To convert Celsius to Fahrenheit, multiply the Celsius temperature by 9/5 (1.8) and add 32: °F = °C × 1.8 + 32. For example, 20 °C × 1.8 = 36, and 36 + 32 = 68 °F. To go the other way, subtract 32 and divide by 1.8.
What is the Celsius to Fahrenheit formula?
°F = (°C × 9/5) + 32
Since 9/5 = 1.8, the same formula is often written as °F = °C × 1.8 + 32. NIST, the US National Institute of Standards and Technology, lists this as the exact conversion.
Two parts do two jobs:
- × 1.8 adjusts for degree size. Water's freezing-to-boiling range covers 100 °C but 180 °F, so one Celsius degree is 1.8 Fahrenheit degrees.
- + 32 adjusts for the starting point. Water freezes at 0 °C but at 32 °F.
The order matters: multiply first, then add.
How do you convert Fahrenheit to Celsius?
Reverse the steps: subtract 32 first, then divide.
°C = (°F − 32) × 5/9, or equivalently (°F − 32) ÷ 1.8
Example: 72 °F − 32 = 40, and 40 ÷ 1.8 = 22.2 °C.
Worked examples
Example 1: a mild day, 25 °C
25 × 1.8 = 45. 45 + 32 = 77 °F.
Example 2: body temperature, 37 °C
37 × 1.8 = 66.6. 66.6 + 32 = 98.6 °F.
Example 3: below freezing, −10 °C
−10 × 1.8 = −18. −18 + 32 = 14 °F. Negative Celsius values follow the same steps; the sign is carried through the multiplication.
Example 4: an oven, 180 °C
180 × 1.8 = 324. 324 + 32 = 356 °F, which recipes usually round to 350 °F.
Example 5: Fahrenheit to Celsius, 212 °F
212 − 32 = 180. 180 ÷ 1.8 = 100 °C, the boiling point of water at standard sea-level pressure.
Celsius to Fahrenheit conversion chart
| Celsius | Fahrenheit | Reference point |
|---|---|---|
| −40 °C | −40 °F | Both scales are equal |
| −18 °C | −0.4 °F | Close to 0 °F |
| 0 °C | 32 °F | Water freezes |
| 4 °C | 39.2 °F | Just above freezing |
| 10 °C | 50 °F | Cool day |
| 20 °C | 68 °F | Room temperature |
| 25 °C | 77 °F | Warm room |
| 30 °C | 86 °F | Hot day |
| 37 °C | 98.6 °F | Body temperature |
| 40 °C | 104 °F | Heat wave |
| 100 °C | 212 °F | Water boils (sea level) |
Oven temperatures
| Celsius | Fahrenheit (exact) | Common recipe setting |
|---|---|---|
| 150 °C | 302 °F | 300 °F |
| 160 °C | 320 °F | 325 °F |
| 175 °C | 347 °F | 350 °F |
| 180 °C | 356 °F | 350 °F |
| 190 °C | 374 °F | 375 °F |
| 200 °C | 392 °F | 400 °F |
| 220 °C | 428 °F | 425 °F |
| 230 °C | 446 °F | 450 °F |
| 250 °C | 482 °F | 475–500 °F |
Oven dials are marked in round steps, so recipes usually pair the nearest setting rather than the exact value.
Why is −40 the same in both scales?
Setting °F equal to °C in the formula gives x = 1.8x + 32. Solving: −0.8x = 32, so x = −40. At −40, both thermometers show the same number. Above −40, Fahrenheit readings are higher; below it, Celsius readings are higher.
Is there a quick mental shortcut?
A common approximation is double the Celsius and add 30.
- 20 °C → 40 + 30 = 70 °F (exact: 68 °F)
- 10 °C → 20 + 30 = 50 °F (exact: 50 °F)
How accurate is the shortcut?
The shortcut computes 2 × °C + 30, while the exact formula is 1.8 × °C + 32. The difference is 0.2 × °C − 2 degrees Fahrenheit. It is exact at 10 °C and grows by 0.2 °F for each degree away from 10.
| Celsius | Shortcut | Exact | Error |
|---|---|---|---|
| −18 °C | −6 °F | −0.4 °F | −5.6 °F |
| 0 °C | 30 °F | 32 °F | −2 °F |
| 10 °C | 50 °F | 50 °F | 0 °F |
| 20 °C | 70 °F | 68 °F | +2 °F |
| 30 °C | 90 °F | 86 °F | +4 °F |
| 37 °C | 104 °F | 98.6 °F | +5.4 °F |
| 100 °C | 230 °F | 212 °F | +18 °F |
| 180 °C | 390 °F | 356 °F | +34 °F |
The shortcut works well for weather between roughly 0 and 30 °C, where it is off by 4 °F or less. It should not be used for body temperature, cooking, or anything technical: a 5.4 °F error at 37 °C makes a normal reading look like a high fever, and a 34 °F error in an oven is enough to burn food.
The reverse shortcut is subtract 30 and halve: 70 °F → 40 → 20 °C (exact: 21.1 °C).
Converting temperature differences
A temperature change converts with the 1.8 factor only, without the +32 offset. If a forecast says it will be 10 °C warmer tomorrow, that is 10 × 1.8 = 18 °F warmer, not 50 °F. This matters for things like thermostat adjustments, climate data, and lab work.
The 9:5 relationship between degree sizes is a simple ratio, so a ratio calculator can scale differences the same way.
Common mistakes
- Adding 32 before multiplying. (20 + 32) × 1.8 = 93.6, which is wrong; the correct answer is 68 °F.
- Using 5/9 instead of 9/5. Going from Celsius to Fahrenheit, the number should get larger for any temperature above −40.
- Applying +32 to a difference. Only actual temperatures need the offset.
- Rounding 98.6 to 99 and back. 99 °F converts to 37.2 °C, so repeated rounding can shift values; keep one decimal place when precision matters.