{
  "id": "flow-rate",
  "version": "772e27591d59",
  "status": "published",
  "name": "Flow Rate Calculator",
  "question": "What is the flow rate?",
  "summary": "Flow rate calculator: the volume flow rate through a pipe from its inside diameter and the flow speed (Q = Av), the speed from the flow rate, or the flow from a volume and a time, in gpm, L/min, m³/h and cfm.",
  "category": "physics",
  "subcategory": "mechanics",
  "url": "https://www.acalculator.org/physics/flow-rate-calculator",
  "markdown": "https://www.acalculator.org/physics/flow-rate-calculator.md",
  "kind": "function",
  "method": "Pipe: A = π × D² ÷ 4 and Q = A × v, or v = Q ÷ A. Volume and time: Q = V ÷ t.",
  "assumptions": [
    "The pipe is round and runs full; v is the average speed over the cross-section.",
    "Gallons are US gallons (231 in³ = 3.785411784 L)."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "find": {
        "title": "Find",
        "description": "Work out the flow from a pipe and speed, the speed from a flow, or the flow from a volume and a time.",
        "type": "string",
        "enum": [
          "flow",
          "speed",
          "volume"
        ]
      },
      "D": {
        "title": "Pipe inside diameter",
        "description": "The inside diameter of the pipe, which runs full.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "minimum": 0.000001,
        "maximum": 100
      },
      "v": {
        "title": "Flow speed",
        "description": "The average speed of the fluid through the pipe.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "speed",
        "minimum": 1e-9,
        "maximum": 100000
      },
      "Q": {
        "title": "Flow rate",
        "description": "The volume of fluid per unit of time, in the unit chosen below.",
        "type": "number",
        "minimum": 1e-9,
        "maximum": 1000000000
      },
      "qu": {
        "title": "Flow unit",
        "description": "The unit of the flow rate you type.",
        "type": "string",
        "enum": [
          "gpm",
          "gph",
          "lpm",
          "lps",
          "m3h",
          "cfm",
          "cfs"
        ]
      },
      "V": {
        "title": "Volume",
        "description": "The volume that flowed, such as a bucket filled.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "volume",
        "minimum": 1e-9,
        "maximum": 1000000000
      },
      "t": {
        "title": "Time",
        "description": "How long that volume took to flow.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "time",
        "minimum": 0.000001,
        "maximum": 1000000000
      }
    }
  },
  "outputs": {
    "result": {
      "label": "Answer",
      "description": "The flow rate or the speed, to 6 significant figures.",
      "format": "text"
    },
    "gpm": {
      "label": "Flow (gal/min)",
      "description": "The flow rate in US gallons per minute.",
      "format": "number"
    },
    "lpm": {
      "label": "Flow (L/min)",
      "description": "The flow rate in litres per minute.",
      "format": "number"
    },
    "lps": {
      "label": "Flow (L/s)",
      "description": "The flow rate in litres per second.",
      "format": "number"
    },
    "m3h": {
      "label": "Flow (m³/h)",
      "description": "The flow rate in cubic metres per hour.",
      "format": "number"
    },
    "cfm": {
      "label": "Flow (ft³/min)",
      "description": "The flow rate in cubic feet per minute.",
      "format": "number"
    },
    "m3s": {
      "label": "Flow (m³/s)",
      "description": "The flow rate in cubic metres per second.",
      "format": "number"
    },
    "mps": {
      "label": "Speed (m/s)",
      "description": "The average flow speed in metres per second.",
      "format": "number"
    },
    "fps": {
      "label": "Speed (ft/s)",
      "description": "The average flow speed in feet per second.",
      "format": "number"
    },
    "area": {
      "label": "Pipe area (in²)",
      "description": "The inside cross-section area of the pipe, π × D² ÷ 4, in square inches.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "find": "flow",
      "D": "2 in",
      "v": "5 ft/s",
      "Q": 50,
      "qu": "gpm",
      "V": "5 gal",
      "t": "30 s"
    },
    "outputs": {
      "result": "Q = 48.9599 gal/min (185.333 L/min)",
      "gpm": 48.959885510490274,
      "lpm": 185.33332755470076,
      "lps": 3.088888792578346,
      "m3h": 11.119999653282045,
      "cfm": 6.544984694978735,
      "m3s": 0.003088888792578346,
      "mps": 1.524,
      "fps": 5,
      "area": 3.141592653589793
    },
    "text": "The answer is Q = 48.9599 gal/min (185.333 L/min)."
  },
  "examples": [
    {
      "given": {
        "find": "flow",
        "D": 0.0508,
        "v": 1.524
      },
      "expect": {
        "gpm": 48.959885510490274,
        "area": 3.141592653589793
      },
      "source": "OpenStax, University Physics Volume 1, §14.5 Fluid Dynamics (Q = Av), https://openstax.org/books/university-physics-volume-1/pages/14-5-fluid-dynamics (retrieved 2026-10-05); NIST SP 811, Appendix B.8 (1 gal = 3.785411784 L; 1 ft = 0.3048 m; 1 in = 0.0254 m), https://www.nist.gov/pml/special-publication-811 (retrieved 2026-10-05); hand calculation in content.mdx: A = π × 2² ÷ 4 = 3.1416 in²; Q = 3.1416 in² × 60 in/s = 188.50 in³/s = 48.960 gal/min",
      "tolerance": 1e-12
    },
    {
      "given": {
        "find": "volume",
        "V": 0.01892705892,
        "t": 30
      },
      "expect": {
        "gpm": 10,
        "lpm": 37.85411784,
        "result": "Q = 10 gal/min (37.8541 L/min)"
      },
      "source": "NIST SP 811, Appendix B.8 (1 gal = 3.785411784 L; 1 ft = 0.3048 m; 1 in = 0.0254 m), https://www.nist.gov/pml/special-publication-811 (retrieved 2026-10-05); hand calculation in content.mdx: 5 gal ÷ 0.5 min = 10 gal/min = 37.854 L/min",
      "tolerance": 1e-12
    },
    {
      "given": {
        "find": "speed",
        "D": 0.1,
        "Q": 1,
        "qu": "lps"
      },
      "expect": {
        "mps": 0.12732395447351627
      },
      "source": "OpenStax, University Physics Volume 1, §14.5 Fluid Dynamics (Q = Av), https://openstax.org/books/university-physics-volume-1/pages/14-5-fluid-dynamics (retrieved 2026-10-05); hand calculation in content.mdx: v = Q ÷ A = 0.001 ÷ (π × 0.1² ÷ 4) = 0.12732 m/s",
      "tolerance": 1e-12
    }
  ],
  "sources": [
    "OpenStax, University Physics Volume 1, §14.5 Fluid Dynamics: flow rate Q = Av, retrieved 2026-10-05. https://openstax.org/books/university-physics-volume-1/pages/14-5-fluid-dynamics",
    "NIST Special Publication 811 (2008), Appendix B.8: 1 gal (US) = 3.785411784 L, 1 ft = 0.3048 m, 1 in = 0.0254 m, retrieved 2026-10-05. https://www.nist.gov/pml/special-publication-811"
  ],
  "related": [
    "reynolds-number",
    "pipe-volume",
    "cfm"
  ],
  "changelog": []
}