{
  "slug": "spoke-length",
  "title": "Spoke Length Calculator",
  "category": "Cycling",
  "category_slug": "cycling",
  "tier": 3,
  "summary": "Calculate radial spoke length from rim ERD, flange radius, and spoke hole count.",
  "description": "This calculator estimates radial spoke length for bicycle wheel building using a simplified geometric formula based on rim ERD (Effective Rim Diameter), hub flange radius, and spoke hole count. It applies the radial approximation L = √((ERD/2)² + flange_radius²) − 1.5 mm, where 1.5 mm accounts for spoke elbow depth, and outputs the required spoke length in millimeters for zero-cross radial lacing. The calculation assumes symmetrical hub geometry with no flange offset and is most accurate for radial-laced wheels; crossed-spoke patterns require additional angular correction factors.",
  "page_url": "https://fitmetriclab.com/en/tools/cycling/spoke-length/",
  "api_url": "https://fitmetriclab.com/api/tools/spoke-length.json",
  "formula": {
    "id": "spoke_length",
    "expression": "L_{radial} = \\sqrt{(\\text{ERD}/2)^{2} + r_{flange}^{2}} - 1.5 \\text{ mm}",
    "variables": [
      {
        "symbol": "R",
        "description": "Rim ERD in mm"
      },
      {
        "symbol": "n",
        "description": "Number of spoke holes"
      },
      {
        "symbol": "r",
        "description": "Flange radius in mm"
      }
    ]
  },
  "inputs": [
    {
      "id": "erd",
      "label": "Rim ERD",
      "type": "number",
      "unit": "mm",
      "default": 600,
      "min": 300,
      "max": 800,
      "step": 0.5
    },
    {
      "id": "hole_count",
      "label": "Spoke Holes",
      "type": "number",
      "unit": "",
      "default": 32,
      "min": 16,
      "max": 48,
      "step": 4
    },
    {
      "id": "flange_radius_mm",
      "label": "Flange Radius",
      "type": "number",
      "unit": "mm",
      "default": 25,
      "min": 10,
      "max": 60,
      "step": 0.5
    }
  ],
  "worked_example": {
    "inputs": {
      "erd": 600,
      "hole_count": 32,
      "flange_radius_mm": 25
    },
    "expected_output": "299.5 mm"
  },
  "result_summary_template": "For a rim with ERD of {erd} mm, {hole_count} spoke holes, and a hub flange radius of {flange_radius_mm} mm, the radial spoke length calculates to {result}.",
  "methodology": "Radial spoke length approximation: L = √((ERD/2)² + flange_radius²) − 1.5 mm. The 1.5 mm subtracts spoke elbow depth. This assumes 0-cross radial lacing, zero hub offset, and symmetrical geometry. The canonical crossed-spoke formula L = √(d² + r² + R² − 2rR·cos(α)) − ø/2 accounts for flange offset d, crossing angle α, and hole diameter ø. Derived from wheelbuilding geometry standards documented in professional spoke calculators (DT Swiss, Sapim).",
  "sources": [
    {
      "label": "Brandt, J. The Bicycle Wheel, 3rd Edition. Palo Alto: Avocet, 1993.",
      "url": "https://www.wheelpro.co.uk/wheelbuilding/book.php"
    },
    {
      "label": "DT Swiss. Spoke Length Calculation Technical Documentation. DT Swiss AG, 2020.",
      "url": "https://www.dtswiss.com/en/wheels/wheels-spare-parts/spoke-calculator"
    },
    {
      "label": "Sapim. Spoke Length Calculator Technical Guide. Sapim NV, 2021.",
      "url": "https://www.sapim.be/spoke-calculator"
    }
  ],
  "faqs": [
    {
      "question": "What is ERD and how is it measured?",
      "answer": "ERD (Effective Rim Diameter) is the diameter measured from spoke-nipple seat to spoke-nipple seat on the opposite side of the rim. It represents the effective circle where spoke nipples sit. Manufacturers often publish ERD specifications; alternatively, it can be measured by laying two spokes across the rim diameter at the nipple seats and measuring between their inside edges, then adding twice the spoke diameter."
    },
    {
      "question": "Why does this calculator give different results than professional spoke calculators?",
      "answer": "This tool assumes radial (0-cross) lacing with zero hub flange offset and symmetrical geometry. Professional calculators account for spoke crossing pattern (1-cross, 2-cross, 3-cross), left and right flange offset from the wheel centerline (dish), and spoke hole diameter. For a typical 3-cross 32-hole rear wheel, the crossing pattern alone can add 3–5 mm to the required spoke length compared to a radial calculation."
    },
    {
      "question": "What is the 1.5 mm subtraction for spoke elbow?",
      "answer": "The 1.5 mm adjustment accounts for the depth of the spoke elbow—the 90-degree bend at the hub end of a J-bend spoke. When the elbow seats in the hub flange hole, approximately 1.5 mm of spoke length is consumed by the bend geometry. Straight-pull spokes and some proprietary hub designs use different values."
    },
    {
      "question": "Can I use this calculator for 3-cross lacing?",
      "answer": "No. The formula assumes radial lacing where spokes run directly from hub to rim without crossing. A 3-cross pattern, where each spoke crosses three others on the same flange, changes the spoke angle and increases required length. The crossing angle α must be incorporated using the full formula L = √(d² + r² + R² − 2rR·cos(α)) − ø/2 for accurate results."
    },
    {
      "question": "How do I measure hub flange radius?",
      "answer": "Hub flange radius is measured from the hub axle centerline to the center of a spoke hole on the flange. Using calipers, measure the diameter across the spoke hole circle (pitch circle diameter or PCD), then divide by two. This measurement is distinct from the outer flange diameter; only the spoke hole circle matters for spoke length calculation."
    }
  ],
  "related_tools": [
    {
      "slug": "chain-length",
      "title": "Chain Length Calculator",
      "api_url": "https://fitmetriclab.com/api/tools/chain-length.json",
      "page_url": "https://fitmetriclab.com/en/tools/cycling/chain-length/"
    },
    {
      "slug": "climbing-watts",
      "title": "Climbing Watts Calculator",
      "api_url": "https://fitmetriclab.com/api/tools/climbing-watts.json",
      "page_url": "https://fitmetriclab.com/en/tools/cycling/climbing-watts/"
    },
    {
      "slug": "cycling-power",
      "title": "Cycling Power Calculator (Watts from Speed)",
      "api_url": "https://fitmetriclab.com/api/tools/cycling-power.json",
      "page_url": "https://fitmetriclab.com/en/tools/cycling/cycling-power/"
    }
  ],
  "last_updated": "2026-04-22",
  "price": {
    "value": 0,
    "currency": "USD"
  },
  "runs_in_browser": true,
  "disclaimer": "Educational estimate produced from a published formula. Not medical, nutritional, or training advice. Calculations are deterministic — apply the formula to the inputs to reproduce the result."
}