Convert °C to °R degrees Celsius ↔ degrees Rankine Free Online Secure
Type a temperature in degrees Celsius and read it in degrees Rankine 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 °C to °R (degrees Celsius ↔ degrees Rankine)
| °C | °R |
|---|---|
| -40 | 419.67 |
| -10 | 473.67 |
| 0 | 491.67 |
| 10 | 509.67 |
| 20 | 527.67 |
| 25 | 536.67 |
| 37 | 558.27 |
| 100 | 671.67 |
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
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.
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.
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.
The Rankine scale: the forgotten absolute scale, from Celsius
Almost everyone knows Celsius, Fahrenheit and kelvin. Fewer have met the Rankine scale, proposed by the Scottish engineer William Rankine in 1859. It starts at absolute zero like the kelvin, but its degrees are the size of Fahrenheit degrees, which made it handy for engineers who worked with English units. To convert °C to °R, add 273.15 and multiply by 9/5: 0 °C is 491.67 °R, 25 °C is 536.67 °R and 100 °C is 671.67 °R. The calculator above does both steps as you type, and the sections below tell the story of the scale, where it still appears and what its numbers mean.
You will find the formula with worked examples, a short profile of each scale, a comparison, a long set of cases from the history of engineering and the slips to avoid. The arithmetic runs in your browser, and what you type is not sent anywhere.
How to convert °C to °R: add 273.15, then multiply by 9/5
The formula
The formula is °R = (°C + 273.15) × 9/5, which is the same as °C × 1.8 + 491.67. So 15 °C is (15 + 273.15) × 1.8 = 518.67 °R, 37 °C is 558.27 °R and −40 °C is 419.67 °R. To go back, divide by 1.8 and subtract 273.15.
Worked examples
Water freezes at 0 °C, which is 491.67 °R, and boils at 100 °C, which is 671.67 °R. Liquid nitrogen at −195.8 °C is 139.2 °R. Steam at 500 °C is 1,391.67 °R, and absolute zero, −273.15 °C, is 0 °R.
Why two steps
Rankine begins at absolute zero, so first you shift the Celsius value by 273.15 to reach kelvin. Then you stretch the degree: a Rankine degree is 5/9 of a kelvin, so you multiply by 9/5.
A quick sanity test
Whatever the input, the Rankine figure must be exactly 1.8 times the kelvin figure. If it is not, the offset or the factor was misapplied.
The Celsius scale
The scale of water
The Celsius scale puts 0 at the freezing point of water and 100 at the boiling point at standard pressure. It is the scale of nearly all countries and the base of kelvin in science.
Where it appears
Thermometers, weather forecasts, laboratories and international standards.
The Rankine scale
An absolute scale in Fahrenheit-sized degrees
Rankine is an absolute thermodynamic scale with zero at absolute zero. One degree Rankine equals one degree Fahrenheit, and the symbol is °R. It was introduced by William John Macquorn Rankine, who held the chair of civil engineering and mechanics at Glasgow.
Where it appears
American thermodynamics textbooks, steam and gas tables in English units, and some aerospace and nuclear handbooks.
Celsius against Rankine
One Celsius degree equals 1.8 Rankine degrees. A rise of 10 °C is a rise of 18 °R. The absolute values are connected by the formula: 20 °C is 527.67 °R. Because Rankine is an absolute scale, ratios of temperatures are the same in Rankine as in kelvin, which is why it works in gas-law and efficiency formulas, while Celsius does not.
The formula is exact, so rounding happens only in the displayed answer. The usual slips are mixing Rankine with Fahrenheit and mixing the scale with the Rankine cycle.
Where the conversion shows up
English-unit property tables
Thermodynamics texts written for American students tabulate air and steam properties in English units. Entropy is in Btu per pound per degree Rankine, and the gas constant for air is 53.35 ft·lbf/(lbm·°R). A student with data in Celsius must run a “convert °C to °R” calculation before looking up or using a value.
Standard atmosphere
The standard atmosphere at sea level is 15 °C, or 518.67 °R. In the lower stratosphere it is −56.5 °C, or 389.97 °R. Aircraft performance charts use the ratio of local to sea-level temperature, a dimensionless number computed from absolute temperatures.
Gas laws
In English units the gas law is written with a universal constant of 10.73 psia·ft³ per lbmol per °R. Using Fahrenheit or Celsius would give nonsense. Engineers first convert to Rankine, then compute. The same arithmetic in SI uses kelvin and 8.314 J/(mol·K).
William Rankine, the engineer
William Rankine, born in Edinburgh in 1820, was a civil engineer who became professor at Glasgow in 1855. He worked on steam engines, shipbuilding, soil and structures and published widely, including a famous manual of applied mechanics. He introduced the terms potential energy and actual energy, the latter later renamed kinetic. He also wrote humorous songs about science, some of which are still sung.
The ideal gas law in a workshop
A compressed-air tank of 10 cubic feet at 100 psia and 520 °R holds about 0.18 pound-moles of air. Heat the tank to 560 °R and the pressure rises by 7.7 per cent, to 107.7 psia. Doing the same in Celsius would require converting both temperatures to an absolute scale first, so the “convert °C to °R” calculation step is unavoidable.
Refrigeration
American refrigeration texts compute the coefficient of performance with Rankine temperatures. For an evaporator at 5 °F, which is 464.67 °R, and a condenser at 100 °F, or 559.67 °R, the Carnot cooling COP is 464.67 divided by 95, which is 4.89. The same answer in kelvin comes from 258.15 divided by 52.8. The ratio is scale-independent as long as the scale is absolute.
Heat transfer by radiation
In English units the Stefan–Boltzmann constant is 0.1714 × 10⁻⁸ Btu per hour per square foot per °R⁴. A surface at 540 °R, which is 300 K, radiates about 146 Btu per hour per square foot. In SI the same surface emits 459 W/m². A “convert °C to °R” calculation converts temperatures, and a separate factor converts the heat flux.
Chemical engineering
Process engineers working in the US petroleum industry used Rankine in older equations of state and correlation charts. Pseudo-critical temperatures of gas mixtures were tabulated in °R. Natural gas with a pseudo-critical temperature of 400 °R is at 222 K, which is −51 °C. Modern software uses kelvin, but legacy charts survive in many handbooks.
Gas turbines
A gas turbine's temperature ratio between the combustor and the compressor inlet is a key design number. With a turbine inlet at 1,500 K, or 2,700 °R, and air at 288 K, or 518 °R, the ratio is 5.2 in either scale. Engineers in the US report these in Rankine, those elsewhere in kelvin, and the ratio does not depend on the choice.
Spreadsheet formulas
Place Celsius values in column A and use =(A2+273.15)*9/5 in column B. For the reverse, use =B2/1.8-273.15. For temperature differences, multiply by 1.8 and add nothing. Label every column with its unit, and use two decimals for values near room temperature.
Rounding and precision
The formula is exact, so a Rankine value has as many correct digits as the Celsius input. Tables list sea-level standard temperature as 518.67 °R. Rounding to 519 is fine for rough work, but not for tables that feed other calculations, where rounding errors compound.
A mental shortcut
Multiply the Celsius value by 1.8 and add 492. For 20 °C that gives 36 plus 492, which is 528, against an exact 527.67. For 100 °C it gives 180 plus 492, which is 672, against 671.67. It is accurate to under half a degree, which is enough for estimates.
Landmarks to memorise
0 °C is 491.67 °R, 15 °C is 518.67 °R, 20 °C is 527.67 °R, 37 °C is 558.27 °R and 100 °C is 671.67 °R. With these you can place any value in an English-unit table. Remember that the Rankine value is always 1.8 times the kelvin value.
Reference ladder
−273.15 °C is 0 °R. −196 °C is 138.9 °R. −40 °C is 419.67 °R. 0 °C is 491.67 °R. 25 °C is 536.67 °R. 100 °C is 671.67 °R. 500 °C is 1,391.67 °R. 1,000 °C is 2,291.67 °R. A ladder like this speeds up checks.
Why Rankine proposed a scale
In 1848 William Thomson, later Lord Kelvin, had proposed an absolute scale with Celsius-sized degrees. Engineers who used Fahrenheit still needed an absolute scale in their own units. Rankine's solution, in 1859, kept the Fahrenheit degree and moved the zero to absolute zero. It was practical for steam tables and for the formulas of the Industrial Revolution.
Checking by reversing
To check any convert °C to °R result, divide by 1.8 and subtract 273.15. If 25 °C became 536.67 °R, then 536.67 divided by 1.8 is 298.15, and subtracting 273.15 gives 25. A second test is the sign: Rankine can never be negative.
Relation to Fahrenheit
Rankine is Fahrenheit plus 459.67. So 77 °F is 536.67 °R, the same as 25 °C. You can reach Rankine from Celsius via Fahrenheit, with °C × 1.8 + 32 and then plus 459.67, which equals °C × 1.8 + 491.67, the formula above. Both routes agree.
Writing the unit correctly
Write the symbol as °R, with a degree sign and a space after the number: 527.67 °R. Unlike the kelvin, Rankine keeps the degree sign. In some American texts a bare R appears, which could be confused with the gas constant, so context matters.
Temperature differences
When a compressor raises air by 25 °C, the rise is 45 °R. A difference of 100 °C is 180 °R. Never add 491.67 to a difference. In heat transfer tables, a temperature drop appears as ΔT in °F or °R, which are identical, and you convert once at the end.
Reading old engineering books
Nineteenth- and early twentieth-century books on steam and gas often used Fahrenheit and Rankine together. Reading them requires care with the symbols. A temperature that looks like 460 + t is the Rankine value. When you see that expression, a “convert °C to °R” calculation or a Fahrenheit conversion tells you the Celsius value of the original.
Cryogenic wind tunnels
Some wind tunnels cool their nitrogen working gas to around 100 K, which is 180 °R, so that the gas is denser and the Reynolds number rises, letting small models behave like large aircraft. A test at 100 K and a test at ambient 288 K differ in temperature by a factor of 2.9 in any absolute scale. Researchers log the data in kelvin, while an English-unit report would use Rankine, and a “convert °C to °R” calculation links them.
Heat exchanger effectiveness
The effectiveness of a heat exchanger is the heat actually transferred divided by the maximum possible, a ratio of temperature differences. A difference of 30 °C is 54 °R, and a difference of 50 °C is 90 °R, so the ratio is 0.6 in either scale. Because the ratio uses differences, Celsius is allowed here, and the “convert °C to °R” calculation step is needed only for absolute values.
Students and exams
An exam question may give a gas at 80 °F and ask for a pressure ratio after heating to 200 °F. The correct approach converts to Rankine, 539.67 °R and 659.67 °R, giving a ratio of 1.222. Using the Fahrenheit numbers directly gives 2.5, which is wrong. Examiners often include this trap, so a quick conversion at the start is a good habit.
The Rankine cycle
The Rankine cycle, named for the same engineer, describes how a steam power plant works: water is pumped to pressure, boiled to steam, expanded in a turbine and condensed. Its ideal efficiency is below that of the Carnot cycle between the same temperatures. For steam at 500 °C, which is 1,391.67 °R, and a condenser at 33 °C, or 551.9 °R, the Carnot limit is 60 per cent, and a real simple cycle reaches about 38 per cent.
Rankine and shock waves
The Rankine–Hugoniot relations describe how pressure, density and temperature change across a shock wave. Across a normal shock at Mach 2 the static temperature rises by a factor of 1.687. Air at −56.5 °C, or 389.97 °R, behind such a shock is at 657.9 °R, which is 92 °C. The ratio is the same in any absolute scale, but not in Celsius.
The Rankine vortex
The Rankine vortex is a simple model of a whirlpool or tornado: a core that rotates like a solid wheel and an outer region where speed falls off with distance. It is named for the same engineer, but has no direct relation to the temperature scale. Students meet both names in fluid mechanics and thermodynamics courses.
Rankine and soil
In soil mechanics, Rankine's earth pressure theory gives the horizontal pressure of soil on a retaining wall. For a soil with a friction angle of 30 degrees, the active pressure coefficient is one third. Civil engineers learn this alongside the temperature scale only by name, but the connection shows how broad Rankine's work was.
Why not just use kelvin
The kelvin is the standard, and most modern textbooks use it. Rankine survives where English units survive, for example in older American data and software that stores everything in feet, pounds and Btu. Converting at the boundary with a “convert °C to °R” calculation is safer than rewriting decades of tables.
Specific heat and the Btu
The British thermal unit is the heat needed to raise a pound of water by one degree Fahrenheit, or one degree Rankine, since the sizes match. This gives water a specific heat of 1 Btu per pound per °R. In SI it is 4.1868 kJ per kg per K. The numbers are linked by 4.1868, not by 1.8, since mass and energy units also change.
Entropy and the second law
Entropy change equals heat divided by absolute temperature. Heat of 1 Btu transferred at 600 °R changes entropy by 1/600 Btu per °R. In SI the same heat is 1.055 kJ at 333 K, which is 0.00317 kJ/K. Formulas of the second law need absolute scales, so Rankine and kelvin both work, and Celsius and Fahrenheit do not.
More values for convert °C to °R
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 °C = 0 °R
- -100 °C = 311.67 °R
- -20 °C = 455.67 °R
- 10 °C = 509.67 °R
- 15 °C = 518.67 °R
- 25 °C = 536.67 °R
- 30 °C = 545.67 °R
- 50 °C = 581.67 °R
Common slips when you convert °C to °R
Confusing Rankine with Fahrenheit
The degrees have the same size but different zero points. 68 °F is 527.67 °R, not 68 °R.
Forgetting 273.15
Multiplying by 1.8 alone is wrong. 20 °C is not 36 °R but 527.67 °R.
Converting a difference as a temperature
A rise of 10 °C is a rise of 18 °R, with no 491.67 added.
Short answers
How do I convert °C to °R?
Add 273.15 and multiply by 1.8.
What is 20 °C in Rankine?
527.67 °R.
What is 0 °C in Rankine?
491.67 °R.
What is absolute zero in Rankine?
0 °R.
Does my number leave my device?
No, the calculation runs in your browser.
More pages and a wrap-up
For other temperature conversions see Convert °C to K, Convert °C to °Ré, Convert °F to °R, Convert K to °R, Convert °R to K, Convert km to mi, Convert mi to km, Convert L to gal, Convert gal to L. The reverse direction is Convert °R to °C.
In short, a “convert °C to °R” calculation means adding 273.15 and multiplying by 1.8, then writing the unit beside the answer. Your number is computed locally, with no account and no upload.