True Airspeed Calculator
Why the Airspeed Indicator Doesn't Tell the Whole Story
An airspeed indicator measures dynamic pressure, not true speed through the air. As altitude increases, air density drops, and the same dynamic pressure corresponds to a faster and faster actual speed. A calibrated airspeed of 140 knots at sea level and 140 knots at 18,000 feet represent very different true speeds — the second is meaningfully faster over the ground in still air. True airspeed corrects for that density difference and is the figure actually used for navigation, range, and time-en-route calculations.
The Formula
This calculator applies the standard ISA atmosphere model to convert calibrated airspeed into true airspeed:
Density Ratio (σ) = Pressure Ratio ÷ (Temp[K] ÷ 288.15)
TAS = CAS ÷ √σ
The density ratio, often written as sigma (σ), compares actual air density at altitude and temperature to sea-level standard density. As sigma drops below 1, true airspeed pulls further ahead of calibrated airspeed — which is why the gap between CAS and TAS grows steadily the higher and warmer the flight.
Where This Calculation Matters
- Navigation and flight planning — true airspeed, not indicated or calibrated airspeed, is what's combined with wind to compute ground speed and time en route.
- High-altitude cruise planning — the CAS-to-TAS gap becomes significant above roughly 10,000 feet, making the correction increasingly important as cruise altitude climbs.
- Performance comparisons — comparing an aircraft's speed capability across different altitudes requires converting to TAS first, since CAS alone understates high-altitude performance.
- Mach number cross-checks — at high altitude, TAS combined with local speed of sound gives Mach number, a key limit on turbine aircraft.
Illustrative CAS-to-TAS Gap by Altitude
Using a constant 140-knot CAS at standard ISA temperature, the true airspeed grows with altitude as air density falls:
| Pressure Altitude | Approx. TAS | CAS-TAS Gap |
|---|---|---|
| Sea level | 140 kt | 0 kt |
| 5,000 ft | 150.8 kt | +10.8 kt |
| 10,000 ft | 162.9 kt | +22.9 kt |
| 15,000 ft | 176.5 kt | +36.5 kt |
| 20,000 ft | 191.8 kt | +51.8 kt |
Figures assume standard ISA temperature at each altitude; non-standard temperatures will shift the exact gap, which is precisely why entering actual OAT below matters.
How to Use This Calculator
- Enter calibrated airspeed (CAS) in knots — indicated airspeed corrected for instrument and position error.
- Enter pressure altitude in feet, read from the altimeter set to 29.92 in Hg (standard setting).
- Enter the outside air temperature in degrees Celsius, taken from the aircraft's OAT gauge.
- Select Calculate to see the density ratio and resulting true airspeed, with the full ISA working shown.
Related Calculations
True airspeed feeds directly into route planning — pair it with the Flight Distance Calculator to estimate flight time, or check Density Altitude to see how temperature and elevation affect performance on the ground.