{
  "id": "drag-force",
  "version": "7c12cab4aca7",
  "status": "published",
  "name": "Drag Force Calculator",
  "question": "What is the drag force?",
  "summary": "Drag force calculator: F = ½CρAv² from the drag coefficient, fluid density, frontal area and speed, or the drag coefficient, area or speed from a known force, with the power to overcome drag.",
  "category": "physics",
  "subcategory": "mechanics",
  "url": "https://www.acalculator.org/physics/drag-force-calculator",
  "markdown": "https://www.acalculator.org/physics/drag-force-calculator.md",
  "kind": "function",
  "method": "F = ½ × C × ρ × A × v²; C = 2F ÷ (ρAv²); A = 2F ÷ (Cρv²); v = √(2F ÷ (CρA)); dynamic pressure q = ½ρv²; power P = F × v.",
  "assumptions": [
    "Drag grows with the square of the speed: large objects at moderate to high speed in air or water (OpenStax §6.4). Very small or slow objects follow Stokes’ law instead.",
    "C and A are for the same reference area (the frontal area); the fluid is still, and v is the relative speed."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "find": {
        "title": "Find",
        "description": "Which value to work out from F = ½ × C × ρ × A × v².",
        "type": "string",
        "enum": [
          "force",
          "cd",
          "area",
          "speed"
        ]
      },
      "F": {
        "title": "Drag force (F)",
        "description": "The drag force on the object.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "force",
        "minimum": 1e-12,
        "maximum": 1000000000000
      },
      "sh": {
        "title": "Shape",
        "description": "The object, which sets its drag coefficient C (OpenStax Table 6.2).",
        "type": "string",
        "enum": [
          "airfoil",
          "sphere",
          "skydiverFeet",
          "bicycle",
          "skydiverFlat",
          "plate",
          "custom"
        ]
      },
      "C": {
        "title": "Drag coefficient (C)",
        "description": "The drag coefficient of the object, a pure number.",
        "type": "number",
        "minimum": 0.001,
        "maximum": 100
      },
      "A": {
        "title": "Frontal area (A)",
        "description": "The area of the object that faces the flow.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "area",
        "minimum": 1e-12,
        "maximum": 1000000
      },
      "v": {
        "title": "Speed (v)",
        "description": "The speed of the object through the fluid (or of the fluid past it).",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "speed",
        "minimum": 1e-9,
        "maximum": 100000
      },
      "fl": {
        "title": "Fluid",
        "description": "The air or water the object moves through, which sets the density ρ.",
        "type": "string",
        "enum": [
          "air15",
          "air0",
          "water20",
          "seawater",
          "custom"
        ]
      },
      "rho": {
        "title": "Fluid density (ρ)",
        "description": "The density of the fluid.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "density",
        "minimum": 0.000001,
        "maximum": 30000
      }
    }
  },
  "outputs": {
    "result": {
      "label": "Answer",
      "description": "The value worked out, to 6 significant figures.",
      "format": "text"
    },
    "force": {
      "label": "Drag force (N)",
      "description": "F = ½ × C × ρ × A × v², in newtons.",
      "format": "number"
    },
    "lbf": {
      "label": "Drag force (lbf)",
      "description": "The drag force in pounds-force.",
      "format": "number"
    },
    "cd": {
      "label": "Drag coefficient C",
      "description": "The drag coefficient, a pure number.",
      "format": "number"
    },
    "area": {
      "label": "Frontal area (m²)",
      "description": "The frontal area in square metres.",
      "format": "number"
    },
    "ft2": {
      "label": "Frontal area (ft²)",
      "description": "The frontal area in square feet.",
      "format": "number"
    },
    "speed": {
      "label": "Speed (m/s)",
      "description": "The speed in metres per second.",
      "format": "number"
    },
    "mph": {
      "label": "Speed (mph)",
      "description": "The speed in miles per hour.",
      "format": "number"
    },
    "kmh": {
      "label": "Speed (km/h)",
      "description": "The speed in kilometres per hour.",
      "format": "number"
    },
    "q": {
      "label": "Dynamic pressure (Pa)",
      "description": "½ × ρ × v², in pascals: the drag force per unit of C × A.",
      "format": "number"
    },
    "power": {
      "label": "Power to overcome drag (W)",
      "description": "P = F × v, in watts.",
      "format": "number"
    },
    "hp": {
      "label": "Power to overcome drag (hp)",
      "description": "The same power in mechanical horsepower (745.7 W).",
      "format": "number"
    },
    "rho": {
      "label": "Density used (kg/m³)",
      "description": "The fluid density in kilograms per cubic metre.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "find": "force",
      "F": "735 N",
      "sh": "skydiverFeet",
      "C": 0.7,
      "A": "0.18 m2",
      "v": 98,
      "fl": "air15",
      "rho": "1.21 kg/m3"
    },
    "outputs": {
      "result": "F = 741.189 N (166.626 lbf)",
      "force": 741.1887,
      "lbf": 166.62584828444838,
      "cd": 0.7,
      "area": 0.18,
      "ft2": 1.93750387500775,
      "speed": 98,
      "mph": 219.2197566213314,
      "kmh": 352.8,
      "q": 5882.45,
      "power": 72636.4926,
      "hp": 97.40714108730579,
      "rho": 1.225
    },
    "text": "F = 741.189 N (166.626 lbf), with C = 0.7, ρ = 1.225 kg/m³, A = 0.18 m² and v = 98 m/s."
  },
  "examples": [
    {
      "given": {
        "find": "force",
        "sh": "skydiverFeet",
        "A": 0.18,
        "v": 98,
        "fl": "custom",
        "rho": 1.21
      },
      "expect": {
        "F": 732.11292,
        "lbf": 164.5855317748429,
        "result": "F = 732.113 N (164.586 lbf)",
        "q": 5810.42
      },
      "source": "OpenStax, University Physics Volume 1, §6.4 Drag Force and Terminal Speed (F_D = ½CρAv²; Table 6.2; skydiver: C = 0.70, A = 0.18 m², ρ = 1.21 kg/m³, 75 kg, v_T = 98 m/s), https://openstax.org/books/university-physics-volume-1/pages/6-4-drag-force-and-terminal-speed (retrieved 2026-10-18); hand calculation in content.mdx: ½ × 0.70 × 1.21 × 0.18 × 98² = 732.11 N, close to the 735 N weight (75 kg × 9.80 m/s²) at terminal speed",
      "tolerance": 1e-12
    },
    {
      "given": {
        "find": "speed",
        "sh": "skydiverFeet",
        "A": 0.18,
        "F": 735,
        "fl": "custom",
        "rho": 1.21
      },
      "expect": {
        "v": 98.19304088496757
      },
      "source": "OpenStax, University Physics Volume 1, §6.4 Drag Force and Terminal Speed (F_D = ½CρAv²; Table 6.2; skydiver: C = 0.70, A = 0.18 m², ρ = 1.21 kg/m³, 75 kg, v_T = 98 m/s), https://openstax.org/books/university-physics-volume-1/pages/6-4-drag-force-and-terminal-speed (retrieved 2026-10-18); v = √(2 × 735 ÷ (0.70 × 1.21 × 0.18)) = 98.19 m/s, the 98 m/s of the text",
      "tolerance": 1e-12
    },
    {
      "given": {
        "find": "cd",
        "A": 0.7,
        "v": 44,
        "F": 819.896,
        "fl": "custom",
        "rho": 1.21
      },
      "expect": {
        "C": 1,
        "result": "C = 1"
      },
      "source": "OpenStax, University Physics Volume 1, §6.4 Drag Force and Terminal Speed (F_D = ½CρAv²; Table 6.2; skydiver: C = 0.70, A = 0.18 m², ρ = 1.21 kg/m³, 75 kg, v_T = 98 m/s), https://openstax.org/books/university-physics-volume-1/pages/6-4-drag-force-and-terminal-speed (retrieved 2026-10-18), Example 6.17 (A = 0.70 m², C = 1.0, v_T = 44 m/s); hand calculation in content.mdx: C = 2 × 819.896 ÷ (1.21 × 0.70 × 44²) = 1",
      "tolerance": 1e-12
    },
    {
      "given": {
        "find": "area",
        "sh": "sphere",
        "v": 10,
        "F": 2.75625,
        "fl": "air15"
      },
      "expect": {
        "A": 0.1,
        "power": 27.5625
      },
      "source": "OpenStax, University Physics Volume 1, §6.4 Drag Force and Terminal Speed (F_D = ½CρAv²; Table 6.2; skydiver: C = 0.70, A = 0.18 m², ρ = 1.21 kg/m³, 75 kg, v_T = 98 m/s), https://openstax.org/books/university-physics-volume-1/pages/6-4-drag-force-and-terminal-speed (retrieved 2026-10-18), Table 6.2 (sphere 0.45); hand calculation in content.mdx: A = 2 × 2.75625 ÷ (0.45 × 1.225 × 10²) = 0.1 m²",
      "tolerance": 1e-12
    }
  ],
  "sources": [
    "OpenStax, University Physics Volume 1, §6.4 Drag Force and Terminal Speed: F_D = ½CρAv²; Table 6.2, typical drag coefficients; skydiver (75 kg, C = 0.70, A = 0.18 m², ρ = 1.21 kg/m³, 98 m/s); Example 6.17 (85 kg, A = 0.70 m², C = 1.0, 44 m/s), retrieved 2026-10-18. https://openstax.org/books/university-physics-volume-1/pages/6-4-drag-force-and-terminal-speed",
    "OpenStax, University Physics Volume 1, §14.1 Fluids, Density, and Pressure: Table 14.1 (air 1.29 kg/m³ at 0 °C and 101.3 kPa) and Table 14.2 (water 998.2 kg/m³ at 20 °C, sea water 1,030 kg/m³ at 0 °C), retrieved 2026-10-18. https://openstax.org/books/university-physics-volume-1/pages/14-1-fluids-density-and-pressure",
    "U.S. Standard Atmosphere, 1976 (COESA; NOAA, NASA and USAF): sea-level density 1.225 kg/m³ at 288.15 K and 101,325 Pa, as given in the definition of the 1976 atmosphere by Public Domain Aeronautical Software, retrieved 2026-10-18. https://www.pdas.com/atmosdef.html (report: https://ntrs.nasa.gov/citations/19770009539)",
    "OpenStax, University Physics Volume 1, §7.4 Power: P = F × v, retrieved 2026-10-18. https://openstax.org/books/university-physics-volume-1/pages/7-4-power",
    "NIST Special Publication 811 (2008), Appendix B.8: 1 lbf = 4.4482216152605 N, 1 ft = 0.3048 m, 1 mph = 0.44704 m/s, 1 knot = 1,852 ÷ 3,600 m/s, 1 hp = 550 ft·lbf/s = 745.69987158227022 W, retrieved 2026-10-18. https://www.nist.gov/pml/special-publication-811"
  ],
  "related": [
    "terminal-velocity",
    "force",
    "air-density",
    "reynolds-number"
  ],
  "changelog": []
}