Temperature Converter: Celsius to Fahrenheit, Kelvin and Rankine

How to use this tool

Type a temperature, pick the scale it is on and the scale you want. The answer is in the dark panel, the same temperature appears on all five scales in the cards below it, and the green note shows the formula and the arithmetic line by line, so 180 °C to Fahrenheit reads 180 × 9/5 = 324, then 324 + 32 = 356. Tap any card to copy its value. Swap reverses the two scales and carries the result across, and the decimal places control applies everywhere on the page. Negative numbers are fine; anything below absolute zero is refused with a note saying what the floor is.

The input people most often get wrong is not the number but the kind of number. A temperature reading, 20 °C say, converts to 68 °F. A temperature difference of 20 °C, the rise across a heat exchanger or the tolerance on a curing oven, converts to 36 °F, because the 32 that places the Fahrenheit zero has nothing to do with a difference. The “this number is” control switches between the two, and the difference mode drops the offsets from every scale at once.

Below the cards, the blue note says where your temperature sits among real things, between room temperature and a warm day say, and adds the oven gas mark and fan oven setting for cooking temperatures or the usual clinical range for body temperatures. The thermometer draws both scales side by side with the value marked; the line chart shows Fahrenheit against Celsius, the single crossing at minus 40, and your point on the line. Every chip and table row is a link with its own address, so a specific figure such as 37.5 °C to °F can be bookmarked or sent to someone. The exports carry the value you entered and nothing else.

What the conversion is doing

Both everyday scales were pinned to water. Celsius puts freezing at 0 and boiling at 100, so a degree Celsius is a hundredth of that gap; Fahrenheit puts freezing at 32 and boiling at 212, so a degree Fahrenheit is a hundred and eightieth of the same gap. That gives the two numbers in the formula: the slope is 180 ÷ 100 = 9/5, and the offset is the 32 that Fahrenheit reads when Celsius reads zero. So °F = °C × 9/5 + 32, and undoing it in the reverse order, °C = (°F − 32) × 5/9. The subtraction has to come before the multiplication going back, because the 32 was added after the scaling going forward.

The absolute scales add a second offset. Kelvin uses Celsius sized degrees but starts at absolute zero, which is 273.15 °C below the freezing point of water, so K = °C + 273.15. Rankine does the same with Fahrenheit sized degrees, so °R = °F + 459.67, and 0 K and 0 °R are the same temperature. The converter turns whatever you typed into kelvin, then into the scale you asked for, and the formula it prints is the two steps combined. Réaumur, the fifth scale, is an old French one with freezing at 0 and boiling at 80; it survives in a few cheese and syrup recipes, and a degree Réaumur is 1.25 °C.

None of this is measured. The Celsius scale is defined from the kelvin, the kelvin has been defined since 2019 by fixing the Boltzmann constant at 1.380649 × 10⁻²³ J/K, and the Fahrenheit and Rankine scales are defined from those by the exact fractions above. So 180 °C is exactly 356 °F, 98.6 °F is exactly 37 °C, and the converter rounds only at the display. The one place a physical fact still leaks in is the freezing point of water, which sits at 273.15 K by convention and within a thousandth of a degree of that in practice.

Why temperature is different from every other unit

Every other converter on this site multiplies by a factor. Metres to feet, psi to bar, newton metres to foot pounds: the zero is the same on both sides, so the ratio is all there is. Temperature scales have different zeros, and that one fact is behind almost every mistake made with them. You cannot say 20 °C is twice as hot as 10 °C, because 68 °F is not twice 50 °F; the ratio changes with the scale, which means it was never a real ratio. Only the absolute scales support ratios, and 300 K really is twice as hot as 150 K in the sense that matters to a gas law.

The same fact is why differences and readings convert differently. A reading of 10 °C is 50 °F, but a rise of 10 °C is a rise of 18 °F, because when you subtract two readings the two 32s cancel and only the 9/5 survives. Engineers meet this in thermal expansion, heat transfer, insulation ratings and temperature tolerances, and cooks meet it when a recipe says to raise the oven by 20 degrees. The difference mode on the converter handles it, and the safe habit is to ask, every time, whether the number is a point on the scale or a gap between two points.

Where the scales came from

Daniel Fahrenheit built his scale in 1724 around three points he could reproduce in his workshop: 0 for the coldest mixture he could make, ice with salt and ammonium chloride, 32 for ice melting in plain water, and 96 for the temperature of a healthy person, chosen so the gaps divided neatly by two. Boiling water landed near 212, and when the scale was later tidied so that freezing and boiling were exactly 180 apart, body temperature drifted to 98.6. Anders Celsius proposed his scale in 1742 with the numbers upside down, 0 for boiling and 100 for freezing, and it was reversed within a couple of years of his death.

William Thomson, later Lord Kelvin, argued in 1848 for a scale that started at the point where a gas would have no pressure at all, absolute zero, and kept the Celsius degree. Rankine did the same in 1859 with the Fahrenheit degree, for the steam engineers who worked in it. The kelvin was fixed to the triple point of water in 1954, then cut loose from water altogether in 2019 and tied to the Boltzmann constant, so that a temperature is now defined through the energy of molecular motion rather than through any substance. The everyday numbers did not move; the definitions underneath them did.

The fixed points worth knowing

A handful of temperatures anchor everything else, and knowing them in both scales lets you sanity check any conversion. Each Celsius value in the first column opens the converter on that temperature.

Oven temperatures, gas marks and fan ovens

Most of the traffic to a temperature converter is someone standing in a kitchen with a recipe from the other side of the Atlantic. The standard oven settings are simple once you see that they are the same few temperatures rounded in each system: 160 °C is 325 °F, 180 °C is 350 °F, 200 °C is 400 °F and 220 °C is 425 °F. The exact conversions are 320, 356, 392 and 428 °F, but ovens are not accurate to within ten degrees anyway, and the rounded figures are what the two traditions have settled on. Gas marks, still printed in British recipes, run from ¼ at 110 °C to 9 at 240 °C in steps of about 14 °C, with mark 4 at 180 °C as the moderate oven that most baking uses.

A fan oven moves the air, so it delivers heat to the food faster at the same thermostat setting, and the usual advice is to set it 20 °C, about 35 °F, lower than a conventional oven for the same result, or to shorten the time by a tenth. The converter shows the gas mark and the fan setting for any temperature between 100 and 300 °C. American recipes assume a conventional oven unless they say convection; most European recipes now give both. At the other end of the kitchen, 100 °C is a rolling boil, 93 °C is the water for drip coffee, 82 °C is the top of a poaching range, and 63 °C is the pasteurising temperature for eggs and the point at which chicken is safe if held long enough.

Body temperature: 37 and 98.6

The 98.6 °F on every drugstore thermometer is 37 °C rounded, and the 37 came from Carl Wunderlich, who averaged about a million readings from 25,000 patients in Leipzig in 1868 and reported a mean of 37 °C. Studies since then with better thermometers have put the average lower, nearer 36.6 to 36.8 °C, 97.9 to 98.2 °F, and shown that it varies by a degree or so through the day, is lower in the morning, higher after exercise, and depends on where it is measured. The figures most references use are a usual range of 36.1 to 37.2 °C, 97 to 99 °F; a fever at or above 38 °C, 100.4 °F; a high fever from 39 °C, 102.2 °F; and 40 °C, 104 °F, as the point to seek care. Below 35 °C, 95 °F, is hypothermia.

The converter names those ranges when a temperature falls between 34 and 43 °C, so that 38.5 °C reads as a fever and 100.4 °F as the threshold, but it is a unit converter, not a diagnosis, and the ranges are the conventional ones rather than a medical opinion about anyone. The body temperature chips below cover the tenths from 36.5 to 40 °C and the common Fahrenheit readings from 97.5 to 103.5, because that is what people type at two in the morning.

Mental arithmetic that gets you close

For weather, double the Celsius and add 30. It is exact at 10 °C, two degrees high at 20, four at 30 and six at 40, and two degrees low at 0, which is good enough to decide on a coat. Going the other way, take 30 off the Fahrenheit and halve it: 70 °F gives 20, against the exact 21.1. The rule works because 2 is close to 1.8 and 30 is close to 32, and it fails in the oven because at 180 °C the doubling has drifted 34 degrees from the truth. For oven temperatures the better trick is to remember the four standard settings above.

An exact method that is still doable in your head: multiply by 2, subtract a tenth of the result, add 32. For 25 °C: 50, minus 5, plus 32, is 77 °F, which is exact. It is exact because 2 minus a tenth of 2 is 1.8. In reverse, subtract 32, halve, and add a ninth of the half: 77 − 32 = 45, half is 22.5, a ninth of that is 2.5, total 25. The converter prints the quick rule alongside the exact answer for weather temperatures so you can see how far off it is today.

A worked check you can repeat on paper

Start with the default, 180 °C to Fahrenheit. Multiply by 9/5: 180 × 9 = 1,620, and 1,620 ÷ 5 = 324. Add 32: 356 °F. In kelvin it is 180 + 273.15 = 453.15 K, in Rankine 453.15 × 9/5 = 815.67 °R, which is also 356 + 459.67, and in Réaumur 180 × 4/5 = 144 °Ré. It is gas mark 4, and a fan oven would be set to 160 °C.

Now 98.6 °F to Celsius. Subtract 32: 66.6. Multiply by 5/9: 66.6 × 5 = 333, and 333 ÷ 9 = 37 °C exactly. Check it forwards: 37 × 9/5 = 66.6, plus 32 is 98.6. In kelvin it is 310.15 K. The quick rule gives (98.6 − 30) ÷ 2 = 34.3, nearly three degrees low, which is why the rule is for the weather and not for a thermometer under the tongue.

Then 300 K to Fahrenheit, a temperature physicists use as room temperature. 300 × 9/5 = 540 °R, and 540 − 459.67 = 80.33 °F. Through Celsius instead: 300 − 273.15 = 26.85 °C, and 26.85 × 1.8 + 32 = 80.33 °F, the same answer by both routes, which is the check the converter runs on every value. Finally a difference: a process tolerance of ±10 °C is ±18 °F, from 10 × 9/5 with no 32 in sight. Type 10 in difference mode and the cards show 18 °F, 10 K, 18 °R and 8 °Ré.

Mistakes that catch people out

Converting a difference as if it were a reading. A 10 °C rise is 18 °F, not 50 °F. Ask whether the number is a point on the scale or a gap between two, and use the difference mode for gaps.

Multiplying before subtracting. °C = (°F − 32) × 5/9, brackets first. Doing 350 × 5/9 − 32 gives 162 instead of 176.7, and a cake that never rises.

Using the weather rule in the oven. Double and add 30 is six degrees out at 40 °C and 34 degrees out at 180 °C. Use the four standard oven settings or the converter.

Writing degrees kelvin. It is 300 K, three hundred kelvin, with no degree sign since 1967. Degrees Celsius, Fahrenheit and Rankine keep the sign.

Taking a ratio of Celsius or Fahrenheit readings. 40 °C is not twice as hot as 20 °C; in kelvin the ratio is 313 to 293, about 7 percent. Ratios only mean anything on an absolute scale.

Setting a fan oven to the conventional figure. A fan oven at 180 °C cooks like a conventional oven at 200 °C. Drop 20 °C, or take a tenth off the time.

Popular temperature conversions

The temperatures people look up most. Each opens the converter on that value with its own address, so you can bookmark or share the exact answer.

Celsius to Fahrenheit: weather and body

Celsius to Fahrenheit: cooking and hot

Fahrenheit to Celsius: weather and body

Fahrenheit to Celsius: cooking

Kelvin

Rankine and Réaumur

How this was checked

The engine was tested in Node before the page was built. The defining points were checked first: 0 °C returns 32 °F and 273.15 K, 100 °C returns 212 °F, 373.15 K, 671.67 °R and 80 °Ré, −40 returns −40, 0 K returns −273.15 °C and −459.67 °F, and 98.6 °F returns exactly 37 °C. Every one of the 20 scale pairs was then round tripped at six temperatures from −300 to 1,000, and all returned the original to within a ten millionth of a degree. The difference mode was checked against the slopes: 10 °C returns 18 °F, 1 K returns 1.8 °R and 5 °C returns 4 °Ré. The printed arithmetic steps were checked to reproduce the result they lead to, and every conversion is also computed a second way, through kelvin, as a running cross check.

The oven lookup was checked to name gas mark 4 for 180 °C and for 350 °F, and to stay silent below 100 °C and above 300 °C; the body temperature note was checked to appear only between 34 and 43 °C and to place 38 °C and 100.4 °F on the fever line. Values below absolute zero are refused with the floor stated in the scale you typed. The live page was then opened at every address linked above and each was checked for a distinct title, the right headline, a thermometer and line chart that rendered, and clean CSV, image and print output containing only that value, on a desktop and a phone width screen.

Common questions

How do you convert Celsius to Fahrenheit?

Multiply by 9/5 and add 32, so °F = °C × 1.8 + 32. For 20 °C: 20 × 1.8 = 36, and 36 + 32 = 68 °F. The 1.8 is there because the gap between freezing and boiling water is 100 degrees on the Celsius scale and 180 on the Fahrenheit scale, and the 32 is there because water freezes at 32 °F rather than 0. A rough version for the weather is to double the Celsius figure and add 30, which is exact at 10 °C and two degrees high by 20 °C.

How do you convert Fahrenheit to Celsius?

Subtract 32, then multiply by 5/9, so °C = (°F − 32) × 0.5556. For 350 °F: 350 − 32 = 318, and 318 × 5/9 = 176.7 °C, which is why a 350 °F oven is written as 180 °C in metric recipes. The subtraction comes first because 32 is an offset, not a scale factor; multiplying first gives a wrong answer. The rough weather version is to take 30 off and halve it: 70 °F becomes 20 °C, against the exact 21.1.

What is 180 °C in Fahrenheit?

356 °F, from 180 × 9/5 = 324 plus 32. In the oven that is gas mark 4, a moderate oven, and American recipes round it to 350 °F, which is 176.7 °C, close enough that no cake notices. A fan oven for the same recipe is set about 20 °C lower, at 160 °C, because moving air carries heat into the food faster. The other standard oven settings are 160 °C for 325 °F, 200 °C for 400 °F and 220 °C for 425 °F.

What is 37 °C in Fahrenheit, and what counts as a fever?

37 °C is 98.6 °F, the figure printed on thermometers since Carl Wunderlich averaged a million readings in 1868. Later studies put the average person nearer 36.6 to 36.8 °C, 97.9 to 98.2 °F, and a normal range of about 36.1 to 37.2 °C, 97 to 99 °F. Most clinical references call 38 °C, 100.4 °F, or above a fever, 39 °C, 102.2 °F, a high fever, and 40 °C, 104 °F, the point to seek care. Below 35 °C, 95 °F, is hypothermia. Readings vary with the site: ear and rectal thermometers read a little higher than oral, and armpit readings a little lower.

Why do Celsius and Fahrenheit meet at minus 40?

Because the two scales are straight lines with different slopes, they cross exactly once, and the crossing is where °C = °F. Put x for both in the formula: x = 1.8x + 32, so −0.8x = 32 and x = −40. Below that Fahrenheit numbers are smaller than Celsius ones; above it they are bigger, by a margin that grows 0.8 for every degree Celsius. −40 is the one temperature you never need to convert, and a cold enough night in Winnipeg or Yakutsk to see it.

What is the difference between kelvin and Celsius?

A kelvin is exactly the size of a degree Celsius, and the two scales differ only in where zero is: 0 K is absolute zero, the coldest anything can be, and 0 °C is 273.15 K, so K = °C + 273.15. Kelvin has no degree sign and no degree in its name; you write 300 K and say three hundred kelvin. Since 2019 the kelvin is defined by fixing the Boltzmann constant at 1.380649 × 10⁻²³ joules per kelvin, so it no longer depends on water at all, although the freezing point of water still comes out at 273.15 K to better than a thousandth of a degree. Rankine is the same idea in Fahrenheit sized degrees: 0 °R is absolute zero and °R = °F + 459.67.

Related Calculators and Reference

• Cups to Grams Converter: baking ingredients by weight, with a different figure per ingredient rather than one density for everything.
• Pressure Converter: tyre and cylinder pressures move with temperature, about 1 psi for every 10 °F.
• Energy Converter: the joules, BTU and kilowatt hours it takes to move a temperature by a given difference.
• R Value to RSI Converter: insulation ratings are defined per degree of temperature difference, Fahrenheit on one side and kelvin on the other.
• Volume and Capacity Converter: cups, millilitres and fluid ounces for the rest of the recipe that gave you the oven temperature.
• Kg to Lbs Converter: grams and pounds for the same recipe.
• Geothermal Resource Calculator: where reservoir temperatures in Celsius meet heat in place and power output.
• Humidex Calculator: what a temperature feels like once humidity is counted.
• Wind Chill Calculator: how much colder the wind makes it feel.
• Turkey Thawing and Cooking Time Calculator: oven and thermometer temperatures for roasting a turkey, including the safe internal temperature from USDA and Health Canada.
• BIPM: the kelvin: the definition of the kelvin through the Boltzmann constant, from which every scale on this page is derived.