geoprimsField-grade geospatial math

Total and static air temperature

Static (outside) air temperature from the total air temperature a probe reads, or the reverse, with the ram rise at your Mach number.

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

Experimental: not yet fully verified. How results are checked

-48.73°C

The static air temperature is -48.73 °C. Ram heating adds 28.73 K.

Total air temperature
Ram rise
Provenance
Computed by
aviation.airspeed.tat-sat 1.0.0, core 0.1.0
Model
SAT = TAT / (1 + 0.2·r·M²)
Accuracy
Exact for the stated recovery factor; real probes have r from about 0.75 to 1.0
Notes
1 shown with the answer
Cites
William Gracey, NASA Langley Research Center, Measurement of Aircraft Speed and Altitude, NASA Reference Publication 1046

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

Model: SAT = TAT / (1 + 0.2·r·M²)

Accuracy: Exact for the stated recovery factor; real probes have r from about 0.75 to 1.0

Worked example: TAT -20 °C at Mach 0.8. Source: add-aviation-suite airspeed scenario: SAT -48.73 °C, ram rise 28.73 K. It is golden test vector v001, and every build checks the tool still gives its answer within its tolerance.

You enter

Mach
0.8
Temperature
-20 °C

You get

Static air temperature
-48.73 °C
Total air temperature
-20 °C
Ram rise
28.73 K

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

Sources

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