The formula: multiply by 9, divide by 5, then add 32
To convert any temperature from Celsius to Fahrenheit, take the Celsius number, multiply it by 9, divide the result by 5, then add 32. That final number is your Fahrenheit temperature.
The formula works the same way every time: (°C × 9/5) + 32 = °F. You can also write it as (°C × 1.8) + 32, since 9 divided by 5 equals 1.8. Both versions give you the same answer.
The reason you add 32 at the end is that the two scales start at different points. Water freezes at 0°C but at 32°F. Water boils at 100°C but at 212°F. The multiplication step handles the different size of each degree; the addition step handles the different starting point.
Key Takeaways
- Multiply the Celsius temperature by 9, divide by 5, then add 32 to get Fahrenheit.
- You can use 1.8 instead of 9/5 — they are the same number and give the same result.
- The number 32 appears in every conversion because water freezes at 0°C and 32°F.
- Rounding to the nearest whole number is usually fine for everyday temperatures.
Working through an example step by step
Say the temperature outside is 25°C and you want to know what that is in Fahrenheit. Start with 25 and multiply by 9: that gives you 225. Now divide 225 by 5: that gives you 45. Finally, add 32: 45 + 32 = 77. So 25°C is 77°F.
Try another one. If it is 0°C (the freezing point of water), multiply 0 by 9 to get 0, divide by 5 to get 0, then add 32 to get 32°F. That matches what you would expect — freezing point is 32°F.
One more: 100°C (boiling water). Multiply by 9 to get 900, divide by 5 to get 180, add 32 to get 212°F. Again, that is correct — water boils at 212°F.
Why the formula has those specific numbers
The Celsius scale divides the space between freezing and boiling water into 100 equal steps. The Fahrenheit scale divides the same space into 180 equal steps. That is why you multiply by 9 and divide by 5 — you are scaling from 100 steps to 180 steps, which is a ratio of 180 to 100, or 9 to 5.
The 32 comes from the fact that Celsius calls the freezing point 0 degrees, but Fahrenheit calls it 32 degrees. So after you scale the temperature difference, you have to shift it up by 32 to match the Fahrenheit scale's starting point.
Quick reference for common temperatures
| Celsius | Fahrenheit | What it means |
|---|---|---|
| 0°C | 32°F | Water freezes |
| 10°C | 50°F | Cool day |
| 20°C | 68°F | Room temperature |
| 25°C | 77°F | Warm day |
| 37°C | 98.6°F | Normal body temperature |
| 100°C | 212°F | Water boils |
Doing the math without a calculator
If you do not have a calculator handy, you can estimate. Multiply the Celsius number by 2 as a rough shortcut, then add 30. This will not be exact, but it gets you close enough for everyday use. For example, 25°C times 2 is 50, plus 30 is 80°F — the real answer is 77°F, so you are within 3 degrees.
The reason this shortcut works is that 1.8 (which is 9/5) is close to 2, and 32 is close to 30. You lose a bit of accuracy, but you gain speed. For temperatures between 0°C and 40°C, this method usually gets you within 5 degrees of the correct answer.
Converting in the other direction: Fahrenheit to Celsius
If you need to go the other way — from Fahrenheit to Celsius — reverse the steps. Subtract 32 first, then multiply by 5, then divide by 9. The formula is (°F − 32) × 5/9 = °C.
For example, if the temperature is 68°F, subtract 32 to get 36, multiply by 5 to get 180, divide by 9 to get 20. So 68°F is 20°C. You can check this against the table above — it matches.
Frequently Asked Questions
Do I have to use 1.8 instead of 9/5?
No. Both give the same result because 9 divided by 5 equals 1.8. Use whichever is easier for you. If your calculator shows decimals, 1.8 is faster. If you are doing it by hand, 9/5 might be clearer.
What if I get a decimal in my answer?
That is normal. For everyday purposes, you can round to the nearest whole number. If the answer is 77.5°F, calling it 78°F is fine. For scientific work, keep the decimal.
Is there a temperature where Celsius and Fahrenheit are the same number?
Yes. At −40 degrees, Celsius and Fahrenheit are equal. You can check it: (−40 × 9/5) + 32 = −72 + 32 = −40. It is the only point where the two scales meet.
Can I convert negative temperatures?
Yes, the formula works for any temperature, positive or negative. For example, −10°C: multiply by 9 to get −90, divide by 5 to get −18, add 32 to get 14°F. Negative Celsius temperatures become negative or positive Fahrenheit depending on how cold they are.