Convert °F to °C

Fahrenheit puts freezing at 32 and boiling at 212, so a Fahrenheit degree is five ninths the size of a Celsius one. Converting therefore takes two steps, not one: a multiplication for the difference in degree size, and a shift for the different zero points.

Celsius puts zero at the freezing point of water and 100 at its boiling point, at sea level. Anders Celsius originally had the scale the other way up, with zero as boiling.

Fahrenheit and Celsius do not start counting from the same place, so no single number converts between them. Multiplying is the mistake this page exists to prevent: it is right at exactly one temperature and wrong everywhere else, and the error grows the further you get from that point.

The two ends of this page's own scale show it. 0 °F is -17.78 °C and 100 °F is 37.78 °C — a hundred steps on one side, 55.56 on the other, and the two zeros in different places. That is why the formula above has two parts, something to multiply by and something to add; drop the addition and the answer stops being wrong slowly and starts being wrong badly.

-40 °C and -40 °F are the same temperature — the one reading that needs no conversion at all. It is the quickest proof that the scales are offset rather than scaled: if a factor were all that separated them, they would only ever agree at zero.

It is also a useful anchor going the other way. Any temperature you convert should land on the far side of -40° from where it started, and if it does not, the addition went in the wrong direction.

Fahrenheit spreads the range that weather occupies over roughly twice as many numbers as Celsius, which is the honest argument in its favour and the reason its figures look inflated. 0 °F is −18 °C, a hard northern winter day. 32 °F is freezing. 50 °F is 10 °C and means a coat. 68 °F is 20 °C, a comfortable room. 86 °F is 30 °C and is hot. 100 °F is 37.8 °C, which is why an American heatwave headline reads "triple digits".

Three landmarks carry most of it: 0, 50 and 100 map to −18 °C, 10 °C and 38 °C. Below 50 is jacket weather, above 90 is uncomfortable, and the span between covers nearly every day an American describes out loud. Celsius compresses the same range into roughly 0 to 35, which is why a single degree carries more information there and why metric forecasts quote fewer of them.

The mental version is to halve the Fahrenheit figure and subtract 15. 70 °F gives 20 against a true 21.1; 60 °F gives 15 against 15.6; 40 °F gives 5 against 4.4. The rule is exact at 50 °F and drifts by about 0.056 °C for each degree away from it, so it stays within a degree or two between roughly 30 °F and 80 °F and falls apart outside that: at 200 °F it reads 85 against a true 93.3.

The exact route is the same two operations in the other order and with a real factor: take 32 off first, then multiply by 5/9. Doing it the other way — dividing by 1.8 and then subtracting — turns 68 °F into 5.8 °C instead of 20, and it is the commonest arithmetic slip on this conversion. The 32 is the offset between the two zeros, and an offset has to be removed before the rescaling, never after it.

350 °F is 176.7 °C, and no oven dial in Europe carries that mark. The convention is to round to the nearest ten: 350 °F becomes 180 °C, 375 °F becomes 190 °C, 400 °F becomes 200 °C, 425 °F becomes 220 °C. Rounding by up to four and a half degrees is immaterial here, because a domestic oven swings wider than that every time the thermostat cycles.

The correction that is not rounding is the fan. A fan or convection oven is conventionally set about 20 °C below a conventional one for the same result, so an American recipe asking for 350 °F means 180 °C conventional or 160 °C fan. US recipes rarely say which they assume, because convection is a setting there rather than the default, while British and European ones often print both numbers. Twenty degrees is the difference between a cake that sets and one that browns first.

98.6 °F is exactly 37 °C, and the run of digits is the giveaway. The figure entered English-language medicine as a conversion of a round Celsius number measured in nineteenth-century Germany, and the apparent precision was manufactured by the arithmetic rather than by a thermometer. Normal body temperature is a band of about a degree Celsius that moves through the day and varies with the site of measurement.

The threshold used clinically is 38 °C, which converts to 100.4 °F — another oddly precise-looking Fahrenheit number with the same explanation. If a US health page quotes 100.4, the underlying rule is 38. Knowing where the decimal came from tells you how much of it to trust: one decimal place in Fahrenheit is 0.06 °C, finer than any consumer thermometer can honestly claim.

A forecast saying tomorrow will be ten degrees warmer is describing a difference, and a difference converts differently from a reading. Ten Fahrenheit degrees is 5.6 Celsius degrees: multiply by 5/9 and stop. Running 10 through the full formula returns −12.2, which is a temperature and not a change, and it is wrong by the entire 32.

The offset belongs to readings only, and the list of places this bites is longer than the weather. A tolerance of ±5 °F on a datasheet is ±2.8 °C. An air conditioner claiming to hold a room within 2 °F holds it within 1.1 °C. A temperature coefficient quoted per °F is 1.8 times smaller than the same coefficient per °C. Whenever the word before the number is "warmer", "cooler", "rise", "drop", "per" or "±", use 5/9 alone.

Daniel Fahrenheit fixed his zero on the coldest temperature he could reproduce reliably: a brine of ice, water and ammonium chloride, which stabilises well below the freezing point of plain water. His upper reference point was human body temperature. Neither anchor had anything to do with water on its own, which is why water freezes and boils at 32 and 212 rather than at anything memorable.

The consolation is the interval between them. Those two points are 180 degrees apart — a number that divides cleanly, and fine enough that whole degrees are usually sufficient for weather without a decimal. That 180 against Celsius’s 100 is where the 9/5 in the formula comes from: each Fahrenheit degree is five ninths the size of a Celsius one, which is a fact about the degrees and not about the readings.

The United States and its territories, a handful of small Caribbean and Pacific states, and Liberia. That is close to the whole list, and it covers weather, cooking and the domestic thermometer rather than everything: American laboratories, American research medicine and every American scientific paper use Celsius or kelvin like everyone else.

The split runs by audience rather than by field. The National Weather Service issues public forecasts in Fahrenheit and publishes the model data underneath them in Celsius. A car sold in the US today will usually toggle its dashboard between the two. What has not moved is speech: an American describing a hot day says ninety, and half a century of voluntary metrication has not changed the number people feel.

One Fahrenheit degree is 0.5556 °C, so a whole-degree Fahrenheit reading already carries about a quarter of a Celsius degree of uncertainty on each side. Converting 73 °F and reporting 22.7778 °C claims six digits of precision the original number never had. One decimal is generous; for a weather figure, none is right.

The conversion itself is exact — 32 and 9/5 are definitions rather than measurements, in the same way the 273.15 between Celsius and kelvin is. What is approximate is the reading, and no amount of arithmetic improves it. Where the Fahrenheit figure was itself converted from a round Celsius one, as 98.6 was, converting back should return the round number; if it does not, something has been rounded twice.