Why temperature needs formulas, not factors
Length and weight scale from a shared zero, so one multiplier is enough. Celsius and Fahrenheit have different zero points as well as different step sizes, so the conversion is affine: multiply and then add an offset. This converter always goes through Celsius, using these formulas:
- Celsius to Fahrenheit:
°F = °C × 9/5 + 32 - Fahrenheit to Celsius:
°C = (°F − 32) × 5/9 - Celsius to Kelvin:
K = °C + 273.15 - Celsius to Rankine:
°R = (°C + 273.15) × 9/5
Kelvin to Fahrenheit chains two of these. A degree Celsius and a kelvin are the same size, so they differ only by the 273.15 offset. By modern SI convention the kelvin is written K with no degree sign, and 2019 redefined it by fixing the Boltzmann constant rather than the triple point of water, while Celsius remains defined as kelvin minus 273.15.
Worked examples
- 100 °C = 100 × 1.8 + 32 = 212 °F, and 37 °C = 98.6 °F = 310.15 K.
- A recipe that says 350 °F is (350 − 32) × 5/9 = 176.67 °C, so use 175 or 180 °C on a Celsius oven. 180 °C is 356 °F.
- The scales meet at −40, where both read −40.
Fixed points across the three scales
| Event | °C | °F | K |
|---|---|---|---|
| Absolute zero | −273.15 | −459.67 | 0 |
| Water freezes (1 atm) | 0 | 32 | 273.15 |
| Typical room | 20 | 68 | 293.15 |
| Normal body | 37 | 98.6 | 310.15 |
| Water boils (1 atm) | 100 | 212 | 373.15 |
Things to watch
- Points versus intervals. The formulas convert a temperature reading. A change of 10 °C is a change of 18 °F, with no +32 involved, so do not use this tool for "rose by 10 degrees" arithmetic.
- Rankine is offered. Rankine (°R) uses Fahrenheit-sized steps from absolute zero, and some US thermodynamics texts use it. It equals the Fahrenheit value plus 459.67, so 32 °F is 491.67 °R.
- Absolute zero is the floor. Typing −300 °C shows a message instead of a result, because nothing can be colder than 0 K (−273.15 °C, −459.67 °F, 0 °R).
- Rounding. Results show seven significant digits, so 72 °F appears as 22.22222 °C rather than a repeating decimal.
Weather, cooking and lab protocols commonly mix scales; the volume converter covers the matching recipe quantities.