{
  "id": "centrifuge",
  "version": "49f7ee527844",
  "status": "published",
  "name": "Centrifuge RCF Calculator",
  "question": "What is the centrifuge RCF (× g)?",
  "summary": "Converts a centrifuge’s speed in rpm and rotor radius to the relative centrifugal force (RCF, × g), or finds the rpm or radius for a given g-force.",
  "category": "biology",
  "subcategory": "lab",
  "url": "https://www.acalculator.org/biology/centrifuge-calculator",
  "markdown": "https://www.acalculator.org/biology/centrifuge-calculator.md",
  "kind": "formulas",
  "method": "RCF = r × ω² ÷ g with ω = 2π × rpm ÷ 60 and g = 9.80665 m/s², which is RCF = 1.11824 × 10⁻⁵ × r(cm) × rpm²; rpm = (60 ÷ 2π) × √(RCF × g ÷ r); r = RCF × g ÷ ω².",
  "assumptions": [
    "The radius is measured from the center of the rotor to the point of interest, usually the bottom of the tube (the maximum radius).",
    "RCF is the centripetal acceleration divided by the standard acceleration of gravity, 9.80665 m/s²; the pull of Earth’s gravity itself is not added.",
    "The constant 1.118 × 10⁻⁵ often quoted for r in cm is (2π ÷ 60)² ÷ 9.80665 ÷ 100 = 1.118244 × 10⁻⁵, rounded; this page uses the unrounded value."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "rpm": {
        "title": "Speed (rpm)",
        "description": "The rotor speed in revolutions per minute.",
        "type": "number",
        "exclusiveMinimum": 0,
        "maximum": 200000
      },
      "r": {
        "title": "Radius",
        "description": "The distance from the center of the rotor to the sample, usually to the bottom of the tube.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "exclusiveMinimum": 0,
        "maximum": 1
      },
      "g": {
        "title": "RCF (× g)",
        "description": "The relative centrifugal force: the acceleration at the radius as a multiple of standard gravity.",
        "type": "number",
        "exclusiveMinimum": 0,
        "maximum": 50000000
      }
    }
  },
  "solve": {
    "fillAny": 2,
    "variables": [
      "rpm",
      "r",
      "g"
    ],
    "inputsOnly": []
  },
  "outputs": {
    "rpm": {
      "label": "Speed (rpm)",
      "description": "60 ÷ 2π × √(RCF × g ÷ r).",
      "format": "number"
    },
    "r": {
      "label": "Radius",
      "description": "RCF × g ÷ ω².",
      "format": "quantity",
      "unit": "cm"
    },
    "rcf": {
      "label": "RCF (× g)",
      "description": "r × ω² ÷ 9.80665 m/s².",
      "format": "number"
    },
    "omega": {
      "label": "Angular speed (rad/s)",
      "description": "ω = 2π × rpm ÷ 60.",
      "format": "number"
    },
    "accel": {
      "label": "Centripetal acceleration (m/s²)",
      "description": "a = r × ω², the acceleration at the radius.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "rpm": 3000,
      "r": "10 cm"
    },
    "outputs": {
      "rcf": 1006.4195623469136,
      "omega": 314.1592653589793,
      "accel": 9869.60440108936
    },
    "text": "At 3,000 rpm and a radius of 10 cm, the relative centrifugal force is 1,006.42 × g."
  },
  "examples": [
    {
      "given": {
        "rpm": 75000,
        "r": 0.075
      },
      "expect": {
        "g": 471759.16985011566,
        "omega": 7853.981633974483
      },
      "source": "OpenStax, College Physics 2e, §6.2 Centripetal Acceleration (a_c = rω²; Example 6.3: a point 7.50 cm from the axis of an ultracentrifuge at 7.50 × 10⁴ rev/min has ω = 7854 rad/s, a_c = 4.63 × 10⁶ m/s², 4.72 × 10⁵ times g = 9.80 m/s²), https://openstax.org/books/college-physics-2e/pages/6-2-centripetal-acceleration (retrieved 2026-10-18); NIST, CODATA 2022, standard acceleration of gravity g_n = 9.806 65 m s⁻² (exact), https://physics.nist.gov/cgi-bin/cuu/Value?gn (retrieved 2026-10-18); hand calculation in content.mdx: 0.075 × 7853.98² ÷ 9.80665 = 471,759 (the book divides by 9.80: 4.72 × 10⁵)"
    },
    {
      "given": {
        "rpm": 3000,
        "r": 0.1
      },
      "expect": {
        "g": 1006.4195623469136,
        "accel": 9869.60440108936
      },
      "source": "OpenStax, College Physics 2e, §6.2 Centripetal Acceleration (a_c = rω²; Example 6.3: a point 7.50 cm from the axis of an ultracentrifuge at 7.50 × 10⁴ rev/min has ω = 7854 rad/s, a_c = 4.63 × 10⁶ m/s², 4.72 × 10⁵ times g = 9.80 m/s²), https://openstax.org/books/college-physics-2e/pages/6-2-centripetal-acceleration (retrieved 2026-10-18); NIST, CODATA 2022, standard acceleration of gravity g_n = 9.806 65 m s⁻² (exact), https://physics.nist.gov/cgi-bin/cuu/Value?gn (retrieved 2026-10-18); hand calculation in content.mdx: 1.118244 × 10⁻⁵ × 10 × 3,000² = 1,006.42"
    },
    {
      "given": {
        "g": 1000,
        "r": 0.1
      },
      "expect": {
        "rpm": 2990.416771972627
      },
      "source": "OpenStax, College Physics 2e, §6.2 Centripetal Acceleration (a_c = rω²; Example 6.3: a point 7.50 cm from the axis of an ultracentrifuge at 7.50 × 10⁴ rev/min has ω = 7854 rad/s, a_c = 4.63 × 10⁶ m/s², 4.72 × 10⁵ times g = 9.80 m/s²), https://openstax.org/books/college-physics-2e/pages/6-2-centripetal-acceleration (retrieved 2026-10-18); NIST, CODATA 2022, standard acceleration of gravity g_n = 9.806 65 m s⁻² (exact), https://physics.nist.gov/cgi-bin/cuu/Value?gn (retrieved 2026-10-18); hand calculation in content.mdx: √(1,000 ÷ (1.118244 × 10⁻⁵ × 10)) = 2,990.4 rpm"
    },
    {
      "given": {
        "g": 16000,
        "rpm": 13300
      },
      "expect": {
        "r": 0.08088726300046525
      },
      "source": "OpenStax, College Physics 2e, §6.2 Centripetal Acceleration (a_c = rω²; Example 6.3: a point 7.50 cm from the axis of an ultracentrifuge at 7.50 × 10⁴ rev/min has ω = 7854 rad/s, a_c = 4.63 × 10⁶ m/s², 4.72 × 10⁵ times g = 9.80 m/s²), https://openstax.org/books/college-physics-2e/pages/6-2-centripetal-acceleration (retrieved 2026-10-18); NIST, CODATA 2022, standard acceleration of gravity g_n = 9.806 65 m s⁻² (exact), https://physics.nist.gov/cgi-bin/cuu/Value?gn (retrieved 2026-10-18); hand calculation in content.mdx: 16,000 ÷ (1.118244 × 10⁻⁵ × 13,300²) = 8.0887 cm"
    }
  ],
  "sources": [
    "OpenStax, College Physics 2e, §6.2 Centripetal Acceleration: a_c = v² ÷ r = rω²; Example 6.3, How Big Is the Centripetal Acceleration in an Ultracentrifuge? (7.50 cm, 7.50 × 10⁴ rev/min, ω = 7854 rad/s, a_c = 4.63 × 10⁶ m/s², 4.72 × 10⁵ times g). https://openstax.org/books/college-physics-2e/pages/6-2-centripetal-acceleration (retrieved 2026-10-18)",
    "NIST, Fundamental Physical Constants (CODATA 2022): standard acceleration of gravity, g_n = 9.806 65 m s⁻² (exact). https://physics.nist.gov/cgi-bin/cuu/Value?gn (retrieved 2026-10-18)"
  ],
  "related": [
    "rpm",
    "serial-dilution",
    "tm",
    "acceleration"
  ],
  "changelog": []
}