{
  "id": "foc",
  "version": "dfc7db90dbe3",
  "status": "published",
  "name": "Arrow FOC Calculator",
  "question": "What is my arrow’s FOC?",
  "summary": "Works out an arrow’s front of center (FOC) percentage from its length and balance point, with Easton’s recommended ranges for target and hunting arrows.",
  "category": "sports",
  "url": "https://www.acalculator.org/sports/foc-calculator",
  "markdown": "https://www.acalculator.org/sports/foc-calculator.md",
  "kind": "function",
  "method": "FOC % = 100 × (A − L ÷ 2) ÷ L, with L the arrow length (nock groove to end of shaft) and A the balance point from the nock throat.",
  "assumptions": [
    "Measure the finished arrow with its point, insert, nock and fletching in place.",
    "L does not include the point; A is measured from the same end (the nock throat).",
    "A balance point behind the middle gives a negative FOC."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "l": {
        "title": "Arrow length (L)",
        "description": "From the bottom of the nock groove to the end of the shaft, not including the point.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "exclusiveMinimum": 0,
        "maximum": 5
      },
      "a": {
        "title": "Balance point (A)",
        "description": "From the nock throat to the point where the finished arrow balances on an edge.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "exclusiveMinimum": 0,
        "maximum": 5
      }
    }
  },
  "outputs": {
    "foc": {
      "label": "FOC",
      "description": "Front of center: how far the balance point is ahead of the middle, as a percent of the length.",
      "format": "percent"
    },
    "center": {
      "label": "Center of the arrow (L ÷ 2)",
      "description": "Half the arrow length, measured from the nock throat.",
      "format": "quantity",
      "unit": "in"
    },
    "ahead": {
      "label": "Balance point ahead of center",
      "description": "A − L ÷ 2: how far the balance point is in front of the middle.",
      "format": "quantity",
      "unit": "in"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "l": 0.7365999999999999,
      "a": 0.4191
    },
    "outputs": {
      "foc": 6.896551724137931,
      "center": 0.36829999999999996,
      "ahead": 0.05080000000000001
    },
    "text": "An arrow 29 in long that balances 16.5 in from the nock has an FOC of 6.9%."
  },
  "examples": [
    {
      "given": {
        "l": 0.7365999999999999,
        "a": 0.4191
      },
      "expect": {
        "foc": 6.896551724137931,
        "center": 0.36829999999999996
      },
      "source": "hand calculation in content.mdx: 29 ÷ 2 = 14.5; 16.5 − 14.5 = 2; 2 × 100 ÷ 29 = 6.9%; Easton Archery, What is F.O.C. and how does it affect arrow flight? (halve the arrow length, measure the balance point from the nock throat, subtract, multiply by 100, divide by the length). https://eastonarchery.com/2014/06/foc/, retrieved 2026-10-02",
      "tolerance": 1e-12
    },
    {
      "given": {
        "l": 0.7111999999999999,
        "a": 0.4445
      },
      "expect": {
        "foc": 12.5
      },
      "source": "hand calculation in content.mdx: 28 ÷ 2 = 14; 17.5 − 14 = 3.5; 3.5 × 100 ÷ 28 = 12.5%, in the hunting range of Easton Archery, FAQs about arrow F.O.C. (front of center): 7–15% indoors, 10–15% outdoors and for hunting. https://eastonarchery.com/2022/03/faqs-about-arrow-f-o-c-front-of-center/, retrieved 2026-10-02",
      "tolerance": 1e-12
    },
    {
      "given": {
        "l": 0.762,
        "a": 0.49529999999999996
      },
      "expect": {
        "foc": 15,
        "ahead": 0.1143
      },
      "source": "hand calculation in content.mdx: 19.5 − 15 = 4.5; 4.5 × 100 ÷ 30 = 15%; Easton Archery, What is F.O.C. and how does it affect arrow flight? (halve the arrow length, measure the balance point from the nock throat, subtract, multiply by 100, divide by the length). https://eastonarchery.com/2014/06/foc/, retrieved 2026-10-02",
      "tolerance": 1e-12
    }
  ],
  "sources": [
    "Easton Archery, What is F.O.C. and how does it affect arrow flight? (divide the length, from the bottom of the nock groove to the end of the shaft, by 2; find the balance point and measure it from the nock throat; subtract; multiply by 100; divide by the length; 10–15% for hunting). https://eastonarchery.com/2014/06/foc/ (retrieved 2026-10-02)",
    "Easton Archery, FAQs about arrow F.O.C. (front of center): 7–15% indoors and 10–15% outdoors for target arrows, 10–15% for hunting. https://eastonarchery.com/2022/03/faqs-about-arrow-f-o-c-front-of-center/ (retrieved 2026-10-02)"
  ],
  "related": [
    "kinetic-energy",
    "muzzle-energy",
    "speed"
  ],
  "changelog": []
}