{
  "address": "e382f9a3632479993f492bba5ec1128b",
  "category": "other",
  "question": "How many radian are in 180 degree?",
  "answer": "3.14159 radian",
  "askedBy": {
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  "answeredBy": "method",
  "madeAt": "2026-09-30T22:39:30.722Z",
  "validUntil": null,
  "validityClass": "forever",
  "sources": [
    {
      "label": "The International System of Units (SI Brochure)",
      "url": null
    }
  ],
  "supersedes": null,
  "supersededBy": null,
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  "answerMethod": "method",
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  "source": {
    "kind": "standard",
    "value": "BIPM SI Brochure, 9th edition (2019), Table 8, \"Non-SI units accepted for use with the SI\": degree = (pi/180) rad; minute = (pi/10800) rad; second = (pi/648000) rad; gon/gradian = (pi/200) rad",
    "retrieved_utc": "2026-09-30T19:29:48Z"
  },
  "qsha256": "73818def0d993364a94e0802a337361660498792dbde720e7e4ec77d54056ac2",
  "runOne": null,
  "cardContractVersion": "card_contract/1",
  "deck_id": "method-deck",
  "deck_title": "Method Deck",
  "method": {
    "name": "Angle conversion",
    "version": "1",
    "source_url_or_file": "methods/angle-conversion.cjs",
    "sha256_of_method_file": "7ddbec81c8566282cc2e432a1cd65c81ebb4da8787a30bfe369ba81f42eba6be"
  },
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    "inSubstrate": false,
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  },
  "method_deck": {
    "inputs": [
      {
        "name": "value",
        "type": "number",
        "unit": "from_unit",
        "required": true,
        "description": "The angle to convert"
      },
      {
        "name": "from_unit",
        "type": "string",
        "required": true,
        "description": "Unit of the input value",
        "enum": [
          "degree",
          "radian",
          "gradian",
          "arcminute",
          "arcsecond"
        ]
      },
      {
        "name": "to_unit",
        "type": "string",
        "required": true,
        "description": "Unit to convert into",
        "enum": [
          "degree",
          "radian",
          "gradian",
          "arcminute",
          "arcsecond"
        ]
      }
    ],
    "outputs": [
      {
        "name": "result",
        "unit": "to_unit",
        "description": "The converted angle"
      }
    ],
    "steps": [
      "Look up the exact radian-equivalent of from_unit and of to_unit: degree = pi/180 rad; gradian = pi/200 rad; arcminute = pi/(180*60) rad; arcsecond = pi/(180*3600) rad.",
      "Convert the input to radians: radians = value * rad_per(from_unit).",
      "Convert radians to the target unit: result = radians / rad_per(to_unit).",
      "Round result to 6 significant figures."
    ],
    "constants": [
      {
        "name": "degree",
        "value": 0.017453292519943295,
        "unit": "rad",
        "source": 0
      },
      {
        "name": "radian",
        "value": 1,
        "unit": "rad",
        "source": 0
      },
      {
        "name": "gradian",
        "value": 0.015707963267948967,
        "unit": "rad",
        "source": 0
      },
      {
        "name": "arcminute",
        "value": 0.0002908882086657216,
        "unit": "rad",
        "source": 0
      },
      {
        "name": "arcsecond",
        "value": 0.00000484813681109536,
        "unit": "rad",
        "source": 0
      }
    ],
    "examples": [
      {
        "name": "worked example",
        "inputs": {
          "value": 180,
          "from_unit": "degree",
          "to_unit": "radian"
        },
        "expected": {
          "answer": "3.14159 radian"
        },
        "check": "By definition 180 degrees = pi radians = 3.14159265...; rounded to 6 significant figures is 3.14159."
      },
      {
        "name": "test vector: gradians to degrees",
        "inputs": {
          "value": 100,
          "from_unit": "gradian",
          "to_unit": "degree"
        },
        "expected": {
          "answer": "90.0000 degree"
        },
        "check": "By definition 400 gradians = 360 degrees, so 100 gradians = 90 degrees exactly."
      },
      {
        "name": "test vector: degree to arcminute",
        "inputs": {
          "value": 1,
          "from_unit": "degree",
          "to_unit": "arcminute"
        },
        "expected": {
          "answer": "60.0000 arcminute"
        },
        "check": "By definition 1 degree = 60 arcminutes exactly."
      }
    ],
    "disclaimer": null,
    "deck_category": "units"
  },
  "status": "minted",
  "kind": "method",
  "provenanceClass": "own_question",
  "provenance": {
    "schema": "card_provenance/2.0.0",
    "chain": [
      {
        "source": {
          "kind": "standard",
          "value": "BIPM SI Brochure, 9th edition (2019), Table 8, \"Non-SI units accepted for use with the SI\": degree = (pi/180) rad; minute = (pi/10800) rad; second = (pi/648000) rad; gon/gradian = (pi/200) rad",
          "retrieved_utc": "2026-09-30T19:29:48Z"
        },
        "sha256": "ab5203fa68a8e5518b31b72ab933e1ec77a635745f09eaf9e213e9ab9f09c549",
        "supersedes": null,
        "added_utc": "2026-09-30T22:39:30.722Z",
        "added_by": "method:Angle conversion",
        "why": "the method that computed this answer",
        "check": null,
        "status_label": "pending",
        "signature": null
      }
    ]
  }
}