How to Convert Celsius to Fahrenheit (and Back)
To convert Celsius to Fahrenheit, multiply by 9/5 and add 32. To go the other way, subtract 32 first, then multiply by 5/9. Both formulas are simple, but the order of operations matters, and there’s a second, less obvious trap: converting a temperature difference works completely differently from converting a temperature reading.
The two formulas
Celsius to Fahrenheit:
F = C × 9/5 + 32Multiply first, add 32 last.
Fahrenheit to Celsius:
C = (F − 32) × 5/9Subtract first, multiply last.
The two formulas are mirror images of each other, but people frequently swap the order when converting by hand. Going from Celsius to Fahrenheit, the mistake is subtracting 32 before multiplying (it should come after). Going from Fahrenheit to Celsius, the mistake is multiplying before subtracting 32 (it should come first). If you keep “multiply-then-add” for one direction and “subtract-then-multiply” for the other, you won’t mix them up.
Both numbers in the formula come from how the two scales were originally built. Celsius sets 0 at water’s freezing point and 100 at its boiling point, a clean 100-degree span. Fahrenheit sets those same two events at 32 and 212, a 180-degree span. Divide 180 by 100 and you get 9/5, which is why every Celsius degree is worth 1.8 Fahrenheit degrees. The 32 is just the gap between the two scales’ zero points. Once you see the formula as “stretch the scale by 1.8, then shift it by 32 to line up the zero points,” the two conversion rules stop feeling like arbitrary numbers to memorize.
Worked examples
A few reference points worth memorizing, since they come up constantly in weather reports, cooking, and health:
| Celsius | Fahrenheit | Context |
|---|---|---|
| -40°C | -40°F | The one point where both scales agree |
| 0°C | 32°F | Water freezes |
| 10°C | 50°F | Cool spring morning |
| 20°C | 68°F | Comfortable room temperature |
| 25°C | 77°F | Warm day |
| 37°C | 98.6°F | Normal human body temperature |
| 38°C | 100.4°F | Low-grade fever |
| 100°C | 212°F | Water boils |
| 180°C | 356°F | Common oven baking temperature |
Take 25°C as a sample calculation: 25 × 9/5 = 45, and 45 + 32 = 77°F. Or check 100.4°F back to Celsius: 100.4 − 32 = 68.4, and 68.4 × 5/9 = 38°C. Same relationship, opposite direction.
Convert with your own numbers
Enter any temperature below to convert it instantly, in either direction.
Common mistakes
Treating a temperature change the same as a temperature reading. This is the one that trips up even people who know the formula cold. If the forecast says tomorrow will be 5°C warmer than today, that 5°C is not a point on the thermometer, it’s a gap between two points, and gaps convert differently from readings. For a difference, only the ×9/5 (or ×1.8) part of the formula applies. The +32 must be left out entirely, because +32 is an offset anchored to the zero points of the two scales, and a gap between two temperatures doesn’t have a zero point to offset.
Run the numbers and the difference is obvious. A rise of 5°C is a rise of 9°F, since 5 × 1.8 = 9. If you mistakenly plug that 5 into the full formula instead, you get 5 × 9/5 + 32 = 41, which is wrong by a wide margin. A 10°C swing works the same way: it’s an 18°F swing (10 × 1.8 = 18), not 82°F. This isn’t a rare edge case. It comes up whenever someone describes a change rather than a reading: “the oven runs 3°C hotter than the dial says,” “her fever went up 2°C overnight,” “today is 6°C cooler than yesterday.” In every one of those, convert the number alone by 1.8 and stop there.
Trusting the “double it and add 30” shortcut too far. It’s a handy mental estimate for casual conversation, but it drifts from the real formula fast, and always in the same direction once you’re above about 10°C.
| Celsius | Shortcut (×2 + 30) | Actual formula | Error |
|---|---|---|---|
| 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 |
| 40°C | 110°F | 104°F | +6°F |
The shortcut happens to land exactly right at 10°C, which is probably why it feels trustworthy, but the gap widens by about 2°F for every 10°C you move away from that point. Fine for guessing whether to grab a jacket, not fine for a body temperature or an oven setting.
Swapping the order of operations. As covered above, Celsius to Fahrenheit multiplies before adding; Fahrenheit to Celsius subtracts before multiplying. Doing it backward in either direction gives you a number that looks plausible but is wrong, since 32 and the 9/5 ratio don’t commute.
Frequently asked questions
How do I convert a temperature change or difference, not a fixed reading? Multiply the Celsius difference by 1.8 (which is the same as 9/5) and stop, don’t add 32. A rise of 5°C is a rise of 9°F. The +32 in the standard formula only applies when you’re converting an actual point on the thermometer, because it aligns the two scales’ zero points, and a gap between two readings has no zero point to align.
Why does “double the Celsius number and add 30” stop working at higher temperatures? It’s a rough approximation of the real ratio (9/5 = 1.8, rounded up to 2) combined with an offset (32, rounded down to 30). Those two roundings happen to cancel out almost exactly at 10°C, which is why the shortcut feels accurate there. Above and below that point the errors compound instead of canceling, growing by roughly 2°F for every 10°C you move away from it.
Is there a temperature that reads the same on both scales? Yes, -40. Both -40°C and -40°F describe the identical temperature, which is the point where the two linear scales cross. It falls out of the algebra: set C = F in the formula and solve, and -40 is the only solution.
How do I convert an oven temperature from a recipe? Treat it as a normal absolute conversion, since a baking temperature is a fixed setting, not a change. A recipe calling for 180°C converts to 356°F; 200°C converts to 392°F. If you’re instead adjusting a temperature you already set, say nudging the oven 10°C hotter than the recipe calls for, that’s a difference, so convert it as 18°F instead of running the full formula.
Is there a fast way to estimate without doing the exact math? For a rough gut check, doubling the Celsius figure and knocking off a bit gets you close in the 0 to 30°C range, which covers most everyday weather. For anything precise, body temperature, a recipe, a lab reading, use the actual formula or the converter above; the shortcut’s error grows too large outside that narrow band to rely on.