Temperature converter

The three scales, and why there are three

The same temperature has three different names depending on where you are and what you are doing. That is not a quirk: each scale was built for a different purpose, and knowing which is which makes the conversions obvious rather than something to memorise.

Celsius, built around water

Celsius takes two things everybody can reproduce in a kitchen and calls them 0 and 100: water freezing and water boiling, at sea level. Everything in between is divided into a hundred equal steps. It is used by most of the world and by every scientific field that is not dealing with absolute temperatures.

Fahrenheit, built around people

Fahrenheit puts 0 at the coldest temperature Daniel Fahrenheit could reliably reproduce with a salt and ice mixture, and 96 near body temperature. On this scale water freezes at an awkward-looking 32 and boils at 212 — a span of 180 degrees rather than 100, which means each Fahrenheit degree is smaller: 1 °C is 1.8 °F. It survives in everyday use in the United States, and that difference in step size is the whole reason the conversion needs a 9/5 in it.

Kelvin, built around physics

Kelvin puts its zero where temperature actually stops: absolute zero, the point at which there is no thermal energy left to remove. Its steps are exactly the size of Celsius steps, so converting is only ever an addition: K = °C + 273.15. Because it never goes negative, it is the scale physics uses whenever a temperature appears in a formula.

Converting, and the one place people slip

Going from Celsius to Fahrenheit means °C × 9/5 + 32, and coming back means (°F − 32) × 5/9. The mistake worth avoiding is the order on the way back: you subtract 32 first and multiply afterwards. Multiplying first gives a number that is wrong by about 18 degrees, which for an oven or a fever is the whole difference.

For rough everyday work there is a shortcut worth knowing: to get Fahrenheit, double the Celsius and add 30. At 20 °C that gives 70 instead of the true 68; at 30 °C it gives 90 instead of 86. Never precise, always close enough to decide what to wear.

The −40 coincidence

There is exactly one temperature that reads the same in Celsius and Fahrenheit, and it is −40. It falls out of the algebra: set x = 9x/5 + 32, and you get −4x/5 = 32, so x = −40. There is no second crossing, because two straight lines with different slopes meet at one point and no more.

Why kelvin never takes a degree sign

You write 298.15 K, not 298.15 °K, and you say "two hundred and ninety-eight kelvin", not "degrees kelvin". The kelvin is a base unit of the SI system in its own right, like the metre or the second, rather than a degree of something. The degree sign was officially dropped in 1967 and has been wrong ever since, though it still turns up everywhere.

Absolute zero is a floor, not a setting

At −273.15 °C there is no thermal energy left to take away, and that is as cold as anything can get. It is not that we lack good enough freezers: colder simply does not exist. That is why this converter refuses to work below it and says so, rather than producing a tidy-looking number that means nothing.

What this converter does not do

It handles Celsius, Fahrenheit and kelvin. It does not do Rankine, Réaumur or the other historical scales, and it does not convert temperature differences — a rise of 10 °C is a rise of 18 °F, not 50 °F, because for a difference you leave out the +32. It also cannot tell you an oven's fan-assisted equivalent, which depends on the oven and not on arithmetic.