{
  "entity_type": "unit_conversion_page",
  "id": "turns-to-radians",
  "name": "Turns (revolutions) to Radians",
  "title": "Turns (revolutions) to Radians Converter (turn to rad)",
  "description": "Convert turns (revolutions) to radians: 1 turn = 6.28319 rad. 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": "turn",
    "display": "turn",
    "name": "turns (revolutions)",
    "singular": "turn"
  },
  "to_unit": {
    "symbol": "rad",
    "display": "rad",
    "name": "radians",
    "singular": "radian"
  },
  "linear": true,
  "factor": 6.283185307,
  "inverse_factor": 0.1591549431,
  "formula": "radians = turns (revolutions) × 6.283185307",
  "reverse_formula": "turns (revolutions) = radians × 0.1591549431",
  "unit_relation": "1 turn = 6.28319 rad",
  "examples": [
    {
      "value": 5,
      "result": 31.4159,
      "text": "5 turn = 31.4159 rad"
    },
    {
      "value": 12.5,
      "result": 78.5398,
      "text": "12.5 turn = 78.5398 rad"
    },
    {
      "value": 100,
      "result": 628.319,
      "text": "100 turn = 628.319 rad"
    }
  ],
  "table": [
    {
      "turn": 1,
      "rad": 6.28319
    },
    {
      "turn": 2,
      "rad": 12.5664
    },
    {
      "turn": 3,
      "rad": 18.8496
    },
    {
      "turn": 4,
      "rad": 25.1327
    },
    {
      "turn": 5,
      "rad": 31.4159
    },
    {
      "turn": 6,
      "rad": 37.6991
    },
    {
      "turn": 7,
      "rad": 43.9823
    },
    {
      "turn": 8,
      "rad": 50.2655
    },
    {
      "turn": 9,
      "rad": 56.5487
    },
    {
      "turn": 10,
      "rad": 62.8319
    },
    {
      "turn": 15,
      "rad": 94.2478
    },
    {
      "turn": 20,
      "rad": 125.664
    },
    {
      "turn": 25,
      "rad": 157.08
    },
    {
      "turn": 30,
      "rad": 188.496
    },
    {
      "turn": 40,
      "rad": 251.327
    },
    {
      "turn": 50,
      "rad": 314.159
    },
    {
      "turn": 75,
      "rad": 471.239
    },
    {
      "turn": 100,
      "rad": 628.319
    },
    {
      "turn": 200,
      "rad": 1256.64
    },
    {
      "turn": 250,
      "rad": 1570.8
    },
    {
      "turn": 500,
      "rad": 3141.59
    },
    {
      "turn": 1000,
      "rad": 6283.19
    }
  ],
  "faq": [
    {
      "q": "How many radians are in one turn?",
      "a": "1 turn = 6.28319 rad. 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 turns (revolutions) to radians?",
      "a": "Multiply the value in turns (revolutions) by 6.283185307: radians = turns (revolutions) × 6.283185307. For example, 5 turn = 31.4159 rad."
    },
    {
      "q": "How do I convert radians back to turns (revolutions)?",
      "a": "Multiply by the inverse factor 0.1591549431 (turns (revolutions) = radians × 0.1591549431), or use the radians-to-turns (revolutions) 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=turn&to_unit=rad",
    "calculator": "https://tttkmbb.com/api/v1/calculate/angle?value=5&from_unit=turn&to_unit=rad",
    "mcp_tool": "convert_units",
    "mcp_arguments": {
      "value": 5,
      "from_unit": "turn",
      "to_unit": "rad"
    }
  },
  "links": {
    "html": "https://tttkmbb.com/conversion/turns-to-radians",
    "markdown": "https://tttkmbb.com/conversion/turns-to-radians.md",
    "json": "https://tttkmbb.com/conversion/turns-to-radians.json",
    "reverse": "https://tttkmbb.com/conversion/radians-to-turns",
    "quantity_converter": "https://tttkmbb.com/conversion/angle",
    "units": "https://tttkmbb.com/api/v1/units?quantity=angle"
  },
  "timestamp": "2026-09-24"
}