The units of temperature
Temperature is the one magnitude that cannot be converted by multiplication alone, because each scale puts its zero somewhere different. Celsius anchors zero at the freezing point of water, Fahrenheit at a brine mixture Daniel Fahrenheit could reproduce in 1724, and Kelvin at absolute zero, the point where thermal motion stops. Kelvin is the SI base unit and the only one with no negative values.
| Unit | Symbol | Equals |
|---|---|---|
| Degrees Celsius | °C | — |
| Degrees Fahrenheit | °F | — |
| Kelvin | K | — |
| Degrees Rankine | °R | — |
How to convert by hand
Every temperature conversion follows the same procedure: take the amount to the base unit, then from there to the target unit. In practice it is a single multiplication, because the two steps combine into one factor.
From Celsius to Fahrenheit: multiply by 1.8 and add 32. Back the other way: subtract 32 first, then divide by 1.8. To Kelvin, simply add 273.15 to the Celsius figure. The order matters: subtracting after dividing gives a different, wrong answer.
The equivalents people look up most
| Conversion | Result |
|---|---|
| Water freezes | 0 °C · 32 °F · 273.15 K |
| Comfortable room | 21 °C · 69.8 °F |
| Body temperature | 37 °C · 98.6 °F |
| Water boils at sea level | 100 °C · 212 °F |
| Absolute zero | −273.15 °C · −459.67 °F · 0 K |
Common mistakes
- Multiplying before subtracting when going from Fahrenheit to Celsius. The 32 comes off first, always.
- Writing “degrees Kelvin”. Kelvin has no degrees: it is simply 300 K, and the symbol has no ° sign.
- Assuming a temperature difference converts like a temperature. A rise of 10 °C is a rise of 18 °F, not 50 °F, because the offset only applies to absolute readings.
- Entering a value below absolute zero. It is not a small error: that temperature cannot exist.