True airspeed from indicated or calibrated airspeed

True airspeed, Mach, and equivalent airspeed from or , pressure altitude, and outside air temperature, by the exact compressible-flow path, with the 2% per 1,000 ft rule beside it.

Go the other way: Calibrated airspeed from true airspeed or Mach →

Planning and education aid. Not for primary navigation. Full disclaimer

Experimental: not yet fully verified. How results are checked

Computing your own values needs JavaScript and WebAssembly. The worked example below was computed when this page was built, and the documentation under "How we got this" applies.

288.6kt

True airspeed is 288.6 kt, Mach 0.4523. The 2% rule gives 300 kt, off by 11.4 kt.

Mach
Calibrated airspeed
Equivalent airspeed
Impact pressure qc
Speed of sound
Dynamic pressure q

Provenance

Computed by: aviation.airspeed.cas-to-tas 1.0.0, core 0.1.0
Model: CAS → impact pressure (sea-level ISA relation) → Mach at the static pressure of the pressure altitude → TAS at the outside air temperature; Rayleigh pitot formula above Mach 1
Accuracy: Exact compressible-flow relations for γ = 1.4 air to double precision; the Rayleigh branch is iterated to 1e-12. Planning aid, not certified for navigation.
Notes: 1 shown with the answer
Cites: William Gracey, NASA Langley Research Center, Measurement of Aircraft Speed and Altitude, NASA Reference Publication 1046; International Civil Aviation Organization, Manual of the ICAO Standard Atmosphere (extended to 80 kilometres (262 500 feet)); Federal Aviation Administration, Pilot's Handbook of Aeronautical Knowledge, FAA-H-8083-25C

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Your values

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Airspeed Like 250 kt · plain numbers mean kt Airspeed typeoptional calibrated (default) or indicated with a calibration table Pressure altitude Like 10000 ft (altimeter set to 29.92 inHg or 1013.25 hPa) · plain numbers mean ft Outside air temperatureoptional Static air temperature, like -5 °C · plain numbers mean °C

More options 7

Temperature sourceoptional measured (default) or isa to assume the standard temperature Calibration tableoptional From the POH/AFM: indicated and calibrated airspeed pairs, in increasing order, like 70 kt indicated and 73 kt calibrated · one per line: indicated, calibrated VS0, stall speed in the landing configurationoptional Bottom of the white arc, like 48 kt · plain numbers mean kt VS1, stall speed cleanoptional Bottom of the green arc, like 55 kt · plain numbers mean kt VFE, maximum flaps extendedoptional Top of the white arc, like 95 kt · plain numbers mean kt VNO, maximum structural cruisingoptional Top of the green arc, like 130 kt · plain numbers mean kt VNE, never exceedoptional The red line, like 160 kt · plain numbers mean kt

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How we got thisFormula, worked example, sources, and proof

Model: CAS → impact pressure (sea-level ISA relation) → Mach at the static pressure of the pressure altitude → TAS at the outside air temperature; Rayleigh pitot formula above Mach 1

Accuracy: Exact compressible-flow relations for γ = 1.4 air to double precision; the Rayleigh branch is iterated to 1e-12. Planning aid, not certified for navigation.

Worked example: 250 KCAS at 10,000 ft and -5 °C. Source: add-aviation-suite airspeed scenario: Mach 0.4523, TAS 288.6 kt, EAS 248.1 kt. It is golden test vector v001, and every build checks the tool still gives its answer within its tolerance.

You enter

Airspeed: 250 kt
Pressure altitude: 10000 ft
Outside air temperature: -5 °C

You get

True airspeed: 288.6 kt
Mach: 0.4523
Calibrated airspeed: 250 kt
Equivalent airspeed: 248.1 kt
Impact pressure qc: 104.98 hPa
Speed of sound: 638.1 kt
Dynamic pressure q: 99.775 hPa
Compressibility correction: 1.9 kt
Flow branch: subsonic (isentropic)
2% per 1,000 ft rule: 300 kt
Rule error: 11.4 kt

Review: Not yet independently reviewed by a flight instructor (CFI).

Last verified: 2026-09-18, when a maintainer last confirmed this tool's sources at the issuer. See the sources ledger.

Status: version 1.0.0, core 0.1.0. See this tool in the verification report.

Checked against: 7 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.

Sources

Measurement of Aircraft Speed and Altitude, NASA Reference Publication 1046, William Gracey, NASA Langley Research Center, NASA RP-1046. Chapter 2 (airspeed equations: subsonic and Rayleigh supersonic pitot relations) and Chapter 16 (temperature).
Manual of the ICAO Standard Atmosphere (extended to 80 kilometres (262 500 feet)), International Civil Aviation Organization, 3rd edition, Doc 7488/3. Section 2 (defining constants and equations) and Table 1. Paid only.
Pilot's Handbook of Aeronautical Knowledge, FAA-H-8083-25C, Federal Aviation Administration, FAA-H-8083-25C. Aircraft Performance and Navigation chapters (pressure and density altitude, wind triangle).

Terms

AFM: Airplane Flight Manual: The FAA-approved manual of an aircraft's limitations and performance. For many light aircraft the POH serves as the AFM. Source: Pilot's Handbook of Aeronautical Knowledge
CAS: calibrated airspeed: Indicated airspeed corrected for instrument and position error. It measures dynamic pressure, which governs how the aircraft flies. Source: Pilot's Handbook of Aeronautical Knowledge
IAS: indicated airspeed: The airspeed read directly from the airspeed indicator, before any correction. Source: Pilot's Handbook of Aeronautical Knowledge
ISA: International Standard Atmosphere: A reference atmosphere: 15 °C and 1013.25 hPa at sea level, cooling 6.5 °C per kilometer up to 11 km. Altimeters and performance charts are built on it. Source: Manual of the ICAO Standard Atmosphere (Doc 7488)
POH: Pilot's Operating Handbook: The manufacturer's handbook for an aircraft: limitations, procedures, performance charts, and weight-and-balance data. Its numbers govern over any calculator. Source: Pilot's Handbook of Aeronautical Knowledge
VFE: maximum flap extended speed: The fastest speed at which the flaps may be extended. It is the top of the white arc on the airspeed indicator. Source: Pilot's Handbook of Aeronautical Knowledge
VNE: never exceed speed: The speed never to be exceeded in any operation. It is the red line on the airspeed indicator. Source: Pilot's Handbook of Aeronautical Knowledge
VNO: maximum structural cruising speed: The fastest speed for normal operation. Above it, in the yellow arc, fly only in smooth air. Source: Pilot's Handbook of Aeronautical Knowledge
VS0: stall speed in the landing configuration: The slowest speed at which the aircraft still flies with the flaps and gear down. It is the bottom of the white arc on the airspeed indicator. Source: Pilot's Handbook of Aeronautical Knowledge
VS1: stall speed in a stated configuration: The slowest speed at which the aircraft still flies in the clean configuration. It is the bottom of the green arc on the airspeed indicator. Source: Pilot's Handbook of Aeronautical Knowledge

Experimental means this tool has not yet met the stable bar: at least 20 golden vectors, differential tests, and an independent worked example.

CAS — calibrated airspeed

Indicated airspeed corrected for instrument and position error. It measures dynamic pressure, which governs how the aircraft flies.

Source: Pilot's Handbook of Aeronautical Knowledge

IAS — indicated airspeed

The airspeed read directly from the airspeed indicator, before any correction.