Convert °R to °C degrees Rankine ↔ degrees Celsius Free Online Secure
Type a temperature in degrees Rankine and read it in degrees Celsius at once. The relation is exact by definition, the arithmetic happens in your browser, and nothing is sent anywhere.
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Common values — Convert °R to °C (degrees Rankine ↔ degrees Celsius)
| °R | °C |
|---|---|
| 0 | -273.15 |
| 200 | -162.038888889 |
| 400 | -50.9277777778 |
| 491.67 | 0 |
| 527.67 | 20 |
| 558.27 | 37 |
| 671.67 | 100 |
| 1000 | 282.405555556 |
Where these units come from
Fahrenheit set his zero in 1724 at the coldest thing he could make reliably — a brine of ice, water and salt — and put body heat near 96, so that his scale could be divided and divided again. Celsius published his in 1742 the other way up, with 0 for boiling and 100 for freezing; it was turned around after his death, which is why he is remembered for a scale he never used. Kelvin is the only one of the four that begins where there is nothing left to take away: absolute zero. Since 2019 it is defined by fixing the Boltzmann constant rather than by the triple point of water, so the kelvin no longer depends on a particular substance. Rankine is Fahrenheit's degree counted from absolute zero, and Réaumur, with 80 degrees between freezing and boiling, survives mostly in old recipes and in a few cheese dairies.
Where you meet them
Celsius runs weather, cooking and medicine almost everywhere; Fahrenheit does the same work in the United States and keeps a foothold in oven settings and in American recipes. Kelvin belongs to physics, to the colour temperature of lamps and screens, and to anything cold enough that negative numbers would be a nuisance. Rankine appears in American thermodynamics, and Réaumur mainly in historical texts — which is exactly why an old recipe can mislead someone reading it as Celsius.
Questions people ask
What is the Rankine scale?
An absolute scale with degrees the size of Fahrenheit degrees. Zero Rankine is absolute zero, and water freezes at 491.67 °R. To convert from kelvin you multiply by 9/5. It appears in some American engineering and thermodynamics work, where Fahrenheit-sized steps are convenient but a true zero is needed.
Why can't I just double the number to double the temperature?
Because three of these scales have arbitrary zeros. Twenty degrees Celsius is not twice as hot as ten; it is ten degrees further along a scale whose zero was chosen for the convenience of water. Only kelvin and Rankine begin at absolute zero, where there is genuinely nothing left, so only on those two does doubling the figure mean doubling the thermal energy. That is also why every conversion here adds or subtracts as well as multiplying.
Is the answer exact?
Where both units are defined in terms of one another by whole numbers, yes — the page says so above the figure, and the only rounding is in how many digits are shown. Where the ratio has no finite decimal, the page shows twelve significant digits and says the relation is approximate rather than pretending otherwise.
Does anything I type leave my device?
No. The arithmetic runs in your browser; nothing is uploaded and there is no server to upload it to. Load the page once and it keeps working with the network switched off.
Reading old NACA reports and power-plant manuals: Rankine into Celsius
A report from the golden age of American aviation says the skin of an experimental aircraft reached 1,660 °R. A 1959 power plant manual boasts of steam at 1,660 °R as well. Written in Rankine, these figures meant something to engineers of the day, but a modern reader needs Celsius to feel them. To convert °R to °C, divide by 1.8 and subtract 273.15: 1,660 °R is 649.1 °C, 518.67 °R is 15 °C and 671.67 °R is 100 °C. The calculator above does both steps as you type, and the sections below show how to read historic and technical documents that quote Rankine.
You will find the formula with worked examples, a short profile of each scale, a comparison, a long set of cases from aerospace and power engineering history, and the slips to avoid. The arithmetic runs in your browser, and what you type is not sent anywhere.
How to convert °R to °C: divide by 1.8, then subtract 273.15
The formula
The formula is °C = °R ÷ 1.8 − 273.15. So 540 °R gives 540 ÷ 1.8 − 273.15 = 26.85 °C, 750 °R gives 143.52 °C and 0 °R gives −273.15 °C. To go back, add 273.15 and multiply by 1.8.
Worked examples
Standard sea-level air at 518.67 °R is 15 °C. Water boiling at 671.67 °R is 100 °C. Liquid oxygen at 162.3 °R is −183 °C. Steam at 1,459.67 °R is 538 °C, and a 3,000 °R combustion gas is 1,393.5 °C.
Why two steps
A Rankine degree is 5/9 of a kelvin, so dividing by 1.8 gives kelvin. The Celsius scale then starts 273.15 below the freezing point of water relative to kelvin, so you subtract 273.15.
A quick sanity test
The Celsius value must be lower than the Rankine value divided by 1.8. If a “convert °R to °C” calculation gives a number far above that, the final subtraction was missed.
The Rankine scale
An absolute scale in Fahrenheit-sized degrees
Rankine starts at absolute zero and uses degrees equal in size to Fahrenheit degrees. Its symbol is °R. Engineers in the English-unit world used it for gas and steam calculations because it combined an absolute zero with familiar degrees.
Where it appears
Old and new American thermodynamics texts, aerospace reports from the mid-twentieth century and some gas-property tables.
The Celsius scale
The scale of most of the world
Celsius puts 0 at the freezing point of water and 100 at the boiling point at standard pressure. It is the scale used in laboratories, weather reports and engineering outside the United States.
Where it appears
Modern textbooks, standards, thermometers and international reports.
Rankine against Celsius
One Celsius degree equals 1.8 Rankine degrees. A drop of 90 °R is a drop of 50 °C. The absolute values are tied by the formula, so 540 °R equals 26.85 °C. Rankine is absolute, so ratios of Rankine temperatures equal ratios of kelvin temperatures, which matters in efficiency and gas formulas.
The formula is exact, so rounding appears only in the answer you read. The traps are mixing Rankine with Fahrenheit and skipping the division by 1.8.
Where the conversion shows up
Mid-century aerospace reports
Reports from the National Advisory Committee for Aeronautics and later NASA often expressed temperatures in °R in the equations and in °F in the results. The skin of the SR-71 at Mach 3 reached about 1,060 °R, which is 316 °C. The Concorde nose at Mach 2 reached about 720 °R, or 127 °C. To read such a report you need a “convert °R to °C” calculation for each number.
The speed of sound
In English units, the speed of sound is 49.02 times the square root of the temperature in °R, in feet per second. At 518.67 °R it is 1,116.4 ft/s, which is 340.3 m/s. At 389.97 °R, the stratospheric temperature of −56.5 °C, it falls to 968 ft/s, or 295 m/s. Students must convert to Rankine before inserting the temperature.
Steam plants
In 1959 the Eddystone Unit 1 power plant in Pennsylvania began operating with steam at about 5,000 psi and 1,200 °F, which is 1,660 °R, or 649 °C, the highest steam temperature of its day. Modern plants run at 600 °C or lower because of materials limits, which a “convert °R to °C” calculation on the old figure makes plain. The manuals of that era are written in °F and °R, and a reader today converts them to Celsius.
Stagnation temperature at Mach 3
An aircraft flying at Mach 3 in the stratosphere, where the air is 389.97 °R, sees a stagnation temperature of 389.97 × (1 + 0.2 × 9) = 1,092 °R. That is 606.6 K, or 333.4 °C. The skin does not reach that exactly, because of heat loss, but the formula shows why titanium was chosen for the Blackbird.
Atmosphere models
Standard atmosphere tables in English units list temperature in °R, pressure in psf and density in slugs per cubic foot. At 36,089 ft the temperature is 389.97 °R. Between sea level and that altitude the lapse rate is 3.566 °R per 1,000 ft, which equals 6.5 K per kilometre. A “convert °R to °C” calculation for each row of such a table gives the Celsius values in modern charts.
Reading symbols in old papers
Old papers sometimes write the absolute temperature as T = t + 460, with t in Fahrenheit. This gives Rankine without naming it. For t = 100 °F, T is 560 °R, which is 38 °C. If you meet the expression, treat it as a Rankine conversion and apply the formula above to reach Celsius.
Computer programs and units
Legacy simulation codes written in English units store temperatures in °R internally. A user who types 15 °C into such a program may get a wrong result unless the input is converted to 518.67 °R. Modern interfaces handle this, but older ones do not. Testing with a known value, such as water boiling at 671.67 °R, reveals the assumption quickly.
Spreadsheet formulas
Place Rankine values in column A and use =A2/1.8-273.15 in column B. For the reverse, use =(B2+273.15)*1.8. For differences, use =A2/1.8, without the subtraction. Format with two decimals, and write the unit in each header, as a table of numbers with no unit is easy to misread.
Rounding and precision
The formula is exact, but old tables are often rounded to one decimal in Rankine, which is 0.06 °C. A value of 518.7 °R converts to 15.02 °C, not exactly 15. Do not over-interpret the third decimal when the source gave only four digits.
A mental shortcut
Multiply by 0.556 and subtract 273. For 540 °R: 300 minus 273 gives 27 °C, against an exact 26.85. For 1,000 °R: 556 minus 273 gives 283 °C, against 282.4. The method is accurate to about one degree, which is enough for checking a report quickly.
Landmarks to memorise
491.67 °R is 0 °C, 518.67 °R is 15 °C, 527.67 °R is 20 °C, 558.27 °R is 37 °C and 671.67 °R is 100 °C. Add 459.67 °R for 0 °F, which is −17.8 °C. With these in mind you can place any Rankine figure on the Celsius scale.
Reference ladder
0 °R is −273.15 °C. 139.2 °R is −195.8 °C. 419.67 °R is −40 °C. 491.67 °R is 0 °C. 540 °R is 26.85 °C. 671.67 °R is 100 °C. 1,391.67 °R is 500 °C. 2,291.67 °R is 1,000 °C. A ladder like this is quick to scan.
Checking by reversing
To check any convert °R to °C result, add 273.15 and multiply by 1.8. If 540 °R became 26.85 °C, then 26.85 plus 273.15 is 300, and 300 times 1.8 returns 540. A second test is the sign: a Rankine value is never negative, and neither is the intermediate kelvin value.
Relation to Fahrenheit
Rankine is Fahrenheit plus 459.67. To convert 527.67 °R, subtract 459.67 to get 68 °F, then convert that with (68 − 32) ÷ 1.8 to get 20 °C. The direct route, 527.67 ÷ 1.8 − 273.15, also gives 20 °C. Using both is a good check on work with mixed units.
Hypersonic flight
At Mach 6 the same formula gives 389.97 × 8.2 = 3,198 °R, which is 1,777 K, or 1,503 °C. At this speed air no longer behaves as an ideal gas, and real temperatures are lower because molecules dissociate. Still, the order of magnitude explains why hypersonic vehicles need special materials and cooling. A “convert °R to °C” calculation on the number puts it in everyday terms.
Temperature differences
A difference of 180 °R is 100 °C. A rise of 27 °R is 15 °C. Never subtract 273.15 from a difference. In heat exchanger work the temperature difference is what matters, and Rankine and Fahrenheit differences are identical, so you convert once at the end.
Writing the unit properly
Write Rankine as °R with a space after the number: 540 °R. Some texts write R alone, which could be read as the gas constant. When quoting in a report, give the unit in full and add the Celsius equivalent in parentheses so that a reader outside the US can follow the numbers.
The wider legacy of English units
The English system survives in American aviation, where altitude is in feet, speed in knots and pressure in inches of mercury. Temperature in the cockpit is in Celsius internationally, but older manuals carry °R in the engine charts. A pilot or engineer who works across eras learns the conversions as a routine skill.
Wind tunnels and old test reports
Mid-century wind tunnel reports list the stagnation temperature of the test gas in °R, for example 560 °R, which is 38 °C, in a blowdown tunnel. A run at Mach 5 may start with air at 1,500 °R, which is 560 °C, to avoid liquefaction during expansion. The test engineers recorded these in Rankine; a modern researcher reading the report needs a “convert °R to °C” calculation for each run.
Museum pieces and archives
Archives of aircraft and engine manuals contain charts with temperatures in °R on the axis. A chart labelled 500 to 700 °R spans 4.6 to 115.7 °C, a plausible range for cabin and cooling air. Scanning old documents, a conservator or historian can quickly guess the scale from the range and from known landmarks such as 491.67 °R for freezing water.
Air data computers and total air temperature
Aircraft temperature probes measure total air temperature, which includes the heating from compression. At Mach 0.8 in air with a static temperature of 389.97 °R, the total temperature is 389.97 × (1 + 0.2 × 0.64) = 439.9 °R, which is −28.8 °C against a static −56.5 °C. Older air data computers worked in °R internally, and a “convert °R to °C” calculation on their outputs reproduces what a modern display shows.
Teaching thermodynamics with English units
Some university courses in the US still teach thermodynamics in English units, with Rankine as the absolute scale, so students solve gas and steam problems in °R, psia and Btu. When they graduate and join an international company they must switch to kelvin, pascals and joules. A short drill with the “convert °R to °C” calculation formula and a few landmarks helps them make the switch without losing marks.
Rocket propellants
Liquid oxygen boils at 162.3 °R, or −183 °C, and liquid hydrogen at 36.5 °R, or −253 °C. A rocket stage with both propellants must be insulated against a temperature difference of about 270 °C with the outside. Documents from the Apollo era give propellant temperatures in °R and engine performance in pounds of thrust, so modern readers convert both.
Combustion chambers
The combustion temperature of a kerosene-oxygen rocket engine is about 3,300 K, or 5,940 °R, or 3,030 °C. The nozzle wall, cooled by fuel, stays at about 900 K, which is 1,620 °R. The difference between gas and wall temperatures is what a regenerative cooling design must handle. Calculations use absolute scales, while public summaries use Celsius, so a “convert °R to °C” calculation bridges the two.
Gas turbine exhaust
Exhaust gas temperature in a jet engine is typically 1,000 to 1,300 °F, which is 1,460 to 1,760 °R, or 538 to 705 °C. Pilots watch this gauge closely at start-up. Engine manuals from the 1950s and 1960s quote °R in thermodynamic tables and °F or °C on cockpit gauges.
Nuclear reactor coolant
A pressurised-water reactor holds primary coolant near 600 °F, which is 1,060 °R, or 315.6 °C, at about 2,250 psi. Boiling-water reactors run at about 550 °F, or 1,010 °R, or 288 °C. Early reports and training manuals from the nuclear industry in the US used all three scales, and a table with the “convert °R to °C” calculation results helps readers cross-check them.
Gas tables and critical temperatures
Gas engineering handbooks list critical temperatures in Rankine: methane 343 °R, which is −82.6 °C, ethane 549.6 °R, or 32.2 °C, propane 665.7 °R, or 96.7 °C, and carbon dioxide 547.6 °R, or 31.1 °C. These show which gases can be liquefied by pressure alone at room temperature: ethane and propane can, methane cannot.
Refrigeration in °R
An old refrigeration text may give the cold-room temperature as 460 °R, which is −17.8 °C, equal to 0 °F. The condenser at 560 °R is 38 °C. The ideal cooling coefficient of performance is 460/100 = 4.6. Because the ratio uses absolute temperatures, Rankine works, and the result is the same as the kelvin calculation 255.4/55.6.
Heat transfer tables
Radiation heat transfer in English units uses the Stefan–Boltzmann constant of 0.1714 × 10⁻⁸ Btu/(h·ft²·°R⁴). A body at 1,000 °R, which is 282 °C, emits 1,714 Btu per hour per square foot. The same body at 2,000 °R, which is 838 °C, emits sixteen times as much. The fourth-power law shows why absolute temperature is required.
More values for convert °R to °C
A longer list of conversions
If the value you need is not in the first list, these further conversions may be close enough to read off directly:
- -273.15 °R = -424.9 °C
- -100 °R = -328.706 °C
- -20 °R = -284.261 °C
- 10 °R = -267.594 °C
- 15 °R = -264.817 °C
- 25 °R = -259.261 °C
- 30 °R = -256.483 °C
- 50 °R = -245.372 °C
Common slips when you convert °R to °C
Mixing up Rankine and Fahrenheit
The degrees are the same size but zero differs. 527.67 °R is 68 °F, not 527.67 °F.
Skipping the division by 1.8
Subtracting 273.15 directly from a Rankine value gives nonsense. 540 °R is not 266.85 °C.
Converting a difference as a temperature
A change of 18 °R is a change of 10 °C, with no 273.15 involved.
Quick questions
What is the method for a “convert °R to °C” calculation?
Divide by 1.8, then take away 273.15.
What is 540 °R in degrees Celsius?
26.85 °C.
What is 491.67 °R in degrees Celsius?
0 °C.
What is 0 °R in degrees Celsius?
−273.15 °C.
Is my figure stored or sent?
No, it stays on your device.
Where to go next
Other temperature converters are listed here: Convert °R to K, Convert °R to °F, Convert °F to °C, Convert K to °C, Convert °C to °Ré, Convert km to mi, Convert mi to km, Convert L to gal, Convert gal to L. If you need the opposite direction, use Convert °C to °R.
The takeaway: a “convert °R to °C” calculation divides by 1.8, subtracts 273.15 and writes °C beside the answer. The figure you enter is processed on your device only.