Rankine to Fahrenheit Converter
Convert °R to °F to turn absolute engineering temperatures, such as standard-atmosphere and engine data, back into readable Fahrenheit.
°F = °R − 459.67
Subtract 459.67
Rankine and Fahrenheit use the same size of degree. Rankine simply counts from absolute zero instead of from Fahrenheit's zero. Converting means removing the 459.67-degree head start, with nothing to multiply.
Engineers calculate in Rankine because gas laws and efficiency formulas need an absolute temperature, then convert the result to Fahrenheit for reports, displays and anyone who isn't doing the math.
Standard Atmosphere Temperatures by Altitude
US aerospace performance work uses the International Standard Atmosphere in Rankine. It starts at 518.67°R (59°F) at sea level and cools by 3.566°R per 1,000 ft up to the tropopause at 36,089 ft. Above that it stays at 389.97°R until about 65,600 ft.
| Altitude (ft) | °R | °F |
|---|---|---|
| 0 | 518.67 | 59 |
| 5,000 | 500.84 | 41.17 |
| 10,000 | 483.01 | 23.34 |
| 20,000 | 447.35 | -12.32 |
| 30,000 | 411.69 | -47.98 |
| 36,089 | 389.97 | -69.7 |
| 45,000 | 389.97 | -69.7 |
Worked Example: 35,000 ft Cruise
What is the standard outside air temperature at a 35,000 ft cruising altitude, in Fahrenheit?
Step 1: Apply the standard lapse rate in Rankine
Step 2: Convert to Fahrenheit
About −66°F on a standard day. Performance charts also use the temperature ratio θ = 393.85 ÷ 518.67 = 0.759, which must be computed in Rankine (or kelvin), not Fahrenheit.
Rankine to Fahrenheit Table
Readings below 459.67°R are below 0°F and come out negative.
| °R | °F |
|---|---|
| 0°R | -459.67°F |
| 100°R | -359.67°F |
| 200°R | -259.67°F |
| 300°R | -159.67°F |
| 400°R | -59.67°F |
| 459.67°R | 0°F |
| 491.67°R | 32°F |
| 518.67°R | 59°F |
| 600°R | 140.33°F |
| 671.67°R | 212°F |
| 1,000°R | 540.33°F |
| 1,500°R | 1,040.33°F |
| 2,000°R | 1,540.33°F |
| 3,000°R | 2,540.33°F |
Frequently asked questions
Why is the Fahrenheit result negative?
Any Rankine value below 459.67 is colder than 0°F. Rankine itself can't go below zero, but Fahrenheit can go down to −459.67°F.
What is 518.67°R?
59°F, the sea-level temperature of the International Standard Atmosphere, and the reference for aircraft and engine performance corrections.
What is the temperature at the tropopause?
In the standard atmosphere, 389.97°R, which is −69.7°F. It stays at that value from 36,089 ft up to about 65,600 ft.
Sources
- NIST Special Publication 811, Guide for the Use of the International System of Units (SI): Rankine and Fahrenheit conversion factors.
- U.S. Standard Atmosphere, 1976 (NOAA/NASA/USAF): standard sea-level temperature and lapse rate.
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