{
  "id": "arrow-speed",
  "version": "d7ebf4b8cb4f",
  "status": "published",
  "name": "Arrow Speed Calculator",
  "question": "What is my arrow speed?",
  "summary": "Estimates the speed of an arrow in ft/s from the bow’s IBO rating, your draw length, draw weight, arrow weight and string weight, with its kinetic energy and momentum.",
  "category": "sports",
  "subcategory": "fitness",
  "url": "https://www.acalculator.org/sports/arrow-speed-calculator",
  "markdown": "https://www.acalculator.org/sports/arrow-speed-calculator.md",
  "kind": "function",
  "method": "Speed (ft/s) = IBO + 10 × (draw length − 30) − (arrow weight − 5 × draw weight) ÷ 3 − string weight ÷ 3; KE = ½ m v²; momentum = m v.",
  "assumptions": [
    "The IBO rating is measured at 70 lb, a 30 in draw, a 350 grain arrow (5 grains per pound) and nothing on the string.",
    "The rules of thumb are linear; real bows differ, so a chronograph gives the true speed.",
    "Arrows lighter than 5 grains per pound of draw weight are outside the rules (and below the IBO test weight)."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "ibo": {
        "title": "IBO speed rating (ft/s)",
        "description": "The bow’s rated speed in feet per second, from its maker.",
        "type": "number",
        "minimum": 100,
        "maximum": 500
      },
      "dl": {
        "title": "Draw length (in)",
        "description": "Your draw length in inches.",
        "type": "number",
        "minimum": 15,
        "maximum": 40
      },
      "dw": {
        "title": "Peak draw weight (lb)",
        "description": "The bow’s peak draw weight in pounds, as you have it set.",
        "type": "number",
        "minimum": 10,
        "maximum": 150
      },
      "aw": {
        "title": "Arrow weight (grains)",
        "description": "The total weight of the arrow with its point, in grains.",
        "type": "number",
        "minimum": 50,
        "maximum": 2000
      },
      "sw": {
        "title": "Weight on the string (grains)",
        "description": "Extra weight on the bowstring (peep sight, nock loop, silencers), in grains; 0 for none.",
        "type": "number",
        "minimum": 0,
        "maximum": 500
      }
    }
  },
  "outputs": {
    "fps": {
      "label": "Arrow speed (ft/s)",
      "description": "The estimated speed of the arrow in feet per second.",
      "format": "number"
    },
    "mps": {
      "label": "Arrow speed (m/s)",
      "description": "The same speed in metres per second.",
      "format": "number"
    },
    "energy": {
      "label": "Kinetic energy (ft·lbf)",
      "description": "½ m v², in foot-pounds.",
      "format": "number"
    },
    "joules": {
      "label": "Kinetic energy (J)",
      "description": "½ m v², in joules.",
      "format": "number"
    },
    "momentum": {
      "label": "Momentum (slug·ft/s)",
      "description": "m v, in slug-feet per second (pound-force seconds).",
      "format": "number"
    },
    "momentumSi": {
      "label": "Momentum (kg·m/s)",
      "description": "m v, in kilogram-metres per second.",
      "format": "number"
    },
    "grainsPerPound": {
      "label": "Arrow grains per pound",
      "description": "Arrow weight ÷ draw weight. The IBO test arrow is 5 grains per pound.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "ibo": 330,
      "dl": 28,
      "dw": 60,
      "aw": 400,
      "sw": 0
    },
    "outputs": {
      "fps": 276.6666666666667,
      "mps": 84.328,
      "energy": 67.97354467680216,
      "joules": 92.15975188451469,
      "momentum": 0.49137502176001563,
      "momentumSi": 2.185744992992,
      "grainsPerPound": 6.666666666666667
    },
    "text": "Your arrow flies at about 276.7 ft/s with 68 ft·lbf of kinetic energy."
  },
  "examples": [
    {
      "given": {
        "ibo": 330,
        "dl": 30,
        "dw": 70,
        "aw": 350,
        "sw": 0
      },
      "expect": {
        "fps": 330,
        "mps": 100.584,
        "grainsPerPound": 5
      },
      "source": "Sunrise Archery, Understanding Bow Speeds (IBO speed rating: 70 lb, 30 in draw, 350 grain arrow). https://sunrisearchery.com/resources/understanding-bow-speeds/; hand calculation in content.mdx: no adjustment at 30 in, 350 gr = 5 × 70"
    },
    {
      "given": {
        "ibo": 330,
        "dl": 28,
        "dw": 60,
        "aw": 400,
        "sw": 0
      },
      "expect": {
        "fps": 276.6666666666667,
        "energy": 67.97354467680216,
        "momentum": 0.49137502176001563
      },
      "source": "N1 Outdoors, Arrow Speed Calculator (draw length ±10 ft/s per inch from 30 in; −1 ft/s per 3 grains of arrow weight above 5 × draw weight; −1 ft/s per 3 grains on the string). https://n1outdoors.com/arrow-speed-calculator/; Sunrise Archery, Understanding Bow Speeds (IBO speed rating: 70 lb, 30 in draw, 350 grain arrow). https://sunrisearchery.com/resources/understanding-bow-speeds/ (this setup shoots about 275 ft/s); NIST SP 811 (2008), Appendix B.8 (1 grain = 64.79891 mg; 1 ft = 0.3048 m; 1 lbf = 4.4482216152605 N). https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8; hand calculation in content.mdx: 330 − 20 − (400 − 300) ÷ 3 = 276.67 ft/s"
    },
    {
      "given": {
        "ibo": 340,
        "dl": 29,
        "dw": 70,
        "aw": 425,
        "sw": 12
      },
      "expect": {
        "fps": 301,
        "joules": 115.90163205062456,
        "energy": 85.48465684000142
      },
      "source": "N1 Outdoors, Arrow Speed Calculator (draw length ±10 ft/s per inch from 30 in; −1 ft/s per 3 grains of arrow weight above 5 × draw weight; −1 ft/s per 3 grains on the string). https://n1outdoors.com/arrow-speed-calculator/; NIST SP 811 (2008), Appendix B.8 (1 grain = 64.79891 mg; 1 ft = 0.3048 m; 1 lbf = 4.4482216152605 N). https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8; hand calculation in content.mdx: 340 − 10 − 75 ÷ 3 − 12 ÷ 3 = 301 ft/s"
    }
  ],
  "sources": [
    "Sunrise Archery & Outdoors, Understanding Bow Speeds (IBO speed rating: 70 lb, 30 in draw, 350 grain arrow; rough changes per inch of draw and per grains of arrow weight; a 330 ft/s bow at 60 lb, 28 in and 400 gr shoots about 275 ft/s). https://sunrisearchery.com/resources/understanding-bow-speeds/ (retrieved 2026-10-02)",
    "N1 Outdoors, Arrow Speed Calculator (each inch of draw length under 30 in takes 10 ft/s from the IBO value, each inch over adds 10; every 3 grains of arrow weight above draw weight × 5 takes 1 ft/s; every 3 grains on the string takes 1 ft/s). https://n1outdoors.com/arrow-speed-calculator/ (retrieved 2026-10-02)",
    "NIST SP 811 (2008), Appendix B.8, Factors for Units Listed Alphabetically (1 grain = 6.479891 × 10⁻⁵ kg; 1 ft = 0.3048 m; 1 lbf = 4.4482216152605 N). https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8 (retrieved 2026-10-02)"
  ],
  "related": [
    "muzzle-energy",
    "kinetic-energy",
    "speed"
  ],
  "changelog": []
}