Temperature Scales: Celsius, Fahrenheit, Kelvin

Most conversions are "linear through zero": zero of one unit equals zero of another, so a single multiplier does the job. Temperature scales are affine instead — they have both a different step size and a different starting point. Celsius puts water's freezing point at 0°, Fahrenheit puts it at 32°. Because the zeros do not line up, you must shift as well as scale.

The Celsius-to-Fahrenheit formula captures both: multiply by 9/5 (the step-size difference) and then add 32 (the offset). To go back, subtract 32 first, then multiply by 5/9. Skip the offset and you will be off by dozens of degrees.

Kelvin shares its step size with Celsius — a change of one kelvin equals a change of one degree Celsius — but its zero is absolute zero, the coldest anything can be, at −273.15 °C. So converting Celsius to Kelvin is a pure offset: just add 273.15. Kelvin has no negative values and no degree symbol, and it is the SI base unit for temperature used throughout physics.

Rankine is to Fahrenheit what Kelvin is to Celsius: an absolute scale that starts at absolute zero but uses Fahrenheit-sized degrees. It appears mainly in some engineering fields. For everyday sense-checking, keep a few landmarks in mind: 0 °C is 32 °F (freezing), 37 °C is about 98.6 °F (body temperature), and 100 °C is 212 °F (boiling at sea level). If a converted value lands far from the nearest landmark, you have probably dropped the offset.

Daniel Fahrenheit fixed his scale in 1724 using reference points he could reproduce in a workshop: zero was the temperature of a brine of ice, water and ammonium chloride, and the upper anchor was roughly human body temperature, which he numbered 96 so the interval could be halved repeatedly. Later recalibration against the freezing and boiling points of water moved body temperature to the familiar 98.6 °F.

Anders Celsius published his scale in 1742 the other way round: 0 for the boiling point of water and 100 for its freezing point. It was inverted to the form we use only after his death, which is why the scale was known as "centigrade" for two centuries before it was formally renamed after him in 1948.

The two scales cross at exactly one point. Solving C = 9C/5 + 32 gives C = −40, so −40 °C and −40 °F are the same temperature — a useful sanity check when you are unsure whether a converter has the offset the right way round.

This is the mistake that catches people who know the formula. A temperature *value* of 10 °C is 50 °F, but a temperature *difference* of 10 °C is 18 °F, not 50. Differences carry only the scale factor of 9/5; the +32 offset belongs to the origin of the scale, and adding it to a delta is meaningless. Anything expressed per degree — a coefficient of expansion, a heating rate, a tolerance band — is a difference.

Kelvin sidesteps the problem because its zero is absolute: 0 K is −273.15 °C and −459.67 °F, the point where the thermal motion that temperature measures reaches its minimum. A kelvin and a degree Celsius are exactly the same size, so converting between them is pure addition. Note the notation too: kelvin takes no degree sign and no capital when spelled out — you write 300 K, and "three hundred kelvin".

The mental shortcut "double it and add 30" is good enough for weather: at 20 °C it gives 70 °F against the true 68 °F. The error grows at both ends, though — at 35 °C it predicts 100 °F instead of 95 °F, and at −10 °C it gives 10 °F instead of 14 °F. Use it to decide on a jacket, not to set an oven or a fridge.