Maps for Math

How do you convert indicated airspeed to true airspeed?

The airspeed indicator measures the push of the air, which depends on air density as well as speed. In thin air it reads low. True airspeed is calibrated airspeed divided by the square root of the density ratio. A quick rule adds about 2 percent per 1,000 feet of altitude.

dial reads 90 ktdashed: standard-day temperaturesTAS 101 kt · Mach 0.16
True airspeed
101 kt
Faster than calibrated by
12.7%
Density altitude
7980 ft
Mach number
×0.158

E6B: Training aid only, not for navigation or flight. Verify with your POH/AFM and approved sources.

Indicated airspeed corrected with the POH airspeed calibration table. In cruise they’re usually within a few knots.
Set 29.92 in the altimeter and read it, or use the density altitude tool.

Play

Climb from sea level to 10,000 ft at the same dial reading. Watch true airspeed rise.

Stuck? Pick one of the examples from the “Try an example” menu, or press “New example.”

Understand

TAS=M⋅a\text{TAS} = M \cdot a

The airspeed indicator is really a pressure gauge. It measures the dynamic pressure 12ρv2\tfrac12\rho v^2 of the oncoming air. It's calibrated for sea-level density, so when the air is thinner it under-reads your true speed.

Setting the pressures equal gives

TAS=CASσ,σ=ρρ0\text{TAS} = \frac{\text{CAS}}{\sqrt{\sigma}}, \qquad \sigma = \frac{\rho}{\rho_0}

where σ\sigma comes from the standard atmosphere with a power of altitude and a temperature correction. The dashed curve is a standard day. Hotter air puts the dot above it.

That simple version is close below about 200 kt. Faster, the air squeezes as it rams into the pitot tube, and the dial reads a little high. The exact method goes through the Mach number: turn the dial reading into the pressure the tube feels, find the Mach number that makes that pressure at your altitude, then multiply by the local speed of sound, TAS=M⋅a\text{TAS} = M \cdot a. "Show the work" walks through each step. The hollow dot marks what the simple formula would have said.

Use

Every input has a unit menu, so you can type values in the units you already have. Results follow your units.

Show the work

  1. The pitot tube feels impact pressure. Airspeed dials are calibrated to sea-level air (a₀ = 661.5 kt is the speed of sound there)\frac{q_c}{P_0} = \left(1 + 0.2\left(\frac{90}{661.5}\right)^2\right)^{3.5} - 1 = 0.01302
  2. Air pressure at your altitude, as a share of sea level\delta = (1 - 6.8756\times10^{-6}\cdot8000)^{5.2559} = 0.7428
  3. The same impact pressure in thinner air means a higher Mach numberM = \sqrt{5\left[\left(\frac{0.01302}{0.7428} + 1\right)^{2/7} - 1\right]} = 0.1577
  4. Speed of sound depends only on temperaturea = 661.5\sqrt{\frac{-1 + 273.15}{288.15}} = 642.9\ \text{kt}
  5. True airspeed\text{TAS} = M \cdot a = 0.1577 \times 642.9 = 101.4\ \text{kt}
  6. Ignoring compressibility (fine below about 200 kt): density ratio σ, then CAS ÷ √σ\sigma = 0.7864,\quad \frac{90}{\sqrt{0.7864}} = 101.5\ \text{kt}\ (0.081\ \text{kt high})
  7. Rule of thumb: +2% per 1,000 ft90 \times (1 + 0.02 \times 8) = 104.4\ \text{kt}

Export

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Enter calibrated airspeed, pressure altitude, and outside air temperature.

  • Pressure altitude is what the altimeter reads with 29.92 set in the window.
  • The result feeds straight into the wind triangle tool.

For learning and estimation. Verify with applicable codes, standards, and a qualified professional before using in design, construction, or safety-critical work.

Cheat card

TAS=CASσ\text{TAS} = \frac{\text{CAS}}{\sqrt{\sigma}}
M=5[(qcP+1)2/7−1], TAS=MaM = \sqrt{5\left[\left(\frac{q_c}{P} + 1\right)^{2/7} - 1\right]},\ \text{TAS} = M a
TAS≈CAS(1+0.02 PA1000)\text{TAS} \approx \text{CAS}\left(1 + 0.02\,\frac{\text{PA}}{1000}\right)
SymbolMeaningUnit
CAS\text{CAS}calibrated airspeed (indicated, corrected)kt
σ\sigmaair density ÷ sea-level standard density
PA\text{PA}pressure altitudeft
  • Use true airspeed in the wind triangle, never indicated.
  • Stall speeds in the POH are indicated, so they stay the same at altitude even though TAS is higher.
  • Above about 200 kt, air compresses in front of the pitot tube. The page corrects for it, and shows how far off the simple formula would be.

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Where it’s used

  • Aerospace
    Pilots convert calibrated to true airspeed for every cross-country plan, since navigation happens in true speed.
  • Physics
    The dial reads dynamic pressure ½ρv². Hold the pressure fixed and thinner air means a faster true speed.

Questions people ask

Why is true airspeed higher than indicated at altitude?

The indicator senses the pressure of oncoming air, ½ρv². Higher up, density ρ is lower, so the airplane must move faster to make the same pressure. The dial shows the same number while you actually go faster.

How much faster is true airspeed?

About 2% per 1,000 ft. At 8,000 ft on a standard day, 110 kt calibrated is about 124 kt true.

What's the difference between indicated and calibrated airspeed?

Calibrated corrects indicated airspeed for errors in the pitot-static system, using a table in the POH. In cruise the two are usually within a few knots.

Updated : Compressible true airspeed (Mach × speed of sound) with every step shown, up to 400 kt; the simple CAS/√σ is shown for comparison. CAS help text points to the POH calibration table.

Change history (3 revisions)
  1. · rev 3: Compressible true airspeed (Mach × speed of sound) with every step shown, up to 400 kt; the simple CAS/√σ is shown for comparison. CAS help text points to the POH calibration table.
  2. · rev 2: Name the trainer preset "like a Cessna 172".
  3. · rev 1: First published.

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Sample EXP-0007 · rev 3 · model EXP-M07 · Level 4 · advanced algebra · updated 2026-10-02