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Celsius, Fahrenheit and Kelvin Without the Confusion
The three temperature scales, the exact formulas, why a simple multiplier never works, and the anchors that let you check any result in your head.
Updated: 2026-10-19 · 5 min read
Temperature is the only common unit conversion where the scales do not share a zero point. That single fact is why every attempt to convert temperature by multiplying goes wrong, and why the formulas look more complicated than they are.
Three scales, two different ideas
Celsius and Fahrenheit are both relative scales: their zero points were chosen for convenience, not for physics. Kelvin is an absolute scale: zero kelvin is absolute zero, the point at which molecular motion reaches its minimum.
That is why Celsius and Kelvin have the same step size — a change of 1 °C is a change of 1 K — but different starting points, while Fahrenheit has both a different step size and a different zero.
The formulas
Fahrenheit from Celsius: multiply by 9/5 and add 32. Celsius from Fahrenheit: subtract 32 and multiply by 5/9. Kelvin from Celsius: add 273.15. Celsius from Kelvin: subtract 273.15.
The 9/5 factor is because there are 180 Fahrenheit degrees between freezing and boiling, and 100 Celsius degrees over the same range. The 32 is because Fahrenheit put freezing at 32 rather than 0.
- °F = °C × 9/5 + 32
- °C = (°F − 32) × 5/9
- K = °C + 273.15
- °C = K − 273.15
Anchors for checking a result
Two reference points catch almost every arithmetic error. Water freezes at 0 °C, 32 °F and 273.15 K. It boils at 100 °C, 212 °F and 373.15 K at standard pressure.
A third useful anchor is −40, the point where Celsius and Fahrenheit read the same number. If a conversion gives a value between −40 and 0 on both scales, that is not a bug.
For a fast estimate, double the Celsius figure and add 30. 20 °C becomes 70 °F against a true 68 °F; 30 °C becomes 90 °F against 86 °F. Good enough for deciding what to wear, not for setting an oven.
Where people actually go wrong
Negative temperatures break the shortcut badly. −10 °C is 14 °F, not 10 °F, because the offset applies after the multiplication and the sign matters.
Oven temperatures are usually given in round numbers in one scale and convert to awkward ones in the other: 180 °C is 356 °F, which is why fan oven charts often just say 350 °F and accept the difference.
Body temperature is the case where precision matters. Normal is around 37 °C or 98.6 °F, and a fever threshold of 38 °C is 100.4 °F. Rounding 37 °C to 98 °F, as many people do, hides almost a full degree of fever.
Kelvin in practice
Kelvin is used where ratios matter: gas laws, colour temperature, cryogenics and astronomy. Doubling a temperature in kelvin doubles the thermal energy; doubling it in Celsius means nothing, because 20 °C to 40 °C is not a doubling of anything physical.
Kelvin never takes a degree symbol and is written as 300 K, not 300 °K. That convention changed in 1967, and older documents that still use the symbol are following the pre-1967 style.