Convert °F to °R degrees Fahrenheit ↔ degrees Rankine Free Online Secure
Type a temperature in degrees Fahrenheit 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 °F to °R (degrees Fahrenheit ↔ degrees Rankine)
| °F | °R |
|---|---|
| -40 | 419.67 |
| 0 | 459.67 |
| 32 | 491.67 |
| 50 | 509.67 |
| 68 | 527.67 |
| 77 | 536.67 |
| 98.6 | 558.27 |
| 212 | 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
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.
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.
Worked problems with an absolute temperature: Fahrenheit into Rankine
Thermodynamics and physics classes in the United States hand out problems such as "a tyre at 50 °F is warmed to 95 °F" or "a can at 70 °F is heated to 130 °F". The right answer needs an absolute temperature, and when the data are in Fahrenheit the natural choice is the Rankine scale. To convert °F to °R, add 459.67: 32 °F is 491.67 °R, 70 °F is 529.67 °R and 212 °F is 671.67 °R. The calculator above adds as you type, and the sections below walk through typical problems that show why the conversion matters and how to avoid the classic mistakes.
You will find the formula with worked examples, a short profile of each scale, a comparison, a collection of solved problems and the slips to avoid. The arithmetic runs in your browser, and what you type is not sent anywhere.
How to convert °F to °R: add 459.67
The formula
The formula is °R = °F + 459.67. So 75 °F gives 534.67 °R, 100 °F gives 559.67 °R and −40 °F gives 419.67 °R. To go back, subtract 459.67. Many textbooks round the constant to 460, which is fine for quick work.
Worked examples
Room air at 70 °F is 529.67 °R. Body temperature, 98.6 °F, is 558.27 °R. A fever of 104 °F is 563.67 °R. Liquid nitrogen at −320 °F is 139.67 °R, and absolute zero at −459.67 °F is 0 °R.
Why only an addition
A Rankine degree and a Fahrenheit degree are the same size. The scales differ only in their zero points, which are 459.67 degrees apart, so one addition does the whole job.
A quick sanity test
Rankine is always 459.67 above Fahrenheit. If your “convert °F to °R” calculation result is lower than the input, you subtracted instead of adding.
The Fahrenheit scale
The everyday American scale
Fahrenheit puts 32 at the freezing point of water and 212 at the boiling point. It is the scale of American thermometers, weather reports and textbook problems, so most data in a US course arrive in these degrees.
Where it appears
Thermometers, textbook problems, appliance labels and weather reports.
The Rankine scale
The absolute scale in English units
Rankine begins at absolute zero and uses degrees the size of Fahrenheit degrees. It never goes negative, so it can be used directly in gas laws, efficiency formulas and radiation laws. The symbol is °R.
Where it appears
American thermodynamics courses, engineering handbooks and gas tables.
Fahrenheit against Rankine
The two scales have the same step, so a change of 50 °F is a change of 50 °R. Only the zero point differs. This matters for ratios: 100 °F is not twice as hot as 50 °F, but 559.67 °R is 1.098 times 509.67 °R. A physical law that uses a ratio of temperatures must use an absolute scale.
The addition is exact, so rounding appears only in the displayed result. The trap is applying a gas law to Fahrenheit numbers directly.
Where the conversion shows up
Problem 1: a warming tyre
A tyre is inflated to 32 psig at 50 °F and driven until it reaches 95 °F. Convert to absolute: pressure is 46.7 psia, and the temperatures are 509.67 °R and 554.67 °R. The ratio is 1.088, so the new pressure is 50.8 psia, which is 36.1 psig. Using Fahrenheit directly would give an absurd answer, which is why a “convert °F to °R” calculation comes first.
Problem 2: a heated aerosol can
A can at 70 psig and 70 °F is heated to 130 °F. Absolute pressure is 84.7 psia, temperatures are 529.67 °R and 589.67 °R. The final pressure is 94.3 psia, which is 79.6 psig. That is why cans carry a warning not to store them above 120 °F.
Problem 3: moles of air
How much air is in 10 cubic feet at 14.7 psia and 70 °F? Using n = PV/RT with R = 10.73 psia·ft³/(lbmol·°R) and T = 529.67 °R, n is 0.0259 lbmol, which is 0.75 lb of air. The temperature must be in Rankine for the value of R to apply.
Problem 4: a balloon in a warm room
A balloon holds 1 ft³ of air at 70 °F. In a warmer room at 100 °F, with the same pressure, it holds 559.67/529.67 = 1.057 ft³. The balloon grows 5.7 per cent. Charles's law uses absolute temperature, so a student who divides 100 by 70 gets 1.43 and a balloon that is almost half again as big, which is plainly wrong.
Problem 5: ram air in flight
An aircraft at Mach 0.8 in air at 60 °F, or 519.67 °R, has a stagnation temperature of 519.67 × (1 + 0.2 × 0.64) = 586.2 °R, which is 126.5 °F. The air on the nose is 66 degrees warmer. Pilots see this as the difference between total and static air temperature. A “convert °F to °R” calculation gives the starting value.
Common-sense checks
Before you submit an answer, check that every temperature in a gas-law formula is absolute and positive. A value like 70 or 100 in a ratio is a warning. Another check is to compare the size of the change: a ratio near 1.05 is typical for a 30-degree change at room temperature, while a ratio of 1.4 means something has gone wrong.
Liquid nitrogen and helium
Liquid nitrogen at −320 °F is 139.7 °R, liquid oxygen at −297 °F is 162.7 °R and liquid helium at −452 °F is 7.7 °R. These small positive numbers show how close the liquids are to absolute zero. Dividing by 1.8 gives 77.6, 90.4 and 4.3 K, the figures used in cryogenic engineering in the rest of the world.
The human body
Body temperature of 98.6 °F is 558.27 °R, and a fever of 104 °F is 563.67 °R, only 1 per cent higher in absolute terms. Heat-transfer models of the body use absolute temperature for radiation, where the difference between skin at 91 °F and a wall at 68 °F shows up as a fourth-power term.
Dry ice and the cold
Dry ice sublimes at −109.3 °F, which is 350.4 °R. Cooled to that temperature, a sealed container of gas loses pressure in proportion to the absolute temperature. A bottle sealed at 70 °F and moved to −109 °F drops to 66 per cent of its pressure, since 350.4/529.67 = 0.66. This would not show with Fahrenheit numbers.
Spreadsheet formulas
Place Fahrenheit values in column A and use =A2+459.67 in column B. For the reverse, use =B2-459.67. For ratios, divide the two Rankine columns directly. Format with two decimals and write the unit in each header. Keep a column of the original values for traceability.
Rounding and precision
Textbooks often round 459.67 to 460. For a ratio of temperatures near 530 °R, the error is 0.06 per cent, which is negligible. For precision work, such as calibrating instruments, keep all digits. Report results with the same number of significant figures as the least precise input.
A mental shortcut
Add 460, then remove one third. For 70 °F that gives 530 − 0.33 = 529.67. For 212 °F it gives 672 − 0.33 = 671.67. In quick estimates 460 is enough, and the correction is only needed for precise tables.
Landmarks to memorise
0 °F is 459.67 °R, 32 °F is 491.67 °R, 59 °F is 518.67 °R, 68 °F is 527.67 °R, 98.6 °F is 558.27 °R and 212 °F is 671.67 °R. With these six, you can place any problem on the scale at a glance.
Reference ladder
−459.67 °F is 0 °R. −320 °F is 139.7 °R. −40 °F is 419.67 °R. 0 °F is 459.67 °R. 32 °F is 491.67 °R. 100 °F is 559.67 °R. 212 °F is 671.67 °R. 1,000 °F is 1,459.67 °R. A ladder like this speeds up checking.
Problem 6: combined gas law
5 ft³ of air at 14.7 psia and 70 °F is compressed to 44.7 psia and heated to 200 °F. The volume is 5 × (14.7/44.7) × (659.67/529.67) = 2.05 ft³. Each ratio is taken from absolute quantities. The final answer shows that compression to three times the pressure reduces the volume by 59 per cent, not 67, because the gas is hotter.
Checking by reversing
To check any convert °F to °R result, subtract 459.67 and see whether you return to the start. If 75 °F became 534.67 °R, then 534.67 minus 459.67 is 75. A second test is the sign: Rankine is never negative, so a negative answer means the input was below absolute zero, which cannot occur.
Link with the kelvin
Rankine equals 1.8 times the kelvin value. 527.67 °R is 293.15 K, which is 20 °C. Students who want to cross-check a result can convert the same temperature to kelvin and compare, since both are absolute scales. The ratio of temperatures should come out the same.
Temperature differences
A change of 50 °F is a change of 50 °R. A change of 25 °F is 25 °R. Never add 459.67 to a difference. In energy balances, q = m cp ΔT, the difference is used, so Fahrenheit and Rankine give the same heat, and a conversion is needed only when absolute values enter.
Writing the unit properly
Write Rankine as °R, with a space after the number, for example 529.67 °R. Some textbooks write R alone, which can be confused with the gas constant. In a report, state the scale beside each value. If a figure is a difference, write "deg R" or "°R" and say so in the text.
Why not just use kelvin
Many courses have moved to SI and kelvin, but a large body of American practice, from boiler codes to older software, uses English units. Learning Rankine lets a student read those sources without translating every number to SI. A short routine with a “convert °F to °R” calculation formula in the head is the practical answer.
Problem 7: a sealed bottle in a hot car
A sealed rigid bottle holds air at 14.7 psia and 70 °F. The car interior reaches 140 °F. Convert to 529.67 °R and 599.67 °R: the pressure becomes 14.7 × 1.132 = 16.6 psia, an increase of 1.9 psi. The cap holds, but a thin can may bulge. Students who use the Fahrenheit ratio of 2 would predict a pressure of 29.4 psia, which is very far off. A quick convert °F to °R shows the difference.
Problem 8: steam table lookups
The saturation temperature of steam at 100 psia is about 328 °F, which is 787.7 °R. Steam at 14.7 psia is at 212 °F, or 671.67 °R. The ratio of absolute saturation temperatures is 1.173, even though the Fahrenheit ratio is 1.55. Property tables list °F in the margin, but entropies and specific heats are per °R, so a conversion is often implied.
Problem 9: speed of sound
In English units, the speed of sound in air is 49.02 times the square root of T in °R, in feet per second. At 70 °F, T is 529.67 °R and the speed is 1,128 ft/s. At 0 °F it is 1,051 ft/s and at 100 °F it is 1,160 ft/s. A freezing morning lowers the speed by about 7 per cent compared with a mild day.
Problem 10: density of air
Air density follows ρ = P/(RT), with R = 53.35 ft·lbf/(lbm·°R) for air. At 59 °F, or 518.67 °R, and 14.7 psia, density is 0.0765 lbm/ft³. At 100 °F, or 559.67 °R, it falls to 0.0709 lbm/ft³. At 0 °F, or 459.67 °R, it rises to 0.0863. Using Fahrenheit in the formula would give infinite density at 0 °F.
Problem 11: Carnot efficiency
An ideal engine takes heat at 1,000 °F and rejects it at 100 °F. Convert to 1,459.67 °R and 559.67 °R. The efficiency is 1 − 559.67/1,459.67 = 61.7 per cent. Real engines manage 30 to 40 per cent. The Fahrenheit numbers would give 1 − 100/1,000 = 90 per cent, a serious overestimate. Every efficiency problem starts with a “convert °F to °R” calculation, because the formula compares two absolute temperatures.
Problem 12: a refrigerator
A freezer at 0 °F in a kitchen at 100 °F has an ideal coefficient of performance of 459.67/100 = 4.6. A real freezer might achieve 1.5 or 2. Raising the room temperature to 110 °F lowers the ideal figure to 4.2. These numbers show how a hot kitchen hurts efficiency, and they follow from absolute temperatures.
Problem 13: a compressor
Air at 70 °F, or 529.67 °R, is compressed adiabatically to six times the pressure. The discharge temperature is 529.67 × 6^0.2857 = 883.7 °R, which is 424 °F. A cooler brings it back to 100 °F before the next stage. Students who forget to convert to Rankine predict 70 × 1.67 = 117 °F, an answer far from reality.
Problem 14: radiation
A hot surface radiates in proportion to the fourth power of its absolute temperature. Raising a surface from 1,000 °F to 1,500 °F, or from 1,459.67 °R to 1,959.67 °R, increases radiation by (1,959.67/1,459.67)⁴ = 3.25 times. With Fahrenheit, one would get 5 times, which overstates the effect.
Problem 15: a heat pump
A heat pump heating a house at 70 °F from outdoor air at 20 °F has an ideal COP of 529.67/50 = 10.6. Real machines reach 3 to 4. When the outdoor temperature falls to 0 °F, the ideal COP drops to 7.6, which shows why performance worsens in deep cold. The calculation requires Rankine for the indoor temperature.
More values for convert °F 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 °F = 186.52 °R
- -100 °F = 359.67 °R
- -20 °F = 439.67 °R
- 10 °F = 469.67 °R
- 15 °F = 474.67 °R
- 25 °F = 484.67 °R
- 30 °F = 489.67 °R
- 50 °F = 509.67 °R
Common slips when you convert °F to °R
Using Fahrenheit in a gas law
Gas laws need absolute temperature. A tyre does not change pressure by the ratio of Fahrenheit numbers.
Adding to a difference
A change of 50 °F is a change of 50 °R. Do not add 459.67.
Confusing Rankine with kelvin
The two scales differ by a factor of 1.8. 529.67 °R is 294.26 K, not 529.67 K.
Short answers
How do I convert °F to °R?
Add 459.67.
What is 68 °F in Rankine?
527.67 °R.
What is 32 °F in Rankine?
491.67 °R.
What is absolute zero in Fahrenheit?
−459.67 °F.
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 °F to K, Convert °F to °Ré, Convert °C to °R, Convert K to °R, Convert °R to °C, Convert km to mi, Convert mi to km, Convert L to gal, Convert gal to L. The reverse direction is Convert °R to °F.
In short, a “convert °F to °R” calculation means adding 459.67 and writing the unit beside the answer. Your number is computed locally, with no account and no upload.