How do you calculate true airspeed from calibrated airspeed?

True airspeed = calibrated airspeed corrected for air density. TAS = CAS ÷ √σ, where σ is the density ratio computed from pressure altitude and outside air temperature. As a rule of thumb, TAS is about 2% higher than CAS for every 1,000 feet of altitude. For example, 125 knots CAS at 8,500 feet pressure altitude and 23 °F works out to about 141 knots TAS.

What is the 2% rule for true airspeed?

Add roughly 2% of your calibrated airspeed per 1,000 feet of altitude. At 8,000 feet, TAS is about 16% higher than CAS: 120 knots indicated becomes roughly 139 knots true. The rule assumes near-standard temperature; on a hot day TAS is higher still, which is why the exact calculation uses temperature.

Why do pilots need true airspeed instead of indicated airspeed?

Indicated airspeed measures dynamic pressure, which falls with air density, so the indicator under-reads your real speed through the air as you climb. True airspeed is your actual speed through the air mass. It is the speed you file in a flight plan, the input to every wind-triangle groundspeed calculation, and the number POH cruise tables publish.

True Airspeed Calculator: CAS to TAS & Mach

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True airspeed = calibrated airspeed corrected for air density (TAS = CAS ÷ √σ), roughly 2% higher per 1,000 ft of altitude. At 8,500 ft and 23 °F, 125 knots CAS is 141 knots TAS. Your airspeed indicator under-reads more the higher and hotter it gets; TAS is the speed you file, the speed the POH cruise table promises, and the input every groundspeed calculation needs.

Calibrated airspeed (kt)

Indicated airspeed corrected per the POH airspeed calibration table (close to IAS in cruise)

Indicated altitude (ft)

What the altimeter reads at your cruise altitude

Altimeter setting (inHg)

Leave at 29.92 to enter pressure altitude directly

Outside air temperature (°C)

At cruise altitude, from the winds/temps aloft forecast or your OAT probe

Enter your cruise numbers to see TAS.

True airspeed – use for flight plans & wind triangle

Mach – fraction of the speed of sound

Pressure altitude – ft

Density altitude – ft (what the airplane feels)

How true airspeed is calculated

Your airspeed indicator measures dynamic pressure: how hard the air pushes into the pitot tube. Thin air pushes less, so the same true speed reads lower and lower as you climb. Converting back takes three steps:

Pressure altitude from indicated altitude and the altimeter setting (about 1,000 ft per inch of mercury away from 29.92).
Density ratio σ from pressure altitude and outside air temperature: how dense the air is compared with sea level on a standard day.
TAS = CAS ÷ √σ. This calculator uses the full compressible-flow equations (the same math inside an E6-B or CX-3), so the result matches the flight-computer answer to a fraction of a knot. Mach is TAS divided by the local speed of sound, which depends only on temperature.

The 2% rule of thumb

For mental math in the cockpit: TAS ≈ CAS + 2% per 1,000 ft. At 6,000 ft add 12%; at 10,000 ft add 20%. So a 110-knot indicated cruise at 9,500 ft is really about 131 knots through the air. The rule assumes standard temperature; hot days push TAS higher, cold days pull it back. When the answer matters (fuel planning on a long leg), use the exact calculation above.

How pilots use TAS

Flight plans file TAS. The cruise speed box on a VFR or IFR flight plan is true airspeed, not indicated.
The wind triangle starts with TAS. Groundspeed, heading, and leg time all come from TAS plus the winds aloft. Run this calculator first, then take the TAS to the heading & groundspeed calculator.
POH cruise tables publish TAS. If the book says 65% power gives 114 knots at 8,000 ft, that is a true airspeed. Comparing it against your indicated airspeed without converting is comparing two different quantities.
Cross-checking in cruise. Compute TAS from what you see (CAS, altitude, OAT) and compare with the book number for your power setting. A TAS that comes up persistently short can be a rigging issue, a tired engine, or ice you have not noticed.

Worked example, straight off a flight computer

Plan: 125 knots CAS at 8,500 ft pressure altitude with an OAT of -5 °C (23 °F).

Density ratio σ at 8,500 ft and -5 °C ≈ 0.78
TAS = 125 ÷ √0.78 ≈ 141 knots
Mach = 141 ÷ 638 (speed of sound at -5 °C) ≈ 0.22

That 16-knot difference is not academic: over a 300 NM leg it changes the no-wind time by about 20 minutes, which is fuel you either have or do not.

Common Questions

What is the difference between IAS, CAS, and TAS?

Indicated airspeed (IAS) is what the needle shows. Calibrated airspeed (CAS) is IAS corrected for known instrument and pitot-static position errors using the POH table; in cruise the two are usually within a knot or two. True airspeed (TAS) is CAS corrected for air density, and it is your real speed through the air mass. Add wind and you get groundspeed.

Should I enter OAT at the surface or at altitude?

At altitude. Use the temperature from the winds and temperatures aloft forecast for your cruise level when planning, or your OAT gauge in flight. Surface temperature belongs in the density altitude calculator for takeoff performance, not here.

Does Mach number matter in a piston airplane?

Not operationally; a 140-knot cruise is around Mach 0.22 and compressibility effects are negligible. It starts to matter above roughly Mach 0.4 (fast turboprops and jets), where indicated-to-true conversions need the compressibility correction this calculator already includes. We show it because knowledge-test questions and flight computers do.

Related tools and guides

Heading & Groundspeed Calculator

Take this TAS into the wind triangle: wind correction angle, heading, and groundspeed.

Density Altitude Calculator

The same air-density math applied to takeoff and climb performance.

Time-Speed-Distance Calculator

Turn groundspeed into leg times and an ETA.

Performance is one of eight risk categories

FlightDecide checks performance alongside winds, ceilings, visibility, NOTAMs, fuel, and W&B for your specific flight window and aircraft, using curated POH cruise data for 40+ types.

Get FlightDecide on the App Store

Educational tool for flight-planning practice. It is advisory only and not a substitute for your POH, an official weather briefing, or your own judgment as pilot in command (14 CFR 91.3). Sources: FAA Pilot's Handbook of Aeronautical Knowledge (FAA-H-8083-25C), Ch. 8 and 16; ICAO Standard Atmosphere. Last reviewed: July 17, 2026.