Airspeed Calculator Formula

Understand the math behind the airspeed calculator. Each variable explained with a worked example.

Formulas Used

True Airspeed (TAS)

tas = ias / sqrt(density_ratio)

True Airspeed

tas_ms = ias / sqrt(density_ratio) * 0.5144

Density Ratio (sigma)

density_ratio_out = density_ratio

Variables

VariableDescriptionDefault
iasIndicated Airspeed (IAS)(knots)250
pressure_altPressure Altitude(ft)10000
oatOutside Air Temperature (OAT)(°C)-5
isa_tempDerived value= 15 - 0.001981 * pressure_altcalculated
density_ratioDerived value= (288.15 / (oat + 273.15)) * pow(1 - 0.000006875 * pressure_alt, 4.2561)calculated

How It Works

Indicated vs True Airspeed

Indicated airspeed (IAS) is what the pitot-static system reads, calibrated for sea-level standard density. As altitude increases and air density decreases, the true airspeed (TAS) becomes higher than the indicated reading.

Simplified Relationship

TAS = IAS / sqrt(sigma)

where sigma is the density ratio (local density divided by sea-level standard density). This approximation is valid for low subsonic speeds where compressibility effects are negligible.

Worked Example

An aircraft reads 250 KIAS at 10,000 ft pressure altitude with OAT of -5°C.

ias = 250pressure_alt = 10000oat = -5
  1. 01ISA temperature at 10,000 ft = 15 - 1.981 × 10 = -4.81°C
  2. 02Temperature ratio component = 288.15 / 268.15 = 1.0746
  3. 03Pressure ratio component = (1 - 0.000006875 × 10000)^4.2561 = 0.6877
  4. 04Density ratio sigma = 1.0746 × 0.6877 = 0.7392
  5. 05TAS = 250 / sqrt(0.7392) = 250 / 0.8598 = 290.8 knots

Ready to run the numbers?

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