{
  "id": "true-airspeed",
  "version": "f4974546472c",
  "status": "published",
  "name": "True Airspeed Calculator",
  "question": "What is my true airspeed?",
  "summary": "True airspeed calculator: TAS from calibrated airspeed, pressure altitude and outside air temperature, with compressibility, the Mach number, the equivalent airspeed and the standard atmosphere values.",
  "category": "physics",
  "subcategory": "weather",
  "url": "https://www.acalculator.org/physics/true-airspeed-calculator",
  "markdown": "https://www.acalculator.org/physics/true-airspeed-calculator.md",
  "kind": "function",
  "method": "p = 101,325 × (1 − 0.0065h ÷ 288.15)^(34.1631947 ÷ 6.5) Pa; qc = p₀[(1 + 0.2(CAS ÷ a₀)²)^3.5 − 1]; M = √(5[(qc ÷ p + 1)^(2/7) − 1]); TAS = M × √(γRT), with γ = 1.4, R = 9.80665 ÷ 0.0341631947 J/(kg·K) and a₀ = √(γR × 288.15).",
  "assumptions": [
    "Subsonic flight (Mach below 1), in the troposphere (pressure altitude up to 11,000 m, 36,089 ft).",
    "CAS already holds the instrument and position corrections; the temperature is the true outside air temperature."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "cas": {
        "title": "Calibrated airspeed (CAS)",
        "description": "The indicated airspeed corrected for instrument and position error.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "speed",
        "minimum": 0.5,
        "maximum": 340
      },
      "pa": {
        "title": "Pressure altitude",
        "description": "The altitude shown with the altimeter set to 29.92 inHg (1013.25 hPa).",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "minimum": -1000,
        "maximum": 11000
      },
      "oat": {
        "title": "Outside air temperature (OAT)",
        "description": "The true temperature of the outside air.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "temperature",
        "minimum": 183.14999999999998,
        "maximum": 333.15
      }
    }
  },
  "outputs": {
    "tas": {
      "label": "True airspeed (TAS)",
      "description": "The speed of the aircraft through the air, in knots.",
      "format": "quantity",
      "unit": "kn"
    },
    "mph": {
      "label": "True airspeed (mph)",
      "description": "TAS in miles per hour.",
      "format": "number"
    },
    "kmh": {
      "label": "True airspeed (km/h)",
      "description": "TAS in kilometres per hour.",
      "format": "number"
    },
    "mach": {
      "label": "Mach number",
      "description": "TAS ÷ the speed of sound at the outside air temperature.",
      "format": "number"
    },
    "eas": {
      "label": "Equivalent airspeed (EAS)",
      "description": "CAS corrected for compressibility: TAS × √(ρ ÷ ρ₀).",
      "format": "quantity",
      "unit": "kn"
    },
    "simple": {
      "label": "TAS without compressibility",
      "description": "CAS ÷ √(ρ ÷ ρ₀): the density-only estimate, which reads high at speed and altitude.",
      "format": "quantity",
      "unit": "kn"
    },
    "pressure": {
      "label": "Static pressure (hPa)",
      "description": "The standard atmosphere pressure at this pressure altitude.",
      "format": "number"
    },
    "isa": {
      "label": "ISA temperature (°C)",
      "description": "15 °C − 6.5 °C per km of pressure altitude.",
      "format": "number"
    },
    "isaDev": {
      "label": "ISA deviation (°C)",
      "description": "The outside air temperature minus the ISA temperature.",
      "format": "number"
    },
    "sigma": {
      "label": "Density ratio ρ ÷ ρ₀",
      "description": "(p ÷ p₀) × (T₀ ÷ T): the air density as a share of sea-level standard.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "cas": 77.16666666666667,
      "pa": 2438.4,
      "oat": 273.15
    },
    "outputs": {
      "tas": 86.9847115414784,
      "mph": 194.57925810101648,
      "kmh": 313.14496154932226,
      "mach": 0.26254104380958637,
      "eas": 76.99850509196591,
      "simple": 87.1746825811789,
      "pressure": 752.6237608980808,
      "isa": -0.8496000000000095,
      "isaDev": 0.8496000000000095,
      "sigma": 0.7835716810932862
    },
    "text": "At 8,000 ft and 0 °C, a CAS of 150 kn is a true airspeed of 169.1 kn (Mach 0.26254)."
  },
  "examples": [
    {
      "given": {
        "cas": 51.44444444444445,
        "pa": 0,
        "oat": 288.15
      },
      "expect": {
        "tas": 51.44444444444445,
        "eas": 51.44444444444445,
        "sigma": 1,
        "mach": 0.15117641839780618
      },
      "source": "14 CFR 1.1 General definitions (calibrated airspeed is equal to true airspeed in standard atmosphere at sea level; true airspeed is equivalent airspeed × (ρ₀ ÷ ρ)^½; Mach number is true airspeed ÷ the speed of sound), https://www.law.cornell.edu/cfr/text/14/1.1 (retrieved 2026-10-18): CAS equals TAS in the standard atmosphere at sea level; NASA Glenn Research Center, Isentropic Flow Equations (M = v ÷ a; a = √(γRT); p ÷ pt = [1 + M²(γ − 1) ÷ 2]^(−γ ÷ (γ − 1))), https://www.grc.nasa.gov/www/k-12/airplane/isentrop.html (retrieved 2026-10-18)",
      "tolerance": 1e-9
    },
    {
      "given": {
        "cas": 77.16666666666667,
        "pa": 2438.4,
        "oat": 273.15
      },
      "expect": {
        "tas": 86.9847115414784,
        "mach": 0.26254104380958637,
        "pressure": 752.6237608980808,
        "isa": -0.8496
      },
      "source": "14 CFR 1.1 General definitions (calibrated airspeed is equal to true airspeed in standard atmosphere at sea level; true airspeed is equivalent airspeed × (ρ₀ ÷ ρ)^½; Mach number is true airspeed ÷ the speed of sound), https://www.law.cornell.edu/cfr/text/14/1.1 (retrieved 2026-10-18); NASA Glenn Research Center, Isentropic Flow Equations (M = v ÷ a; a = √(γRT); p ÷ pt = [1 + M²(γ − 1) ÷ 2]^(−γ ÷ (γ − 1))), https://www.grc.nasa.gov/www/k-12/airplane/isentrop.html (retrieved 2026-10-18); U.S. Standard Atmosphere, 1976, as defined by Public Domain Aeronautical Software (101,325 Pa, 288.15 K, −6.5 K/km to 11 km, hydrostatic constant 34.1631947 K/km), https://www.pdas.com/atmosdef.html (retrieved 2026-10-18); hand calculation in content.mdx",
      "tolerance": 1e-9
    },
    {
      "given": {
        "cas": 128.61111111111111,
        "pa": 9144,
        "oat": 228.14999999999998
      },
      "expect": {
        "tas": 202.3026983219315,
        "mach": 0.6681074603686261,
        "sigma": 0.3750574390109346,
        "simple": 210.00498229426935
      },
      "source": "14 CFR 1.1 General definitions (calibrated airspeed is equal to true airspeed in standard atmosphere at sea level; true airspeed is equivalent airspeed × (ρ₀ ÷ ρ)^½; Mach number is true airspeed ÷ the speed of sound), https://www.law.cornell.edu/cfr/text/14/1.1 (retrieved 2026-10-18); NASA Glenn Research Center, Isentropic Flow Equations (M = v ÷ a; a = √(γRT); p ÷ pt = [1 + M²(γ − 1) ÷ 2]^(−γ ÷ (γ − 1))), https://www.grc.nasa.gov/www/k-12/airplane/isentrop.html (retrieved 2026-10-18); U.S. Standard Atmosphere, 1976, as defined by Public Domain Aeronautical Software (101,325 Pa, 288.15 K, −6.5 K/km to 11 km, hydrostatic constant 34.1631947 K/km), https://www.pdas.com/atmosdef.html (retrieved 2026-10-18); hand calculation in content.mdx",
      "tolerance": 1e-9
    }
  ],
  "sources": [
    "14 CFR 1.1 General definitions: calibrated, equivalent, indicated and true airspeed; true airspeed equals equivalent airspeed × (ρ₀ ÷ ρ)^½; calibrated airspeed equals true airspeed in standard atmosphere at sea level; Mach number, retrieved 2026-10-18. https://www.law.cornell.edu/cfr/text/14/1.1",
    "NASA Glenn Research Center, Beginner’s Guide to Aeronautics, Isentropic Flow Equations: M = v ÷ a, a = √(γRT), p ÷ pt = [1 + M²(γ − 1) ÷ 2]^(−γ ÷ (γ − 1)), retrieved 2026-10-18. https://www.grc.nasa.gov/www/k-12/airplane/isentrop.html",
    "NASA Glenn Research Center, Specific Heats: γ = 1.4 for air on a standard day, retrieved 2026-10-18. https://www.grc.nasa.gov/www/k-12/airplane/specheat.html",
    "U.S. Standard Atmosphere, 1976 (COESA): sea-level pressure 101,325 Pa and temperature 288.15 K, lapse rate −6.5 K/km from 0 to 11 km, hydrostatic constant 34.1631947 K/km, as given by Public Domain Aeronautical Software, retrieved 2026-10-18. https://www.pdas.com/atmosdef.html (report: https://ntrs.nasa.gov/citations/19770009539)",
    "NIST, CODATA 2022: standard acceleration of gravity 9.80665 m/s² (exact), retrieved 2026-10-18. https://physics.nist.gov/cgi-bin/cuu/Value?gn",
    "NIST, CODATA 2022: standard atmosphere 101,325 Pa (exact), retrieved 2026-10-18. https://physics.nist.gov/cgi-bin/cuu/Value?stdatm",
    "NIST Special Publication 811 (2008), Appendix B.8: 1 knot = 1,852 ÷ 3,600 m/s, 1 ft = 0.3048 m, 1 mph = 0.44704 m/s, retrieved 2026-10-18. https://www.nist.gov/pml/special-publication-811"
  ],
  "related": [
    "density-altitude",
    "pressure-altitude",
    "e6b",
    "crosswind"
  ],
  "changelog": []
}