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How to Convert Celsius to Fahrenheit (and Back Again)
The formula to convert Celsius to Fahrenheit is:
\[°F = °C \times \frac{9}{5} + 32\]Multiply the Celsius temperature by 9/5 (or 1.8), then add 32. To go the other direction, from Fahrenheit to Celsius:
\[°C = (°F - 32) \times \frac{5}{9}\]Subtract 32 from the Fahrenheit temperature, then multiply by 5/9 (or divide by 1.8). Both formulas are rearrangements of the same equation, so learning one gives you the other.
Why 9/5 and 32?
The two scales use different reference points and different step sizes. On the Celsius scale, water freezes at 0 degrees and boils at 100 degrees, giving a range of 100 degrees between those two benchmarks. On the Fahrenheit scale, water freezes at 32 degrees and boils at 212 degrees, giving a range of 180 degrees.
Because 180 Fahrenheit degrees cover the same physical range as 100 Celsius degrees, the ratio between the two step sizes is 180/100, which simplifies to 9/5. Each Celsius degree represents a larger temperature change than each Fahrenheit degree. The 32 in the formula accounts for the offset: Fahrenheit’s freezing point starts at 32 rather than 0.
Worked examples
To convert 25°C to Fahrenheit:
\[°F = 25 \times \frac{9}{5} + 32 = 45 + 32 = \textbf{77°F}\]A warm spring day at 25°C is 77°F.
Going the other direction, convert 98.6°F (normal body temperature) to Celsius:
\[°C = (98.6 - 32) \times \frac{5}{9} = 66.6 \times 0.5556 = \textbf{37°C}\]Negative temperatures work the same way. Convert -40°C to Fahrenheit:
\[°F = -40 \times \frac{9}{5} + 32 = -72 + 32 = \textbf{-40°F}\]This is the one temperature where Celsius and Fahrenheit are equal. It is the only point where the two scales intersect, and it makes a useful sanity check: plugging -40 into either formula returns -40.
The temperature converter handles all three scales (Fahrenheit, Celsius, and Kelvin) instantly if you want to skip the arithmetic.
Quick reference table
| Celsius | Fahrenheit | Context |
|---|---|---|
| -40 | -40 | Extreme arctic cold; where scales meet |
| 0 | 32 | Water freezes |
| 10 | 50 | Cool day |
| 20 | 68 | Room temperature |
| 25 | 77 | Warm day |
| 30 | 86 | Hot day |
| 37 | 98.6 | Normal body temperature |
| 100 | 212 | Water boils |
The mental math shortcut
The exact formula requires multiplying by 1.8, which is awkward to do in your head. A faster approximation: double the Celsius value and add 30.
For 20°C: double is 40, plus 30 is 70°F. The exact answer is 68°F, so the shortcut is off by 2 degrees. For 30°C: double is 60, plus 30 is 90°F. The exact answer is 86°F, off by 4 degrees.
The shortcut consistently overshoots because doubling is 2.0 instead of the correct 1.8, and adding 30 instead of 32 only partially compensates. The approximation works well enough for everyday use: deciding what to wear, judging whether a foreign weather forecast means warm or cold, or estimating oven temperatures while cooking. For anything requiring precision, use the full formula or the temperature converter.
Kelvin: the third scale
Scientific work uses Kelvin, which starts at absolute zero (the lowest physically possible temperature) and uses the same step size as Celsius. Converting between Celsius and Kelvin requires no multiplication at all:
\[K = °C + 273.15\] \[°C = K - 273.15\]Room temperature of 20°C is 293.15 K. Water boils at 373.15 K. Absolute zero is 0 K, which corresponds to -273.15°C or -459.67°F. Unlike Celsius and Fahrenheit, the Kelvin scale has no negative values because nothing can be colder than absolute zero.
To convert directly from Fahrenheit to Kelvin, convert to Celsius first, then add 273.15. There is no commonly used shortcut for that conversion because the situations where you need it (lab work, physics problems, engineering calculations) are exactly the situations where precision matters and a calculator is already at hand.
When each scale is used
The United States is the only major country that still uses Fahrenheit for everyday purposes. Weather forecasts, cooking recipes, and thermostat settings in the U.S. are all in Fahrenheit. Virtually every other country uses Celsius for daily life.
Science and engineering use Celsius or Kelvin everywhere, including in the U.S. Medical settings often use both: a doctor might record body temperature as 37°C or 98.6°F depending on the country and the equipment.
If you travel or follow international weather, being able to convert between the two scales is a practical skill. The mental math shortcut covers casual situations; the formula covers everything else. For quick conversions between all three temperature scales at once, the temperature converter does the work for you.