Celsius to Fahrenheit Formula and Conversion Examples
The calculator for this page is switched off while it is checked. The formula is below, and the worked example in the article shows how to use it by hand.
To convert Celsius (°C) to Fahrenheit (°F), multiply the Celsius temperature by 9/5, then add 32: °F = (°C × 9/5) + 32. Enter a Celsius temperature to get its Fahrenheit equivalent; the calculator also shows the intermediate multiplication so you can follow the conversion.
Formula
The standard Celsius-to-Fahrenheit formula is:
°F = (°C × 9/5) + 32
- °C is the temperature in degrees Celsius.
- °F is the corresponding temperature in degrees Fahrenheit.
- 9/5 (or 1.8) adjusts for the different size of the two temperature scales’ degree increments.
- 32 is the Fahrenheit reading that corresponds to 0°C.
The calculator’s second output, “Celsius times nine-fifths,” is the scaled temperature difference before the 32-degree offset is added. It is an intermediate value, not the final Fahrenheit temperature.
Worked Example
Using the calculator’s default input, 20°C:
- Multiply by 9/5: 20 × 9/5 = 36.
- Add 32: 36 + 32 = 68°F.
The result is 68.00°F. The intermediate scaled value is 36.00 Fahrenheit degrees; adding 32°F gives the final reading.
Why the Formula Uses 9/5 and 32
Celsius and Fahrenheit assign different numbers to the same physical temperatures, and their degree increments are different sizes. On the Celsius scale, water freezes at 0°C and boils at 100°C at standard atmospheric pressure. On the Fahrenheit scale, those reference points are 32°F and 212°F. The same 100-degree Celsius interval therefore spans 180 Fahrenheit degrees, giving the scale factor 180/100 = 9/5.
The scales also have different zero points. Since 0°C equals 32°F, the conversion must add 32 after scaling. Multiplication alone would incorrectly map 0°C to 0°F.
This relationship is linear: a change of 1°C equals a change of 1.8°F. That statement concerns a temperature difference, not the conversion of a temperature reading. To convert an actual reading, include the 32-degree offset.
How to Convert Celsius by Hand
For a temperature in Celsius, multiply by 1.8 and add 32. For instance, 25°C becomes 25 × 1.8 + 32 = 77°F. You can also multiply by 9 and divide by 5 before adding 32; both methods are mathematically equivalent.
For a quick mental estimate, doubling the Celsius value and adding 30 is sometimes used. At 20°C, that gives 70°F rather than the exact 68°F. It is an approximation, not a replacement for the formula, and its error varies with the temperature. Use the exact formula when precision matters.
Common Temperatures and Useful Checks
- −40°C = −40°F. This is the point where the two scales show the same number.
- 0°C = 32°F, the freezing point of water under standard conditions.
- 20°C = 68°F.
- 37°C = 98.6°F.
- 100°C = 212°F, the boiling point of water under standard conditions.
These reference points can help catch a sign, arithmetic, or scale-direction error. For example, a result for 0°C should be 32°F, not 0°F. For temperatures below zero, keep the negative sign through the multiplication: −10°C × 1.8 + 32 = 14°F.
Reverse Conversion, Rounding, and Limits
To convert Fahrenheit back to Celsius, reverse the operations: subtract 32, then multiply by 5/9. The formula is °C = (°F − 32) × 5/9. For example, 68°F gives (68 − 32) × 5/9 = 20°C.
Keep extra digits while calculating and round only the final answer to the precision you need. The displayed two decimal places are a formatting choice; they do not mean every temperature is known to a hundredth of a degree. A measured value may be less precise, and rounding should reflect its source.
The conversion changes the numeric scale only: it does not change the physical temperature. It also does not account for measurement uncertainty or differences in local conditions. The familiar freezing and boiling points of water assume standard atmospheric pressure; boiling temperature, in particular, changes with pressure. This formula remains a scale conversion, not a prediction of those conditions.
Frequently Asked Questions
What is the formula to change C to F?
Use °F = (°C × 9/5) + 32. Multiply the Celsius reading by 1.8, then add 32.
How do I convert 30°C to Fahrenheit?
Calculate 30 × 9/5 + 32. The result is 86°F.
Why do you add 32 when converting Celsius to Fahrenheit?
The scales have different zero points: 0°C corresponds to 32°F. Adding 32 accounts for that offset after adjusting the degree size.
Is multiplying Celsius by 2 and adding 30 accurate?
It is a quick estimate, not the exact conversion. Use 1.8 times the Celsius value plus 32 for the standard formula.
At what temperature are Celsius and Fahrenheit equal?
They have the same numerical value at −40: −40°C = −40°F.
Related
Formula used
in c | Celsius temperature | °C | 20 | out f | Fahrenheit temperature | °F | c * 9 / 5 + 32 | 2 out scaled | Celsius times nine-fifths | °F difference | c * 9 / 5 | 2
Each line is one input (in, sel, list) or one result (out: label, unit, formula, decimals). How the calculators work
Method: the standard formula for this calculation, rounded as each result states. See how the calculators work or report an error.