Celsius to Fahrenheit Formula (and Fahrenheit to Celsius)
The exact formulas to convert Celsius to Fahrenheit and back, worked examples, a quick mental shortcut, a table of common temperatures and how Kelvin fits in.
· 3 min read
To convert Celsius to Fahrenheit, multiply by 9/5 (or 1.8) and add 32: °F = °C × 9/5 + 32. To go the other way, subtract 32 and multiply by 5/9: °C = (°F − 32) × 5/9. So 20 °C is 68 °F, and 98.6 °F is 37 °C.
The formulas explained
The two scales differ in two ways:
- Different starting points. Water freezes at 0 °C but at 32 °F. That is why you add or subtract 32.
- Different degree sizes. Between freezing and boiling there are 100 Celsius degrees but 180 Fahrenheit degrees. One Celsius degree is therefore 180 ÷ 100 = 1.8 Fahrenheit degrees, which is where 9/5 comes from.
Celsius to Fahrenheit: °F = °C × 1.8 + 32 Fahrenheit to Celsius: °C = (°F − 32) ÷ 1.8
The order matters in the second formula: subtract 32 first, then divide.
Worked examples
1. A warm day: 25 °C in Fahrenheit
25 × 1.8 = 45, then 45 + 32 = 77 °F
2. Body temperature: 98.6 °F in Celsius
98.6 − 32 = 66.6, then 66.6 ÷ 1.8 = 37 °C
3. An oven setting: 350 °F in Celsius
350 − 32 = 318, then 318 ÷ 1.8 = 176.67 °C. Recipes usually round this to 175 or 180 °C, which makes little difference in practice.
Common temperatures
| Celsius | Fahrenheit | What it is |
|---|---|---|
| −40 °C | −40 °F | The point where both scales meet |
| 0 °C | 32 °F | Water freezes |
| 20 °C | 68 °F | Mild room temperature |
| 37 °C | 98.6 °F | Typical body temperature |
| 100 °C | 212 °F | Water boils (at sea level) |
−40 is the only temperature that reads the same on both scales, which makes it a handy check for any formula you write.
A quick mental approximation
For a rough idea, double the Celsius value and add 30. It is an approximation, not the real formula:
- 10 °C → 10 × 2 + 30 = 50 °F (exact: 50 °F)
- 20 °C → 70 °F (exact: 68 °F)
- 30 °C → 90 °F (exact: 86 °F)
- 37 °C → 104 °F (exact: 98.6 °F)
The shortcut is spot on at 10 °C and drifts further the further you move from it, so it is fine for weather but not for a fever, an oven or anything precise. The reverse shortcut is subtract 30 and halve: 72 °F → about 21 °C (exact: 22.2 °C).
What about Kelvin?
Kelvin is the scale used in science. It uses the same degree size as Celsius but starts at absolute zero, so K = °C + 273.15: 20 °C is 293.15 K and 0 K is −273.15 °C. Kelvin is written without the degree sign. From Fahrenheit, convert to Celsius first, then add 273.15. The Temperature converter also handles Rankine, the Fahrenheit-based equivalent of Kelvin.
Quick method with our tools
- Open the Celsius to Fahrenheit converter.
- Enter the temperature in °C and read the value in °F, with a table of common temperatures.
- For the reverse, use the Fahrenheit to Celsius converter.
- For Kelvin or Rankine, or to see all four scales at once, use the Temperature converter.
Common mistakes
- Adding 32 before multiplying. 20 °C is (20 × 1.8) + 32 = 68 °F, not (20 + 32) × 1.8 = 93.6 °F.
- Dividing before subtracting in the Fahrenheit to Celsius formula.
- Converting temperature differences with the full formula. A rise of 10 °C is a rise of 18 °F (10 × 1.8), with no +32, because a difference has no starting point.
- Relying on the shortcut for precise values, such as medical or cooking temperatures.