Length, mass and volume all convert by multiplication. Temperature does not, and the reason is worth understanding rather than memorising: temperature scales disagree about two things at once — how big a degree is, and where zero sits.
Get either one wrong and the answer is wrong. Get the order wrong and the answer is wrong in a way that still looks plausible, which is worse.
The three scales at a glance
| Celsius | Fahrenheit | Kelvin | |
|---|---|---|---|
| Zero point | Water freezes | A brine freezing mixture | Absolute zero |
| Water freezes | 0 °C | 32 °F | 273.15 K |
| Water boils | 100 °C | 212 °F | 373.15 K |
| Degrees between those points | 100 | 180 | 100 |
| Degree size | Same as kelvin | 5/9 of a Celsius degree | Same as Celsius |
| Can it go negative? | Yes | Yes | No |
| Written as | 25 °C | 77 °F | 298.15 K (no degree sign) |
Two facts fall straight out of this table. First, Celsius and kelvin share a degree size, so converting between them is pure addition. Second, Fahrenheit packs 180 degrees into the interval that Celsius covers in 100, so a Fahrenheit degree is 5/9 as large — which is where the ratio in every Celsius–Fahrenheit formula comes from.
The formulas, and why the order matters
| Conversion | Formula |
|---|---|
| Celsius → Fahrenheit | °F = (°C × 9/5) + 32 |
| Fahrenheit → Celsius | °C = (°F − 32) × 5/9 |
| Celsius → kelvin | K = °C + 273.15 |
| Kelvin → Celsius | °C = K − 273.15 |
| Fahrenheit → kelvin | K = (°F − 32) × 5/9 + 273.15 |
The classic error. Converting 100 °F to Celsius: subtracting first gives (100 − 32) × 5/9 = 37.8 °C, which is a fever. Multiplying first gives (100 × 5/9) − 32 = 23.6 °C, which is a warm room. Both are believable temperatures. Nothing in the answer tells you which one you did.
Landmarks worth knowing by heart
Converting is easy; having a sense of whether an answer is sane is more useful. These pairs anchor the everyday range:
| °C | °F | What it is |
|---|---|---|
| −40 | −40 | The one point where both scales agree |
| −18 | 0 | Standard freezer setting |
| 0 | 32 | Water freezes |
| 4 | 39 | Recommended fridge temperature |
| 10 | 50 | A cool day |
| 20 | 68 | Room temperature |
| 30 | 86 | A hot day |
| 37 | 98.6 | Body temperature |
| 100 | 212 | Water boils at sea level |
| 180 | 356 | A common baking temperature |
The mental shortcut for weather is double it and add 30: 20 °C gives 70 against a true 68. It drifts as the temperature rises — at 40 °C it gives 110 against a true 104 — so it is a road-sign approximation, not a calculation.
Absolute readings versus differences
This is the second big trap, and it is quieter than the first. A temperature difference converts differently from a temperature.
- A room at 10 °C is at 50 °F.
- A rise of 10 °C is a rise of 18 °F — not 50 °F.
Differences use only the degree-size ratio, with no offset, because the offset cancels when you subtract two readings. The same applies to rates and coefficients: a thermal expansion coefficient quoted per °C is 1.8 times the per-°F value, and a heat capacity per kelvin equals one per °C exactly. UnitFlip keeps a separate temperature-interval converter for this reason.
Why kelvin exists
Physics needs a scale whose zero means "no thermal energy to extract", because that is what makes ratios meaningful. Doubling the absolute temperature of an ideal gas doubles its pressure at constant volume; the same statement in Celsius is nonsense, and at temperatures below 0 °C it produces negative pressures.
Since 2019 the kelvin has been defined by fixing the Boltzmann constant at exactly 1.380 649 × 10⁻²³ J/K, replacing the old definition based on the triple point of water. That change is why the Celsius offset is exactly 273.15 rather than something derived from a measurement — the offset is now a defined constant.
One notational point that is worth getting right: the kelvin takes no degree sign. Write 300 K, not 300 °K, and say "300 kelvin" rather than "300 degrees kelvin". The degree sign was dropped in 1967.
A note on 98.6 °F
The famous figure for normal body temperature is a conversion artefact. The original 19th-century measurement was 37 °C, stated to two significant figures. Converting that gives 98.6 °F, which reads as a three-significant- figure number and implies a precision the original never had. Normal body temperature varies between people, across the day, and with how it is measured. It is a good demonstration of the wider point that a conversion cannot add precision to a measurement.