{
  "id": "crosswind",
  "version": "b1ffc3fb76b2",
  "status": "published",
  "name": "Crosswind Calculator",
  "question": "What is the crosswind component?",
  "summary": "Splits a reported wind into its crosswind and headwind (or tailwind) components for a runway, from the runway number, the wind direction and the wind speed, with the gust crosswind.",
  "category": "physics",
  "subcategory": "weather",
  "url": "https://www.acalculator.org/physics/crosswind-calculator",
  "markdown": "https://www.acalculator.org/physics/crosswind-calculator.md",
  "kind": "function",
  "method": "Angle = wind direction − runway number × 10, taken from −180° to 180°; crosswind = speed × |sin(angle)| (from the right when the angle is positive); headwind = speed × cos(angle), negative for a tailwind.",
  "assumptions": [
    "The runway heading is its number × 10 degrees. Real runway headings can differ by a few degrees from the number.",
    "The wind direction and the runway use the same reference (both magnetic, as ATIS and the tower give winds)."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "rwy": {
        "title": "Runway",
        "description": "The runway number, from 1 to 36: its heading in tens of degrees (runway 27 points 270°).",
        "type": "integer",
        "minimum": 1,
        "maximum": 36
      },
      "dir": {
        "title": "Wind direction",
        "description": "The direction the wind blows from, in degrees, from 1 to 360 (360 is north).",
        "type": "integer",
        "minimum": 1,
        "maximum": 360
      },
      "ws": {
        "title": "Wind speed",
        "description": "The steady wind speed.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "speed",
        "minimum": 0,
        "maximum": 128.61111111111111
      },
      "g": {
        "title": "Gusts",
        "description": "The gust speed, if the report gives one. Leave empty if there are none.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "speed",
        "minimum": 0,
        "maximum": 128.61111111111111
      }
    }
  },
  "outputs": {
    "crosswind": {
      "label": "Crosswind",
      "description": "The part of the wind across the runway: speed × |sin(angle)|.",
      "format": "quantity",
      "unit": "kn"
    },
    "side": {
      "label": "Crosswind from",
      "description": "Which side of the runway the crosswind comes from.",
      "format": "text"
    },
    "headwind": {
      "label": "Headwind",
      "description": "The part of the wind along the runway: speed × cos(angle); negative is a tailwind.",
      "format": "quantity",
      "unit": "kn"
    },
    "along": {
      "label": "Along the runway",
      "description": "Headwind, tailwind or none.",
      "format": "text"
    },
    "angle": {
      "label": "Wind angle off the runway",
      "description": "The angle between the wind direction and the runway heading, from 0° to 180°.",
      "format": "number"
    },
    "gustCrosswind": {
      "label": "Gust crosswind",
      "description": "The gust speed × |sin(angle)|.",
      "format": "quantity",
      "unit": "kn"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "rwy": 27,
      "dir": 300,
      "ws": 7.716666666666667
    },
    "outputs": {
      "crosswind": 3.8583333333333334,
      "side": "The right",
      "headwind": 6.682829365869919,
      "along": "Headwind",
      "angle": 30
    },
    "text": "On runway 27 with wind from 300° at 15 kn, the crosswind is 7.5 kn and the headwind 13 kn."
  },
  "examples": [
    {
      "given": {
        "rwy": 27,
        "dir": 300,
        "ws": 10.28888888888889
      },
      "expect": {
        "crosswind": 5.144444444444445,
        "side": "The right",
        "headwind": 8.910439154493224,
        "angle": 30
      },
      "source": "FAA, Pilot’s Handbook of Aeronautical Knowledge (FAA-H-8083-25C), Chapter 11 Aircraft Performance, Crosswind and Headwind Component Chart, https://www.faa.gov/regulations_policies/handbooks_manuals/aviation/phak; hand calculation in content.mdx: 20 × sin 30° = 10 kn; 20 × cos 30° = 17.3 kn",
      "tolerance": 1e-12
    },
    {
      "given": {
        "rwy": 9,
        "dir": 180,
        "ws": 15.433333333333334
      },
      "expect": {
        "crosswind": 15.433333333333334,
        "headwind": 0,
        "side": "The right",
        "along": "None"
      },
      "source": "University of British Columbia, ATSC 113 Crosswinds and Headwinds (aircraft heading 90°, wind from 180° at 30 knots: zero headwind, 30 knot crosswind from the right), https://www.eoas.ubc.ca/courses/atsc113/flying/met_concepts/02-met_concepts/02d-crosswind/index.html",
      "tolerance": 1e-12
    },
    {
      "given": {
        "rwy": 36,
        "dir": 40,
        "ws": 15.433333333333334,
        "g": 20.57777777777778
      },
      "expect": {
        "crosswind": 9.920355442828923,
        "headwind": 11.822619238802893,
        "gustCrosswind": 13.227140590438564,
        "angle": 40
      },
      "source": "FAA, Pilot’s Handbook of Aeronautical Knowledge (FAA-H-8083-25C), Chapter 11 Aircraft Performance, Crosswind and Headwind Component Chart, https://www.faa.gov/regulations_policies/handbooks_manuals/aviation/phak; hand calculation in content.mdx: 30 × sin 40° = 19.3 kn, 30 × cos 40° = 23.0 kn, 40 × sin 40° = 25.7 kn",
      "tolerance": 1e-12
    },
    {
      "given": {
        "rwy": 18,
        "dir": 330,
        "ws": 5.144444444444445
      },
      "expect": {
        "crosswind": 2.5722222222222224,
        "side": "The right",
        "headwind": -4.455219577246612,
        "along": "Tailwind"
      },
      "source": "FAA, Pilot’s Handbook of Aeronautical Knowledge (FAA-H-8083-25C), Chapter 11 Aircraft Performance, Crosswind and Headwind Component Chart, https://www.faa.gov/regulations_policies/handbooks_manuals/aviation/phak; hand calculation in content.mdx: angle 330 − 180 = 150°; 10 × sin 150° = 5 kn from the right; 10 × cos 150° = −8.7 kn, a tailwind",
      "tolerance": 1e-12
    }
  ],
  "sources": [
    "FAA, Pilot’s Handbook of Aeronautical Knowledge (FAA-H-8083-25C, 2023), Chapter 11 Aircraft Performance: Crosswind and Headwind Component Chart. https://www.faa.gov/regulations_policies/handbooks_manuals/aviation/phak (retrieved 2026-10-01)",
    "University of British Columbia, ATSC 113 Crosswinds and Headwinds: an aircraft heading 90° with wind from 180° at 30 knots has zero headwind and a 30 knot crosswind from the right. https://www.eoas.ubc.ca/courses/atsc113/flying/met_concepts/02-met_concepts/02d-crosswind/index.html (retrieved 2026-10-01)"
  ],
  "related": [
    "wind-chill",
    "speed"
  ],
  "changelog": []
}