Celsius to Fahrenheit Formula
Convert any temperature in degrees Celsius to Fahrenheit using a simple linear formula.
°F = °C × 9/5 + 32
How it works
The two scales disagree about two separate things, and the formula has to fix both. They put zero in different places, and they use a different size of degree. Multiplying by 9/5 rescales the degree: there are 180 Fahrenheit degrees between the freezing and boiling points of water where Celsius has 100, and 180/100 reduces to 9/5, or 1.8. Adding 32 then shifts the zero point, because water freezes at 0 °C but at 32 °F. Order matters absolutely. Scale first, then add. Adding the 32 before multiplying overstates every single answer by 25.6 °F, whatever temperature you started from — 20 °C would come out as 93.6 °F instead of the correct 68 °F. There is one number worth memorising as a check: the scales cross at −40, which reads the same on both. And a separate rule applies to differences rather than temperatures. If you are converting a change of 10 °C rather than a reading of 10 °C, you multiply by 9/5 and do not add anything at all, because the offset cancels between the two readings. A 10-degree Celsius rise is an 18-degree Fahrenheit rise.
Variables
- °FTemperature in Fahrenheit (result)
- °CTemperature in Celsius (input)
Worked examples
| Input | Result |
|---|---|
| 0 °C | 32 °F (freezing point of water) |
| 100 °C | 212 °F (boiling point of water) |
| 37 °C | 98.6 °F (body temperature) |
Practical applications
- Setting an oven from a recipe written in the other scale
- Reading a US weather forecast from outside the country, or a foreign one from inside it
- Converting a body-temperature reading, where 37 °C is 98.6 °F
- Interpreting older engineering, meteorological and medical records, which are frequently Fahrenheit
Common mistakes
- Adding 32 before multiplying. Every answer then comes out 25.6 °F too high.
- Using 1.8 as an offset rather than a ratio. It scales the degree; it does not shift the zero.
- Applying the full formula to a temperature difference. For a change, multiply by 9/5 and add nothing.
- Rounding 9/5 to 2 for mental arithmetic. It is quick but drifts badly at higher temperatures — 200 °C would be out by more than 40 degrees.
Used in
Use it in a tool
FAQs
Why isn't the formula a simple multiplication?+
Because the two scales have different zero points. Celsius zero is the freezing point of water; Fahrenheit zero is much colder, so you have to scale (×9/5) and offset (+32).
When do °C and °F meet?+
At exactly −40°. That's the single temperature where both scales give the same number.