Convert °R to °F degrees Rankine ↔ degrees Fahrenheit Free Online Secure
Type a temperature in degrees Rankine and read it in degrees Fahrenheit 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 °F (degrees Rankine ↔ degrees Fahrenheit)
| °R | °F |
|---|---|
| 0 | -459.67 |
| 200 | -259.67 |
| 400 | -59.67 |
| 491.67 | 32 |
| 527.67 | 68 |
| 558.27 | 98.6 |
| 671.67 | 212 |
| 1000 | 540.33 |
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.
Is it true that −40 °C and −40 °F are the same?
Yes, and it is the only place the two scales meet. Fahrenheit degrees are smaller than Celsius ones — nine of them to every five — and the two scales start from different zeros; the one temperature where the difference in size and the difference in starting point cancel out exactly is minus forty. Below that, the Fahrenheit number is the lower of the two.
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.
HVAC formulas and chiller sheets: Rankine into Fahrenheit
The American heating, cooling and ventilation trade runs on Fahrenheit, yet its formulas for air density, gas behaviour and ideal efficiency are written for absolute temperature in Rankine. A technician reading a calculation that says 527.67 °R needs to know that this is a 68 °F room. To convert °R to °F, subtract 459.67: 491.67 °R is 32 °F, 527.67 °R is 68 °F and 671.67 °R is 212 °F. The calculator above subtracts as you type, and the sections below show how the Rankine figures in air-conditioning, ventilation and chiller calculations map back onto the thermostat scale.
You will find the formula with worked examples, a short profile of each scale, a comparison, a set of practical cases from building services and the slips to avoid. The arithmetic runs in your browser, and what you type is not sent anywhere. For design work, rely on a licensed engineer.
How to convert °R to °F: subtract 459.67
The formula
The formula is °F = °R − 459.67. So 559.67 °R is 100 °F, 459.67 °R is 0 °F and 0 °R is −459.67 °F. To go the other way, add 459.67. For quick work, many technicians subtract 460, which is accurate within a third of a degree.
Worked examples
A supply air temperature of 514.67 °R is 55 °F. A room at 529.67 °R is 70 °F. A chilled-water temperature of 503.67 °R is 44 °F. A boiler water temperature of 639.67 °R is 180 °F, and a steam temperature of 859.67 °R is 400 °F.
Why only a subtraction
A Rankine degree and a Fahrenheit degree are the same size, so no scaling is needed. The scales differ only in their zero points. Absolute zero is 0 °R and −459.67 °F.
A quick sanity test
The Fahrenheit figure is always 459.67 lower. If a “convert °R to °F” calculation result is higher than the input, you added instead of subtracting.
The Rankine scale
Absolute temperature in Fahrenheit-sized degrees
Rankine starts at absolute zero, so every value is positive. It appears in formulas that need a true temperature ratio, such as air density and the efficiency of ideal cycles, in the English-unit world of building services.
Where it appears
Design formulas, engineering handbooks and ASHRAE-style reference tables.
The Fahrenheit scale
The scale on every American thermostat
Fahrenheit has 32 at freezing and 212 at boiling. It is the scale of thermostats, gauges, chilled-water set points and equipment nameplates in the United States, so every calculation result is eventually translated back into it.
Where it appears
Thermostats, nameplates, commissioning sheets and service gauges.
Rankine against Fahrenheit
The scales have the same degree. A temperature difference of 20 degrees is the same number in both. The absolute values differ by 459.67, so 70 °F is 529.67 °R. Because Rankine starts at absolute zero, ratios such as 559.67 to 529.67 are physically meaningful, while the ratio of 100 to 70 Fahrenheit is not.
The subtraction is exact, so rounding appears only in the displayed result. The usual slips are forgetting the sign below 459.67 °R and applying the conversion to a difference.
Where the conversion shows up
Air density
ASHRAE-style tables give air density as 1.325 times the pressure in inches of mercury divided by the absolute temperature in °R. At 29.92 inHg and 527.67 °R, which is 68 °F, density is 0.0751 lb/ft³. At 95 °F, or 554.67 °R, it falls to 0.0715. A “convert °R to °F” calculation turns the intermediate Rankine figure back into the thermostat number.
Sensible heat formula
The familiar formula Q = 1.08 × CFM × ΔT in Btu per hour comes from 60 minutes times 0.075 lb/ft³ times 0.24 Btu per pound per degree. The ΔT is a difference, so it is the same in °F and °R. Air at 20 degrees above the room, moving at 1,000 CFM, carries 21,600 Btu per hour.
Chiller efficiency limits
A chiller with chilled water at 44 °F, or 503.67 °R, and condenser water at 85 °F, or 544.67 °R, has an ideal coefficient of performance of 503.67 divided by 41, which is 12.3. That corresponds to 0.29 kW per ton, against a real figure of about 0.6. The ratio needs absolute temperatures.
Superheat and subcooling
Technicians measure superheat as the temperature of the suction line minus the saturation temperature at the suction pressure. A typical superheat of 10 to 15 degrees is the same number in °F and °R. If a handbook gives the saturation temperature as 499.67 °R and the line is at 512.17 °R, the superheat is 12.5 degrees, and the line is at 52.5 °F.
Ductwork and expansion
Galvanised steel duct expands by about 0.0000067 per °F. A 100 ft run heated from 60 °F to 180 °F, a rise of 120 degrees, grows by 0.96 inch. The difference is the same in Rankine. Expansion joints are specified in inches per 100 ft per 100 °F, so a technician needs only the difference, not the absolute scale.
Glycol and freeze protection
A 30 per cent propylene glycol solution freezes near 8 °F, or 467.67 °R, and a 40 per cent solution near −5 °F, or 454.67 °R. Cold-climate hydronic systems choose the mix according to the lowest design temperature. Burst protection is lower than freeze point, so labels give both numbers in Fahrenheit.
Dehumidification
Air at 75 °F and 50 per cent relative humidity has a dew point near 55 °F, which is 514.67 °R. A cooling coil below that temperature removes moisture. A coil at 45 °F, or 504.67 °R, removes more. Psychrometric charts are drawn with Fahrenheit axes, but the calculations behind them use absolute temperature in the gas law for water vapour.
Gas-fired equipment
A furnace with a flue gas at 400 °F, or 859.67 °R, loses more heat than one at 300 °F, or 759.67 °R. A condensing furnace brings the gas down to 120 °F, or 579.67 °R, and so recovers latent heat. Efficiency calculations use the flue temperature rise above the room, which is a difference, and the “convert °R to °F” calculation step is needed only for gas density.
Spreadsheet formulas
Place Rankine values in column A and use =A2-459.67 in column B. For the reverse, use =B2+459.67. For differences, copy the value unchanged. Format with one decimal and label every column with its unit, so that the sheet can be handed to a colleague without a note.
Rounding and precision
The subtraction is exact. Field thermometers read to a degree, so quoting 527.67 °R for a 68 °F room adds nothing. Give Rankine figures to one or two decimals in calculations, and round the final result to the resolution of the controller, usually one degree.
A mental shortcut
Subtract 460 and add a third. For 530 °R: 70 plus 0.33 gives 70.33 °F, close to the exact 70.33. For 560 °R: 100.33 °F. In the field, 460 is the number every technician remembers, and the third of a degree rarely matters.
Landmarks to memorise
459.67 °R is 0 °F, 491.67 °R is 32 °F, 519.67 °R is 60 °F, 529.67 °R is 70 °F, 559.67 °R is 100 °F and 671.67 °R is 212 °F. These six cover most of the temperatures in building services work.
Reference ladder
0 °R is −459.67 °F. 419.67 °R is −40 °F. 459.67 °R is 0 °F. 491.67 °R is 32 °F. 503.67 °R is 44 °F. 514.67 °R is 55 °F. 529.67 °R is 70 °F. 559.67 °R is 100 °F. 671.67 °R is 212 °F. A ladder like this makes a quick scan possible.
Checking by reversing
To check any convert °R to °F result, add 459.67 and see whether you return to the start. If 529.67 °R became 70 °F, then 70 plus 459.67 is 529.67. A second test is the sign: the Fahrenheit value must be lower, and it turns negative below 459.67 °R.
Altitude and air density
At 5,000 ft the pressure is about 24.9 inHg, and the same formula gives a density of 0.0625 lb/ft³ at 527.67 °R, 17 per cent lower than at sea level. Fans move the same volume, but the mass of air and the heat it carries are smaller. A designer corrects capacities by the density ratio and states temperatures in Fahrenheit on the drawings.
Link with kelvin and Celsius
Rankine divided by 1.8 gives kelvin. 529.67 °R is 294.26 K, which is 21.1 °C. Engineers on international projects switch between the three. The shortest route from Rankine to Celsius is dividing by 1.8 and subtracting 273.15, while the route through Fahrenheit takes two steps but is easier to check against a thermostat.
Temperature differences
A difference of 18 °R is a difference of 18 °F, and also of 10 K or 10 °C. Never subtract 459.67 from a difference. The common ΔT of 20 degrees across a coil is the same in °F and °R, and is 11.1 K in the SI system.
Writing the unit properly
Write Rankine as °R and Fahrenheit as °F, each with a space after the number. In a design document, state the scale at the head of every column. A table that mixes °R for density and °F for set points should say so, as a reader skimming might otherwise take 529.67 for a room temperature.
Software and sensors
Building automation systems store temperatures in Fahrenheit or Celsius and convert to absolute when a calculation needs it. A sensor reading of 70.0 °F that appears in an equation as 529.67 °R shows the conversion at work. If a point shows 529.67 on a trend graph, someone has wired the wrong variable, and the “convert °R to °F” calculation step identifies the problem at once.
Commissioning checks
During commissioning, engineers compare measured temperatures with design values. A design supply air of 55 °F, or 514.67 °R, and a measured value of 58 °F, or 517.67 °R, differ by 3 degrees. Whether that is acceptable depends on tolerance, usually 2 to 3 degrees. The comparison is done in Fahrenheit, and Rankine is used only for calculated values like air density.
Fan laws and temperature
When the temperature of the air in a duct system changes, the mass flow through a fixed fan changes with density, which is inversely proportional to absolute temperature. Air at 70 °F is 529.67 °R, and at 140 °F it is 599.67 °R, so the mass flow drops by 11.7 per cent. A technician commissioning a heating coil adjusts airflow targets, and a quick convert °R to °F translates the Rankine figure back to the thermostat reading.
Compressed air in a plant
An air compressor in a plant room lifts air from 80 °F to over 300 °F at the discharge. In absolute terms it is 539.67 °R rising to 759.67 °R or more, depending on the pressure ratio. The aftercooler brings the air back to within 15 degrees of the cooling water. Maintenance staff track the discharge and aftercooler outlet temperatures in Fahrenheit, but the ideal work calculation uses Rankine.
Heat pump limits
An ideal heat pump heating a building at 70 °F from outdoor air at 17 °F has a limit of 529.67 divided by 53, which is 10. Real machines manage 2.5 to 4 at that temperature. The absolute scale is used for the limit, while the nameplate gives performance at 47 °F and 17 °F, which are 506.67 °R and 476.67 °R.
Heat recovery ventilators
The effectiveness of a heat recovery ventilator is a ratio of temperature differences. With outdoor air at 10 °F, indoor at 70 °F and supply air at 65 °F, the effectiveness is 55 divided by 60, which is 0.92. These differences are the same in Rankine and Fahrenheit. Only when absolute values enter, as in density, must a “convert °R to °F” calculation be used.
Cooling towers
A cooling tower cools water to within a few degrees of the wet-bulb temperature. With a wet bulb of 78 °F, or 537.67 °R, the leaving water might be 85 °F, or 544.67 °R. The approach is 7 degrees. Tower ratings are written in Fahrenheit, while the heat and mass transfer equations behind them work with absolute temperatures.
Boilers and steam
A low-pressure steam boiler runs at 5 psig, with steam at about 228 °F, or 687.7 °R. A high-pressure unit at 150 psig produces steam at 366 °F, or 825.7 °R. Steam tables list the temperature in Fahrenheit and pressure in psia, with entropy per °R. Technicians use the Fahrenheit column and rarely see Rankine.
Refrigerant saturation charts
Pressure-temperature charts list saturation temperatures in Fahrenheit for each refrigerant. Behind them, thermodynamic software works in Rankine or kelvin. For R-410A at 118 psig, the saturation temperature is about 40 °F, or 499.67 °R. A technician reads the chart in °F and never needs the absolute scale, unless writing the equations that produced it.
Ice and thermal storage
Ice thermal storage makes ice at 25 °F, or 484.67 °R, and releases cooling at 34 to 40 °F. The latent heat of water is 144 Btu per pound, which is 334 kJ/kg. A tank of 20,000 pounds of ice stores 2.88 million Btu, or 240 ton-hours. The temperatures in the design are in Fahrenheit, while efficiency limits use Rankine.
Absorption chillers
Absorption chillers run on heat, such as steam at 250 °F or hot water at 190 °F, which are 709.67 °R and 649.67 °R. Their efficiency limit depends on three absolute temperatures: the heat source, the cooling water and the chilled water. Manufacturers state the three in Fahrenheit, and a designer working out the limit converts all of them with a “convert °R to °F” calculation.
More values for convert °R to °F
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 = -732.82 °F
- -100 °R = -559.67 °F
- -20 °R = -479.67 °F
- 10 °R = -449.67 °F
- 15 °R = -444.67 °F
- 25 °R = -434.67 °F
- 30 °R = -429.67 °F
- 50 °R = -409.67 °F
Common slips when you convert °R to °F
Forgetting the sign
Below 459.67 °R the Fahrenheit value is negative. 419.67 °R is −40 °F, not 40 °F.
Converting a difference
A difference of 20 degrees is 20 degrees in both scales. Do not subtract 459.67.
Confusing Rankine with kelvin
The scales differ by a factor of 1.8. 529.67 °R is 294.26 K, not 529.67 K.
Quick questions
What is the method for a “convert °R to °F” calculation?
Take away 459.67.
What is 527.67 °R in degrees Fahrenheit?
68 °F.
What is 491.67 °R in degrees Fahrenheit?
32 °F.
What is 0 °R in degrees Fahrenheit?
−459.67 °F.
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 °C, Convert °R to K, Convert K to °F, Convert °Ré to °F, Convert °F to K, Convert km to mi, Convert mi to km, Convert L to gal, Convert gal to L. If you need the opposite direction, use Convert °F to °R.
The takeaway: a “convert °R to °F” calculation subtracts 459.67 and labels the result °F. The figure you enter is processed on your device only.