{
  "entity_type": "unit_conversion_page",
  "id": "rad-per-second-to-rpm",
  "name": "Radians per second to Revolutions per minute (rpm)",
  "title": "Radians per second to Revolutions per minute (rpm) Converter (rad/s to rpm)",
  "description": "Convert radians per second to revolutions per minute (rpm): 1 rad/s = 9.5493 rpm. Exact conversion factor, formula, 22-row table and worked examples, with JSON API and MCP access.",
  "quantity": "frequency",
  "quantity_name": "Frequency",
  "base_unit": "Hz",
  "from_unit": {
    "symbol": "rad/s",
    "display": "rad/s",
    "name": "radians per second",
    "singular": "radian per second"
  },
  "to_unit": {
    "symbol": "rpm",
    "display": "rpm",
    "name": "revolutions per minute (rpm)",
    "singular": "rpm"
  },
  "linear": true,
  "factor": 9.549296586,
  "inverse_factor": 0.1047197551,
  "formula": "revolutions per minute (rpm) = radians per second × 9.549296586",
  "reverse_formula": "radians per second = revolutions per minute (rpm) × 0.1047197551",
  "unit_relation": "1 rad/s = 9.5493 rpm",
  "examples": [
    {
      "value": 5,
      "result": 47.7465,
      "text": "5 rad/s = 47.7465 rpm"
    },
    {
      "value": 12.5,
      "result": 119.366,
      "text": "12.5 rad/s = 119.366 rpm"
    },
    {
      "value": 100,
      "result": 954.93,
      "text": "100 rad/s = 954.93 rpm"
    }
  ],
  "table": [
    {
      "rad/s": 1,
      "rpm": 9.5493
    },
    {
      "rad/s": 2,
      "rpm": 19.0986
    },
    {
      "rad/s": 3,
      "rpm": 28.6479
    },
    {
      "rad/s": 4,
      "rpm": 38.1972
    },
    {
      "rad/s": 5,
      "rpm": 47.7465
    },
    {
      "rad/s": 6,
      "rpm": 57.2958
    },
    {
      "rad/s": 7,
      "rpm": 66.8451
    },
    {
      "rad/s": 8,
      "rpm": 76.3944
    },
    {
      "rad/s": 9,
      "rpm": 85.9437
    },
    {
      "rad/s": 10,
      "rpm": 95.493
    },
    {
      "rad/s": 15,
      "rpm": 143.239
    },
    {
      "rad/s": 20,
      "rpm": 190.986
    },
    {
      "rad/s": 25,
      "rpm": 238.732
    },
    {
      "rad/s": 30,
      "rpm": 286.479
    },
    {
      "rad/s": 40,
      "rpm": 381.972
    },
    {
      "rad/s": 50,
      "rpm": 477.465
    },
    {
      "rad/s": 75,
      "rpm": 716.197
    },
    {
      "rad/s": 100,
      "rpm": 954.93
    },
    {
      "rad/s": 200,
      "rpm": 1909.86
    },
    {
      "rad/s": 250,
      "rpm": 2387.32
    },
    {
      "rad/s": 500,
      "rpm": 4774.65
    },
    {
      "rad/s": 1000,
      "rpm": 9549.3
    }
  ],
  "faq": [
    {
      "q": "How many revolutions per minute (rpm) are in one radian per second?",
      "a": "1 rad/s = 9.5493 rpm. 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 per second to revolutions per minute (rpm)?",
      "a": "Multiply the value in radians per second by 9.549296586: revolutions per minute (rpm) = radians per second × 9.549296586. For example, 5 rad/s = 47.7465 rpm."
    },
    {
      "q": "How do I convert revolutions per minute (rpm) back to radians per second?",
      "a": "Multiply by the inverse factor 0.1047197551 (radians per second = revolutions per minute (rpm) × 0.1047197551), or use the revolutions per minute (rpm)-to-radians per second 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%2Fs&to_unit=rpm",
    "calculator": "https://tttkmbb.com/api/v1/calculate/frequency?value=5&from_unit=rad%2Fs&to_unit=rpm",
    "mcp_tool": "convert_units",
    "mcp_arguments": {
      "value": 5,
      "from_unit": "rad/s",
      "to_unit": "rpm"
    }
  },
  "links": {
    "html": "https://tttkmbb.com/conversion/rad-per-second-to-rpm",
    "markdown": "https://tttkmbb.com/conversion/rad-per-second-to-rpm.md",
    "json": "https://tttkmbb.com/conversion/rad-per-second-to-rpm.json",
    "reverse": "https://tttkmbb.com/conversion/rpm-to-rad-per-second",
    "quantity_converter": "https://tttkmbb.com/conversion/frequency",
    "units": "https://tttkmbb.com/api/v1/units?quantity=frequency"
  },
  "timestamp": "2026-09-24"
}