{
  "entity_type": "unit_conversion_page",
  "id": "radians-to-turns",
  "name": "Radians to Turns (revolutions)",
  "title": "Radians to Turns (revolutions) Converter (rad to turn)",
  "description": "Convert radians to turns (revolutions): 1 rad = 0.159155 turn. 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": "turn",
    "display": "turn",
    "name": "turns (revolutions)",
    "singular": "turn"
  },
  "linear": true,
  "factor": 0.1591549431,
  "inverse_factor": 6.283185307,
  "formula": "turns (revolutions) = radians × 0.1591549431",
  "reverse_formula": "radians = turns (revolutions) × 6.283185307",
  "unit_relation": "1 rad = 0.159155 turn",
  "examples": [
    {
      "value": 5,
      "result": 0.795775,
      "text": "5 rad = 0.795775 turn"
    },
    {
      "value": 12.5,
      "result": 1.98944,
      "text": "12.5 rad = 1.98944 turn"
    },
    {
      "value": 100,
      "result": 15.9155,
      "text": "100 rad = 15.9155 turn"
    }
  ],
  "table": [
    {
      "rad": 1,
      "turn": 0.159155
    },
    {
      "rad": 2,
      "turn": 0.31831
    },
    {
      "rad": 3,
      "turn": 0.477465
    },
    {
      "rad": 4,
      "turn": 0.63662
    },
    {
      "rad": 5,
      "turn": 0.795775
    },
    {
      "rad": 6,
      "turn": 0.95493
    },
    {
      "rad": 7,
      "turn": 1.11408
    },
    {
      "rad": 8,
      "turn": 1.27324
    },
    {
      "rad": 9,
      "turn": 1.43239
    },
    {
      "rad": 10,
      "turn": 1.59155
    },
    {
      "rad": 15,
      "turn": 2.38732
    },
    {
      "rad": 20,
      "turn": 3.1831
    },
    {
      "rad": 25,
      "turn": 3.97887
    },
    {
      "rad": 30,
      "turn": 4.77465
    },
    {
      "rad": 40,
      "turn": 6.3662
    },
    {
      "rad": 50,
      "turn": 7.95775
    },
    {
      "rad": 75,
      "turn": 11.9366
    },
    {
      "rad": 100,
      "turn": 15.9155
    },
    {
      "rad": 200,
      "turn": 31.831
    },
    {
      "rad": 250,
      "turn": 39.7887
    },
    {
      "rad": 500,
      "turn": 79.5775
    },
    {
      "rad": 1000,
      "turn": 159.155
    }
  ],
  "faq": [
    {
      "q": "How many turns (revolutions) are in one radian?",
      "a": "1 rad = 0.159155 turn. 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 turns (revolutions)?",
      "a": "Multiply the value in radians by 0.1591549431: turns (revolutions) = radians × 0.1591549431. For example, 5 rad = 0.795775 turn."
    },
    {
      "q": "How do I convert turns (revolutions) back to radians?",
      "a": "Multiply by the inverse factor 6.283185307 (radians = turns (revolutions) × 6.283185307), or use the turns (revolutions)-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=turn",
    "calculator": "https://tttkmbb.com/api/v1/calculate/angle?value=5&from_unit=rad&to_unit=turn",
    "mcp_tool": "convert_units",
    "mcp_arguments": {
      "value": 5,
      "from_unit": "rad",
      "to_unit": "turn"
    }
  },
  "links": {
    "html": "https://tttkmbb.com/conversion/radians-to-turns",
    "markdown": "https://tttkmbb.com/conversion/radians-to-turns.md",
    "json": "https://tttkmbb.com/conversion/radians-to-turns.json",
    "reverse": "https://tttkmbb.com/conversion/turns-to-radians",
    "quantity_converter": "https://tttkmbb.com/conversion/angle",
    "units": "https://tttkmbb.com/api/v1/units?quantity=angle"
  },
  "timestamp": "2026-09-24"
}