"
 ],
 "faq": [
  {
   "q": "How do I calculate a compression spring rate?",
   "a": "k = G·d⁴ / (8·D³·n): shear modulus 79.3 GPa for music wire, d wire diameter, D mean coil diameter (OD − d), n active coils. 1 mm wire, 10 mm OD, 10 coils → 1.36 N/mm."
  },
  {
   "q": "What is the solid height of a compression spring?",
   "a": "About (total coils) × wire diameter: a 10-coil, 1 mm wire spring with closed ends is 12 mm solid; usable travel is about 80% of free length minus solid height."
  },
  {
   "q": "Can I 3D print springs?",
   "a": "Only in TPU for light duty (pawl returns, detents, compliant mechanisms); rigid filaments fatigue in a few cycles. Use the printed envelope to check the pocket, then buy the steel spring."
  }
 ],
 "files_license": null,
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   "note": "compression spring envelope: wire 0.5, OD 6, 20 mm, 8 coils"
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   "stl": "https://xemstudio.com/files/hardware/springs/compression-d0.8-od8-l25.stl",
   "note": "compression spring envelope: wire 0.8, OD 8, 25 mm, 10 coils"
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   "note": "compression spring envelope: wire 1.0, OD 10, 30 mm, 10 coils"
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   "stl": "https://xemstudio.com/files/hardware/springs/compression-d1.2-od12-l40.stl",
   "note": "compression spring envelope: wire 1.2, OD 12, 40 mm, 12 coils"
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   "file": "compression-d1.6-od16-l50",
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   "note": "compression spring envelope: wire 1.6, OD 16, 50 mm, 10 coils"
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   "note": "extension spring envelope: wire 0.6, OD 6, 30 mm, 20 coils"
  },
  {
   "file": "extension-d1-od10-l50",
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   "note": "extension spring envelope: wire 1.0, OD 10, 50 mm, 25 coils"
  },
  {
   "file": "torsion-d0.8-od8-l10",
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   "note": "torsion spring envelope: wire 0.8, OD 8, 10 mm, 6 coils"
  }
 ],
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}