{
  "id": "speeds-and-feeds",
  "version": "716d31704df2",
  "status": "published",
  "name": "Speeds and Feeds Calculator",
  "question": "What is the SFM, rpm and feed rate?",
  "summary": "Works out the spindle speed in rpm from the surface speed (SFM or m/min) and the tool diameter, or the SFM from the rpm, and the feed rate from the chip load and the number of flutes.",
  "category": "physics",
  "subcategory": "mechanics",
  "url": "https://www.acalculator.org/physics/speeds-and-feeds-calculator",
  "markdown": "https://www.acalculator.org/physics/speeds-and-feeds-calculator.md",
  "kind": "function",
  "method": "Inch: rpm = 12 × SFM ÷ (π × D), SFM = π × D × rpm ÷ 12. Metric: rpm = 1,000 × Vc ÷ (π × D), Vc = π × D × rpm ÷ 1,000. Feed = rpm × chip load × flutes.",
  "assumptions": [
    "The surface speed and chip load come from your tool maker or a machining handbook for the tool and material; the calculator does not pick them.",
    "For a drill, type the feed per revolution as the chip load with 1 flute.",
    "Machines often run slower than the formula on manual setups; UF’s example uses 60% of the computed values."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "units": {
        "title": "Units",
        "description": "Inch units (SFM, inches, in/min) or metric (m/min, millimeters, mm/min).",
        "type": "string",
        "enum": [
          "inch",
          "metric"
        ]
      },
      "find": {
        "title": "Find",
        "description": "The spindle speed from the surface speed, or the surface speed from the spindle speed.",
        "type": "string",
        "enum": [
          "rpm",
          "sfm"
        ]
      },
      "d": {
        "title": "Tool diameter",
        "description": "The cutter or drill diameter, in inches (inch units) or millimeters (metric).",
        "type": "number",
        "minimum": 0.0001,
        "maximum": 10000
      },
      "sfm": {
        "title": "Surface speed",
        "description": "The cutting speed at the tool’s edge: surface feet per minute (SFM), or meters per minute in metric.",
        "type": "number",
        "minimum": 0.001,
        "maximum": 100000
      },
      "rpm": {
        "title": "Spindle speed (rpm)",
        "description": "The spindle speed in revolutions per minute.",
        "type": "number",
        "minimum": 0.001,
        "maximum": 10000000
      },
      "cl": {
        "title": "Chip load",
        "description": "The feed per tooth (per flute): inches per tooth, or millimeters per tooth in metric.",
        "type": "number",
        "minimum": 0,
        "maximum": 100
      },
      "z": {
        "title": "Flutes",
        "description": "The number of cutting teeth (flutes). A drill counts as 1 when the chip load is its feed per revolution.",
        "type": "integer",
        "minimum": 1,
        "maximum": 100
      }
    }
  },
  "outputs": {
    "rpm": {
      "label": "Spindle speed (rpm)",
      "description": "N = 12 × SFM ÷ (π × D in inches), or 1,000 × m/min ÷ (π × D in mm).",
      "format": "number"
    },
    "speed": {
      "label": "Surface speed",
      "description": "SFM = π × D × rpm ÷ 12 (inch), or m/min = π × D × rpm ÷ 1,000 (metric).",
      "format": "number"
    },
    "feed": {
      "label": "Feed rate",
      "description": "rpm × chip load × flutes: inches per minute, or millimeters per minute in metric.",
      "format": "number"
    },
    "perRev": {
      "label": "Feed per revolution",
      "description": "Chip load × flutes: inches (or millimeters) per revolution.",
      "format": "number"
    },
    "other": {
      "label": "Surface speed in the other unit",
      "description": "The surface speed in m/min (inch units) or SFM (metric): 1 ft = 0.3048 m.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "units": "inch",
      "find": "rpm",
      "d": 0.5,
      "sfm": 300,
      "rpm": 2000,
      "cl": 0.002,
      "z": 4
    },
    "outputs": {
      "rpm": 2291.831180523293,
      "speed": 300,
      "feed": 18.334649444186343,
      "perRev": 0.008,
      "other": 91.44
    },
    "text": "Run the spindle at 2,292 rpm for a surface speed of 300."
  },
  "examples": [
    {
      "given": {
        "units": "inch",
        "find": "rpm",
        "d": 0.25,
        "sfm": 100,
        "cl": 0.004,
        "z": 1
      },
      "expect": {
        "rpm": 1527.8874536821952,
        "feed": 6.111549814728781
      },
      "source": "University of Florida, Mechanical and Aerospace Engineering design lab, Speeds and Feeds (N [rpm] = 12 V [sfm] ÷ (π D [in]); milling feed f [in/min] = N × feed per tooth × number of teeth; a ¼ in drill at 100 sfm runs at about 1,500 rpm and 6 in/min at 0.004 in/rev), https://web.mae.ufl.edu/designlab/Advanced%20Manufacturing/Speeds%20and%20Feeds/Speeds%20and%20Feeds.htm (retrieved 2026-10-02): N = 12 × 100 ÷ (π × 0.25) ≈ 1,500 rpm and f ≈ 6 in/min; Python 3: 1200/(math.pi*0.25)"
    },
    {
      "given": {
        "units": "inch",
        "find": "rpm",
        "d": 0.5,
        "sfm": 300,
        "cl": 0.002,
        "z": 4
      },
      "expect": {
        "rpm": 2291.831180523293,
        "feed": 18.33464944418634,
        "perRev": 0.008,
        "other": 91.44
      },
      "source": "hand calculation in content.mdx: N = 3,600 ÷ (π × 0.5); f = N × 0.002 × 4; University of Florida, Mechanical and Aerospace Engineering design lab, Speeds and Feeds (N [rpm] = 12 V [sfm] ÷ (π D [in]); milling feed f [in/min] = N × feed per tooth × number of teeth; a ¼ in drill at 100 sfm runs at about 1,500 rpm and 6 in/min at 0.004 in/rev), https://web.mae.ufl.edu/designlab/Advanced%20Manufacturing/Speeds%20and%20Feeds/Speeds%20and%20Feeds.htm (retrieved 2026-10-02)"
    },
    {
      "given": {
        "units": "inch",
        "find": "sfm",
        "d": 0.5,
        "rpm": 2000,
        "z": 2
      },
      "expect": {
        "sfm": 261.79938779914943
      },
      "source": "hand calculation in content.mdx: SFM = π × 0.5 × 2,000 ÷ 12; University of Florida, Mechanical and Aerospace Engineering design lab, Speeds and Feeds (N [rpm] = 12 V [sfm] ÷ (π D [in]); milling feed f [in/min] = N × feed per tooth × number of teeth; a ¼ in drill at 100 sfm runs at about 1,500 rpm and 6 in/min at 0.004 in/rev), https://web.mae.ufl.edu/designlab/Advanced%20Manufacturing/Speeds%20and%20Feeds/Speeds%20and%20Feeds.htm (retrieved 2026-10-02)"
    },
    {
      "given": {
        "units": "metric",
        "find": "rpm",
        "d": 10,
        "sfm": 120,
        "cl": 0.05,
        "z": 3
      },
      "expect": {
        "rpm": 3819.718634205488,
        "feed": 572.9577951308232
      },
      "source": "hand calculation in content.mdx: N = 1,000 × 120 ÷ (π × 10), the inch formula with 1,000 mm in a meter in place of 12 in in a foot; f = N × 0.05 × 3; Virasak, Manufacturing Processes 4-5, Unit 2: Speed and Feed (Workforce LibreTexts; cutting speed in ft/min or m/min; the shop rule RPM = cutting speed × 4 ÷ diameter, a 3/8 in drill at 100 sfm runs at about 1,066 rpm), https://workforce.libretexts.org/Bookshelves/Manufacturing/Manufacturing_Processes_4-5_(Virasak)/02%3A_Lathe_Machines/02.2%3A_Unit_2%3A_Speed_and_Feed (retrieved 2026-10-02)"
    }
  ],
  "sources": [
    "University of Florida, Mechanical and Aerospace Engineering design lab, Speeds and Feeds (spindle speed and feed rate formulas; worked HSS drill example). https://web.mae.ufl.edu/designlab/Advanced%20Manufacturing/Speeds%20and%20Feeds/Speeds%20and%20Feeds.htm (retrieved 2026-10-02)",
    "Virasak, Manufacturing Processes 4-5, Unit 2: Speed and Feed, Workforce LibreTexts (cutting speed in ft/min or m/min; the RPM = CS × 4 ÷ D shop rule). https://workforce.libretexts.org/Bookshelves/Manufacturing/Manufacturing_Processes_4-5_(Virasak)/02%3A_Lathe_Machines/02.2%3A_Unit_2%3A_Speed_and_Feed (retrieved 2026-10-02)"
  ],
  "related": [
    "rpm",
    "gear-ratio",
    "speed"
  ],
  "changelog": []
}