True airspeed calculator
Indicated airspeed measures dynamic pressure. As air thins, the same dynamic pressure means a higher true speed.
kt
ft
kt
True airspeed
135.56kt
- Ground speed
- 121.42 kt
- True airspeed
- 251.06 km/h
- True airspeed
- 156.00 mph
- Headwind component Negative means a tailwind.
- 14.14 kt
- Crosswind component
- 14.14 kt
- Density ratio
- 0.783 58
- Mach number
- 0.2105
Show the working
- Indicated airspeed = 120
- Pressure altitude = 8000
- Outside air temperature = 0
- Wind speed = 20
- Angle between wind and track = 45
- isa_temp = 15 - 1.98 * 8000 / 1000 = -0.84
- temp_k = 0 + 273.15 = 273.15
- pressure_ratio = (1 - 6.87535e-6 * 8000)^5.2559 = 0.742 789
- Density ratio = 0.742 789 * 288.15 / 273.15 = 0.783 579
- True airspeed = 0.783 579 > 0 ? 120 / sqrt(0.783 579) : 0 = 135.563
- True airspeed = 135.563 * 1.15077944802354 = 156.003
- True airspeed = 135.563 * 1.852 = 251.062
- Headwind component = 20 * cos(rad(45)) = 14.1421
- Crosswind component = 20 * sin(rad(45)) = 14.1421
- Ground speed = 135.563 - 14.1421 = 121.42
- Mach number = sqrt(1.4 * 287.058 * 273.15) > 0 ? 135.563 * 0.514444 / sqrt(1.4 * 287.058 * 273.15) : 0 = 0.210 489
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- TAS = IAS / sqrt(density ratio)
- density ratio = pressure ratio x 288.15 / temperature in kelvin
- the rule of thumb of 2% per thousand feet is this relation linearised
This ignores compressibility, which starts to matter above about 200 knots and 10 000 feet. For fast jets, calibrated airspeed and Mach corrections are needed.
This is a planning and study tool. Use certified charts, an approved flight manual and official publications for anything operational.