{
  "entity_type": "unit_conversion_page",
  "id": "radians-to-degrees",
  "name": "Radians to Degrees",
  "title": "Radians to Degrees Converter (rad to °)",
  "description": "Convert radians to degrees: 1 rad = 57.2958 °. Exact conversion factor, formula, 22-row table and worked examples, with JSON API and MCP access.",
  "quantity": "angle",
  "quantity_name": "Angle",
  "base_unit": "rad",
  "from_unit": {
    "symbol": "rad",
    "display": "rad",
    "name": "radians",
    "singular": "radian"
  },
  "to_unit": {
    "symbol": "deg",
    "display": "°",
    "name": "degrees",
    "singular": "degree"
  },
  "linear": true,
  "factor": 57.29577951,
  "inverse_factor": 0.01745329252,
  "formula": "degrees = radians × 57.29577951",
  "reverse_formula": "radians = degrees × 0.01745329252",
  "unit_relation": "1 rad = 57.2958 °",
  "examples": [
    {
      "value": 5,
      "result": 286.479,
      "text": "5 rad = 286.479 °"
    },
    {
      "value": 12.5,
      "result": 716.197,
      "text": "12.5 rad = 716.197 °"
    },
    {
      "value": 100,
      "result": 5729.58,
      "text": "100 rad = 5729.58 °"
    }
  ],
  "table": [
    {
      "rad": 1,
      "deg": 57.2958
    },
    {
      "rad": 2,
      "deg": 114.592
    },
    {
      "rad": 3,
      "deg": 171.887
    },
    {
      "rad": 4,
      "deg": 229.183
    },
    {
      "rad": 5,
      "deg": 286.479
    },
    {
      "rad": 6,
      "deg": 343.775
    },
    {
      "rad": 7,
      "deg": 401.07
    },
    {
      "rad": 8,
      "deg": 458.366
    },
    {
      "rad": 9,
      "deg": 515.662
    },
    {
      "rad": 10,
      "deg": 572.958
    },
    {
      "rad": 15,
      "deg": 859.437
    },
    {
      "rad": 20,
      "deg": 1145.92
    },
    {
      "rad": 25,
      "deg": 1432.39
    },
    {
      "rad": 30,
      "deg": 1718.87
    },
    {
      "rad": 40,
      "deg": 2291.83
    },
    {
      "rad": 50,
      "deg": 2864.79
    },
    {
      "rad": 75,
      "deg": 4297.18
    },
    {
      "rad": 100,
      "deg": 5729.58
    },
    {
      "rad": 200,
      "deg": 11459.2
    },
    {
      "rad": 250,
      "deg": 14323.9
    },
    {
      "rad": 500,
      "deg": 28647.9
    },
    {
      "rad": 1000,
      "deg": 57295.8
    }
  ],
  "faq": [
    {
      "q": "How many degrees are in one radian?",
      "a": "1 rad = 57.2958 °. The factor comes from the SI definitions of both units (NIST SP 811 / BIPM), so it is exact or correct to at least 10 significant figures."
    },
    {
      "q": "What is the formula to convert radians to degrees?",
      "a": "Multiply the value in radians by 57.29577951: degrees = radians × 57.29577951. For example, 5 rad = 286.479 °."
    },
    {
      "q": "How do I convert degrees back to radians?",
      "a": "Multiply by the inverse factor 0.01745329252 (radians = degrees × 0.01745329252), or use the degrees-to-radians page."
    }
  ],
  "sources": [
    {
      "name": "NIST Special Publication 811 – Guide for the Use of the International System of Units (SI), Appendix B conversion factors",
      "url": "https://www.nist.gov/pml/special-publication-811",
      "type": "standard",
      "retrieved_at": "2026-09-24"
    },
    {
      "name": "BIPM – The International System of Units (SI Brochure, 9th edition)",
      "url": "https://www.bipm.org/en/publications/si-brochure",
      "type": "standard",
      "retrieved_at": "2026-09-24"
    },
    {
      "name": "Wikipedia – Conversion of units",
      "url": "https://en.wikipedia.org/wiki/Conversion_of_units",
      "type": "reference",
      "retrieved_at": "2026-09-24"
    }
  ],
  "freshness": {
    "type": "static",
    "max_age_seconds": null,
    "note": "Fixed conversion factors (NIST/BIPM definitions); results never go stale."
  },
  "api": {
    "convert": "https://tttkmbb.com/api/v1/convert?value=5&from_unit=rad&to_unit=deg",
    "calculator": "https://tttkmbb.com/api/v1/calculate/angle?value=5&from_unit=rad&to_unit=deg",
    "mcp_tool": "convert_units",
    "mcp_arguments": {
      "value": 5,
      "from_unit": "rad",
      "to_unit": "deg"
    }
  },
  "links": {
    "html": "https://tttkmbb.com/conversion/radians-to-degrees",
    "markdown": "https://tttkmbb.com/conversion/radians-to-degrees.md",
    "json": "https://tttkmbb.com/conversion/radians-to-degrees.json",
    "reverse": "https://tttkmbb.com/conversion/degrees-to-radians",
    "quantity_converter": "https://tttkmbb.com/conversion/angle",
    "units": "https://tttkmbb.com/api/v1/units?quantity=angle"
  },
  "timestamp": "2026-09-24"
}