Temperature Converter
Convert between celsius, fahrenheit, kelvin, rankine and reaumur.
About
Temperature Converter
Three temperature scales are in common use and two more survive in corners of engineering. They differ in where zero sits and how large a degree is, which is all a conversion has to reconcile.
The formulas
| Conversion | Formula |
|---|---|
| Celsius to fahrenheit | °F = °C × 9/5 + 32 |
| Fahrenheit to celsius | °C = (°F - 32) × 5/9 |
| Celsius to kelvin | K = °C + 273.15 |
| Fahrenheit to rankine | °R = °F + 459.67 |
| Celsius to réaumur | °Ré = °C × 0.8 |
The 9/5 appears because a fahrenheit degree is smaller: 180 of them span freezing to boiling where celsius uses 100. The 32 appears because fahrenheit puts zero somewhere other than freezing.
Worked examples
- 25 °C to fahrenheit: 25 × 1.8 + 32 = 77 °F
- 98.6 °F to celsius: (98.6 - 32) × 0.5556 = 37 °C
- 25 °C to kelvin: 25 + 273.15 = 298.15 K
The mental shortcut
For celsius to fahrenheit: double it and add 30. For 20 °C that gives 70, against a true 68. For 25 it gives 80 against 77.
The error grows with the temperature because doubling overstates the 1.8 factor, so the shortcut is good to within a few degrees across ordinary weather and poor for cooking. Going the other way, subtract 30 and halve: 70 °F gives 20 °C, against a true 21.1.
Where the scales came from
Fahrenheit set zero at the coldest temperature he could reproduce, a brine of ice, water and ammonium chloride, and used body temperature as another fixed point. The result put water freezing at 32 and boiling at 212, which looks arbitrary because the reference points were something else entirely.
Celsius used water directly, at 0 and 100, though he originally had them the other way round with 0 as boiling. The scale was inverted after his death.
Kelvin starts at absolute zero, the point where thermal motion is at its minimum, and uses the same degree size as celsius. It is the SI unit, and since 2019 it has been defined by fixing the Boltzmann constant rather than by any property of water.
Reference points
| Point | °C | °F | K |
|---|---|---|---|
| Absolute zero | -273.15 | -459.67 | 0 |
| Nitrogen boils | -195.79 | -320.42 | 77.36 |
| Dry ice sublimes | -78.5 | -109.3 | 194.65 |
| Water freezes | 0 | 32 | 273.15 |
| Room temperature | 20 | 68 | 293.15 |
| Human body | 37 | 98.6 | 310.15 |
| Water boils | 100 | 212 | 373.15 |
| Moderate oven | 180 | 356 | 453.15 |
The point where the scales meet
Celsius and fahrenheit read the same number at exactly -40. Setting x = 9x/5 + 32 and solving gives x = -40, and it is the only solution because two straight lines with different slopes cross once.
It makes a useful checkpoint, since -40 needs no conversion in either direction, and it is why industrial specifications often quote that figure without a unit.
Converting a difference, not a temperature
This is the error worth guarding against. A change of 10 °C is a change of 18 °F, not 50 °F, because only the scaling factor applies to a difference and the offset of 32 does not.
A rise from 20 °C to 30 °C is 68 °F to 86 °F, a difference of 18. Running the full formula on the 10 gives 50, which would be the temperature 10 °C corresponds to rather than the size of the change.
A change of 1 °C equals a change of 1 K exactly, since those scales share a degree size and differ only in where zero sits. The same holds between fahrenheit and rankine.
Rankine and Réaumur
Rankine is absolute like kelvin but uses fahrenheit-sized degrees, so absolute zero is 0 °R and water freezes at 491.67 °R. It survives in some US engineering work, particularly thermodynamics, where an absolute scale is required and the rest of the calculation is in imperial units.
Réaumur puts water freezing at 0 and boiling at 80. It was widely used in Europe in the eighteenth and nineteenth centuries and is now essentially extinct, surviving in a few traditional cheese and syrup recipes.
Oven temperatures and gas marks
Gas marks are their own scale, and the published equivalents are rounded rather than exact conversions.
| Gas mark | °C | °F | Description |
|---|---|---|---|
| 1 | 140 | 275 | Very slow |
| 3 | 165 | 325 | Moderate |
| 4 | 180 | 350 | Moderate |
| 6 | 200 | 400 | Hot |
| 7 | 220 | 425 | Hot |
| 9 | 240 | 475 | Very hot |
The celsius and fahrenheit columns do not convert exactly into each other: 350 °F is really 176.7 °C rather than 180. The figures were rounded to convenient numbers when the tables were drawn up, and ovens are not accurate to a few degrees anyway.
Fan ovens are the other adjustment. A fan circulates hot air and cooks faster, so recipes written for a conventional oven usually want the temperature dropped by about 20 °C, or one gas mark.
What it feels like is not the temperature
Two adjusted figures are widely reported alongside air temperature, and neither is a temperature reading.
Wind chill estimates how cold exposed skin feels, since moving air strips away the thin warm layer the body maintains. At 0 °C with a 30 km/h wind the equivalent still-air feel is around -6 °C. It applies to exposed skin only and does not change the actual temperature, so water still freezes at 0 °C regardless of the wind.
Heat index does the same in the other direction, accounting for humidity slowing the evaporation of sweat. At 32 °C and 70% humidity the apparent temperature is around 40 °C, which is why humid heat is dangerous at figures that sound survivable.
Body temperature
The familiar 98.6 °F comes from a nineteenth-century German study that measured 37 °C and was converted with more precision than the original warranted. Later work suggests the average is slightly lower, nearer 36.6 °C, and that it varies by person, by time of day and by measurement site.
Oral readings run below rectal ones by several tenths of a degree, and armpit readings lower still. Fever is generally defined from 38 °C, though the threshold depends on where the reading was taken, which is why thermometers specify a site.
Why the two scales survive side by side
Fahrenheit persists in the United States for weather and cooking largely because its degrees are finer, so everyday temperatures span a wider range of whole numbers. Nought to a hundred fahrenheit covers roughly the span of habitable outdoor conditions, which is a genuinely convenient property for a weather scale.
Celsius wins everywhere the reference points matter, since freezing and boiling water are things people need to reason about. American science, medicine and engineering all use celsius or kelvin regardless of what the weather forecast says, which is why the two coexist within the same country rather than one replacing the other.
Measuring accurately
A thermometer reads its own temperature, not the temperature of what you are interested in, which is why placement matters more than precision. An air thermometer in direct sun reads far above the true air temperature, and official weather readings come from a shaded, ventilated enclosure for exactly that reason.
Contact thermometers need time to equilibrate, and pulling a probe out too early gives a reading part way between the sample and the room. Infrared thermometers measure surface temperature only and are affected by how reflective the surface is, so a shiny pan reads cooler than it is.
Common mistakes
Converting a difference with the full formula. Differences take only the scaling factor.
Writing degrees kelvin. It is 300 K, not 300 °K, since the scale is absolute.
Using 273 instead of 273.15. Fine for weather, not for laboratory work.
Trusting the mental shortcut for cooking. Doubling and adding 30 is several degrees out at oven temperatures.
Common questions
Frequently asked questions
Multiply by 9/5, which is 1.8, then add 32. So 25 degrees celsius is 25 times 1.8 plus 32, which is 77 fahrenheit. A rough mental version is to double the celsius figure and add 30, which is accurate to a few degrees in ordinary weather.
At exactly -40. It is the only point where the two scales agree, which follows from solving x equals 9x over 5 plus 32. Two straight lines with different slopes cross once, so there is no second answer.
Because Fahrenheit built the scale around different reference points. Zero was the coldest temperature he could reproduce with a brine mixture, and body temperature was another fixed point. Water freezing landed at 32 as a consequence rather than by design.
The temperature at which thermal motion reaches its minimum, at -273.15 celsius or -459.67 fahrenheit. It defines zero on the kelvin and rankine scales. It cannot be reached in practice, though laboratories have come within a billionth of a degree.
No. Kelvin takes no degree sign and no word degrees, so it is 300 K. The convention marks it as an absolute scale measured from a physical zero rather than from an arbitrary reference point.
Apply only the scaling factor and leave out the offset. A change of 10 celsius is a change of 18 fahrenheit, not 50. A change of 1 celsius equals a change of 1 kelvin exactly, since those two scales share a degree size.
It is an absolute scale using fahrenheit-sized degrees, with absolute zero at 0 rankine and water freezing at 491.67. It appears in US engineering thermodynamics, where an absolute temperature is required and the rest of the working is in imperial units.
The United States and a small number of territories including the Cayman Islands, Palau and the Marshall Islands. The rest of the world uses celsius for everyday purposes and kelvin for scientific work.