Celsius, Fahrenheit and Kelvin: How to Convert Temperatures
The formulas, a quick mental shortcut, key reference points and the reasons Kelvin and Rankine exist, with worked examples.
Temperature is the one common conversion that cannot be done with a single multiplier, because the scales start at different zero points. Celsius and Fahrenheit disagree on where zero is and on how big a degree is. That is why a conversion needs two steps, and why it is easy to get wrong in your head. This guide gives the formulas, a shortcut that is good enough for everyday use, the reference points worth memorising and the reasons the other scales exist.
The formulas
| To convert | Formula |
|---|---|
| Celsius to Fahrenheit | °F = °C × 9/5 + 32 |
| Fahrenheit to Celsius | °C = (°F − 32) × 5/9 |
| Celsius to Kelvin | K = °C + 273.15 |
| Kelvin to Celsius | °C = K − 273.15 |
| Fahrenheit to Rankine | °R = °F + 459.67 |
The fraction 9/5 is 1.8. One Celsius degree is the same size as one kelvin, and 1.8 times as large as one Fahrenheit degree.
Worked examples
- A 20 °C room. 20 × 1.8 = 36, plus 32 gives 68 °F.
- A 98.6 °F body temperature. 98.6 − 32 = 66.6, times 5/9 gives 37 °C.
- A 350 °F oven. 350 − 32 = 318, times 5/9 gives 176.7 °C, which recipes usually round to 175 or 180 °C.
- A fever of 38 °C. 38 × 1.8 = 68.4, plus 32 gives 100.4 °F.
- A 25 °C day in kelvin. 25 + 273.15 = 298.15 K.
A mental shortcut
For quick estimates between Celsius and Fahrenheit:
- Celsius to Fahrenheit: double it and add 30. For 20 °C that gives 70 °F (the exact value is 68).
- Fahrenheit to Celsius: subtract 30 and halve it. For 70 °F that gives 20 °C (exactly 21.1).
Across everyday weather, from 0 to 30 °C, the shortcut is within about 4 °F (or 2 °C) of the true value. It drifts for very hot and very cold values, so do not use it for cooking or for science.
Reference points
| What | °C | °F | K |
|---|---|---|---|
| Absolute zero | −273.15 | −459.67 | 0 |
| Water freezes (standard pressure) | 0 | 32 | 273.15 |
| A cool room | 20 | 68 | 293.15 |
| Normal body temperature | 37 | 98.6 | 310.15 |
| Water boils (sea level) | 100 | 212 | 373.15 |
Two facts are worth remembering. First, −40 is the same in both scales: −40 °C equals −40 °F. Second, water boils at lower temperatures at altitude, because the air pressure is lower. At about 1,600 m, in Denver, it boils at roughly 95 °C, which is why some recipes need longer cooking at high elevation.
Oven temperatures
Recipes in the US use Fahrenheit, much of the rest of the world uses Celsius, and ovens are often marked in 10 or 20 degree steps. The exact conversions and the values recipes usually print are:
| °F | Exact °C | Usually written as |
|---|---|---|
| 325 | 162.8 | 160–165 |
| 350 | 176.7 | 175–180 |
| 375 | 190.6 | 190 |
| 400 | 204.4 | 200–205 |
| 425 | 218.3 | 220 |
| 450 | 232.2 | 230 |
A fan-assisted (convection) oven cooks hotter than the dial says, so many recipes lower the temperature by about 20 °C (25 °F) for a fan oven. Follow the recipe's own instructions for the type of oven.
Temperature differences are different
The +32 offset applies only to points on the scale. When you convert a difference, such as "the temperature rose by 10 degrees", leave it out: a change of 10 °C is a change of 18 °F, and a change of 10 K. Forgetting this is the most common error in homework and in spreadsheets.
Why do Kelvin and Rankine exist?
Celsius and Fahrenheit are relative scales, anchored to the behaviour of water or to an arbitrary reference. Kelvin is an absolute scale: zero kelvin is absolute zero, the lowest possible temperature, where matter has the least thermal energy. It is the base unit of temperature in the International System of Units, written without a degree sign (300 K, not 300 °K). Science and engineering use it whenever temperature appears in a formula, because ratios and products only make sense from a true zero. Since 2019 the kelvin has been defined by fixing the value of the Boltzmann constant, and the Celsius scale is now defined from it as K − 273.15.
Rankine does the same for Fahrenheit: it starts at absolute zero but uses Fahrenheit-sized degrees. It appears mainly in some American thermodynamics and engineering work.
A short history
Daniel Gabriel Fahrenheit introduced his scale in the 1720s, and Anders Celsius proposed his in 1742. Celsius's original scale was the other way round, with 100 for the freezing point of water and 0 for the boiling point. It was reversed soon after. Today the Fahrenheit scale is the everyday standard in only a few places, including the United States, while almost everywhere else uses Celsius.
For other units, see the metric and imperial cheat sheet.