Temperature Converter

Temperature looks like the simplest thing to convert until you try, because Celsius, Fahrenheit, and Kelvin don’t share a zero. Celsius and Fahrenheit are offset scales whose zero points were set by convention, while Kelvin starts at absolute zero, the coldest anything can physically get.

Celsius to Fahrenheit: °F = (°C × 9/5) + 32

Fahrenheit to Celsius: °C = (°F - 32) × 5/9

Celsius to Kelvin: K = °C + 273.15

Kelvin to Celsius: °C = K - 273.15

Reference points:

• Water freezes: 0°C = 32°F = 273.15 K
• Water boils: 100°C = 212°F = 373.15 K
• Body temperature: 37°C = 98.6°F = 310.15 K
• Absolute zero: -273.15°C = -459.67°F = 0 K

The “+32” is what catches people. You can’t convert a temperature difference the same way you convert a temperature. A rise of 10°C is a rise of 18°F, not 50°F, because the offset applies to the reading, not to the gap between two readings. Weather forecasts trip over this constantly: “five degrees warmer tomorrow” means nine Fahrenheit degrees, not thirty-seven.

It’s also why “twice as hot” is meaningless in Celsius or Fahrenheit. 20°C is not twice as hot as 10°C in any physical sense. Only on the Kelvin scale, which begins at true zero, does doubling the number actually double the thermal energy. For everyday weather, Celsius and Fahrenheit are fine; for physics, you almost always want Kelvin.

Where the two scales cross

There is exactly one temperature where Celsius and Fahrenheit agree, and it is -40. Minus forty Celsius is minus forty Fahrenheit. Set the two formulas equal and solve and that falls straight out, which makes it a handy sanity check on any conversion you have just done by hand. It is also a real temperature rather than a curiosity: a cold winter night in Siberia or northern Canada reaches it, and it is where most weather stations stop caring which scale they are reporting in.

Kelvin has no degree sign

Write 300 K, not 300°K. The degree symbol was dropped from the kelvin in 1967, because a kelvin is an absolute unit rather than a position on a graduated scale. The same applies to the size of the unit: a kelvin and a Celsius degree are exactly the same size, which is why converting between them is pure addition with no multiplication at all. Fahrenheit degrees are smaller, five ninths the size, which is the whole reason the 9/5 turns up in the other two formulas.

A note on boiling

Water boils at 100°C at sea level and nowhere else. Pressure drops with altitude, and so does the boiling point: roughly a degree Celsius for every 300 metres you climb. In Denver, at about 1,600 metres, water boils near 95°C, which is why the back of a cake packet carries separate high-altitude instructions. Absolute zero, by contrast, is fixed. Nothing about pressure or location moves it, because it is the point where a substance holds the minimum energy quantum mechanics allows.