The four scales and their formulas
Celsius and Fahrenheit are the two everyday scales, and converting between them takes both a slope and an offset: °F = °C × 9/5 + 32, and °C = (°F − 32) × 5/9. The 9/5 comes from the degree sizes — 100 Celsius degrees span the same range as 180 Fahrenheit degrees between the freezing and boiling points of water.
Kelvin is the SI unit and starts at absolute zero, so K = °C + 273.15 with no scaling: one kelvin is exactly the same size as one Celsius degree. Since the 2019 SI revision the kelvin is defined by fixing the Boltzmann constant at 1.380649 × 10⁻²³ J/K. Kelvin values are written without a degree sign — 300 K, not 300 °K.
Rankine is the absolute scale built on Fahrenheit degrees: °R = °F + 459.67, and °R = K × 9/5. It survives in US thermodynamics and HVAC calculations, where absolute temperature is required but the rest of the worksheet is in Fahrenheit units.
Worked examples
Celsius to Fahrenheit. 20 °C × 9/5 = 36, plus 32 = 68 °F. Body temperature: 37 × 1.8 = 66.6, plus 32 = 98.6 °F. An oven at 180 °C is 180 × 1.8 + 32 = 356 °F, which American recipes round down to 350 °F.
Fahrenheit to Celsius. Subtract first, then scale: (98.6 − 32) × 5/9 = 66.6 × 0.5556 = 37 °C. A US weather forecast of 75 °F is (75 − 32) × 5/9 = 23.9 °C, and 100 °F is 37.8 °C. Doing the two steps in the wrong order is the single most common error here.
Absolute scales. 25 °C is 298.15 K and 536.67 °R. Absolute zero is 0 K = −273.15 °C = −459.67 °F = 0 °R, and the tool refuses anything below it rather than returning a physically impossible number. There is one temperature where the two everyday scales meet: −40 °C is exactly −40 °F.
Reference points worth memorising
- Absolute zero: 0 K = −273.15 °C = −459.67 °F = 0 °R
- Water freezes: 0 °C = 32 °F = 273.15 K · Water boils (at 101,325 Pa): 100 °C = 212 °F
- The scales cross: −40 °C = −40 °F · Freezer: −18 °C = −0.4 °F
- Room temperature: 21 °C = 69.8 °F · Warm summer day: 30 °C = 86 °F · 35 °C = 95 °F
- Body temperature: 37 °C = 98.6 °F · Fever threshold: 38 °C = 100.4 °F
- Oven: 160 °C = 320 °F · 180 °C = 356 °F · 200 °C = 392 °F · 220 °C = 428 °F
A reading is not a difference
This converter turns one point on a scale into the same point on another scale. A thermostat reading of 10 °C is 50 °F. But a temperature that rises by 10 °C rises by 18 °F, because a difference only carries the slope, never the +32 offset: ΔF = ΔC × 9/5.
The distinction shows up in specifications more often than in weather. A tolerance of “±2 °C” is “±3.6 °F”, a heating rate of 5 °C per minute is 9 °F per minute, and a thermal coefficient given per kelvin is numerically identical per Celsius degree — because kelvin and Celsius degrees are the same size, only offset.
If you need a difference, convert both endpoints and subtract, or multiply the gap by 1.8 directly. Converting the gap as if it were a reading adds a spurious 32 degrees and is the reason so many spec sheets contain a “+32” that should not be there.
Common mistakes
The “double it and add 30” shortcut. It is only good near room temperature: 20 °C gives 70 instead of 68, an error of 2 degrees, but 35 °C gives 100 instead of 95 and 200 °C gives 430 instead of 392. The error grows by 0.2 degrees for every Celsius degree, so it fails exactly where accuracy matters — fevers and ovens.
Order of operations. Going from Fahrenheit you must subtract 32 before multiplying by 5/9. Multiplying first turns 98.6 °F into 54.8 °C rather than 37 °C. Going the other way, multiply by 9/5 before adding 32.
Confusing colour temperature with a reading. A “2700 K” bulb or a “6500 K” monitor preset describes the spectrum of the light, not how hot the device is, so converting it to Celsius produces a meaningless number. The same goes for a “feels like” or wind-chill figure, which is a model output rather than a measured temperature.
Writing degrees with kelvin, or ignoring the boiling-point caveat. Kelvin takes no degree sign. And water boils at 100 °C only at standard atmospheric pressure — in Denver at about 1,600 m it boils near 95 °C, which is why high-altitude baking instructions exist.
Where each scale is used
Fahrenheit is the everyday scale in the United States and a handful of territories including the Cayman Islands, Palau and Liberia. Almost everywhere else, including all of Europe, Asia and Latin America, uses Celsius for weather, cooking and medicine — which is why converting a US recipe or forecast is one of the most common conversions on the web.
Kelvin is the scientific standard, used wherever a temperature ratio has to make sense — gas laws, radiation, cryogenics, semiconductor datasheets. Any equation with a temperature in a denominator or an exponent needs an absolute scale, so Celsius has to be shifted by 273.15 before it goes in.
Cooking sits across all of it. Oven dials are marked in Celsius in Europe, Fahrenheit in the US and gas marks in the UK — gas mark 4 is 180 °C or 350 °F, and each mark up adds 25 °F. Meat safety targets are usually published in both: 74 °C / 165 °F for poultry, 63 °C / 145 °F for whole cuts of beef.