The Celsius to Fahrenheit Formula
Answer: The Celsius to Fahrenheit formula is the mathematical equation used to convert temperatures from the Celsius scale to the Fahrenheit scale. This formula is essential for understanding temperature conversions in various contexts, from weather forecasting to cooking.
To use the C to F formula, simply multiply the Celsius temperature by 9/5 (or 1.8) and then add 32 to the result.
Using the Celsius to Fahrenheit conversion formula is straightforward:
- Take the temperature in Celsius
- Multiply it by 9/5 (or 1.8)
- Add 32 to the result
Example: Convert 20°C to Fahrenheit
20 × 9/5 = 36
36 + 32 = 68°F
Need to calculate conversions quickly? Use our C to F Calculator for instant results.
Last updated: 2026-02-10
Easy Approximation Method
For quick mental estimates, you can use this simplified version of the C to F formula:
This method is not exact but provides a close estimate for everyday temperatures.
Example: 20°C ≈ (20×2)+30 = 70°F (actual 68°F)
Interactive Formula Demonstration
Enter a Celsius temperature to see the C to F formula in action with step-by-step calculation:
Calculation Steps:
Step 1: Multiply Celsius value by 9/5: 20 × 9/5 = 36.0
Step 2: Add 32 to the result: 36.0 + 32 = 68.0
Final Result: 20°C = 68.0°F
Derivation of the Celsius to Fahrenheit Formula
The Celsius to Fahrenheit equation is derived from the relationship between the two temperature scales. The key reference points are the freezing and boiling points of water:
- Water freezes at 0°C and 32°F
- Water boils at 100°C and 212°F
This gives us a 100° range for Celsius and a 180° range for Fahrenheit between the same two points. Therefore, each degree Celsius is equivalent to 1.8 degrees Fahrenheit (180/100 = 9/5 = 1.8).
Determine the Ratio
The difference between the freezing and boiling points is 100° in Celsius and 180° in Fahrenheit.
Account for the Offset
The Fahrenheit scale has a 32° offset at the freezing point (0°C = 32°F).
Final Formula
Combining both elements gives us the complete C to F conversion formula.
The fraction 9/5 (which equals 1.8) represents the ratio between Fahrenheit and Celsius degree sizes. The +32 accounts for the different zero points of the two scales - 0°C equals 32°F, so we need to add this offset to get the correct Fahrenheit temperature.
Celsius to Fahrenheit Conversion Table
Celsius to Fahrenheit Conversion Table
| Celsius (°C) | Fahrenheit (°F) | Description |
|---|---|---|
| -40 | -40 | Temperature where Celsius and Fahrenheit are equal |
| -18 | 0 | Freezing temperature in Fahrenheit |
| 0 | 32 | Water freezing point |
| 5 | 41 | Cool refrigerator temperature |
| 20 | 68 | Room temperature |
| 25 | 77 | Pleasant warm day |
| 30 | 86 | Warm day |
| 37 | 98.6 | Average human body temperature |
| 100 | 212 | Water boiling point |
| 200 | 392 | Moderate oven temperature |
Other Temperature Conversion Formulas
Fahrenheit to Celsius Formula
To convert Fahrenheit to Celsius, subtract 32 from the Fahrenheit temperature, then multiply by 5/9.
Example: Convert 68°F to Celsius: (68 - 32) × 5/9 = 36 × 5/9 = 20°C
Quick Approximation
°C ≈ (°F - 30) ÷ 2
Example: 70°F ≈ (70-30)÷2 = 20°C (actual 21.1°C)
Celsius to Kelvin Formula
To convert Celsius to Kelvin, simply add 273.15 to the Celsius temperature.
Example: Convert 25°C to Kelvin: 25 + 273.15 = 298.15K
Kelvin to Celsius Formula
°C = K - 273.15
Example: 300K = 300 - 273.15 = 26.85°C
How to Convert 30°C to Fahrenheit
Let's walk through the conversion of 30°C to Fahrenheit using the officially recognized Celsius to Fahrenheit equation:
Start with the formula
Plug in the Celsius value
Multiply 30 by 9/5
Add 32 to the result
Final result
Using the approximation method: (30 × 2) + 30 = 90°F, which is a close estimate for most Celsius to Fahrenheit calculator needs.
Common Mistakes When Converting Celsius to Fahrenheit
- Forgetting to add 32: Many people multiply the Celsius value by 1.8 but forget to add the final 32 degree offset.
- Using 5/9 instead of 9/5: Remember that Fahrenheit degrees are smaller, so the multiplier from Celsius to Fahrenheit must be greater than 1 (9/5 = 1.8).
- Order of operations: Always perform the multiplication (or division) before adding 32.
When Do You Need to Convert Celsius to Fahrenheit?
Understanding the C to F formula is useful in several real-world scenarios:
- Weather Forecasts: Comparing international weather reports when traveling between countries that use different scales.
- Cooking and Baking: Following recipes that use Fahrenheit in an oven calibrated to Celsius, or vice versa.
- International Travel: Adjusting thermostats and understanding local climate during trips to the United States or its territories.
- Scientific Education: Understanding the fundamental physical properties of temperature scales in chemistry and physics.
Celsius vs Fahrenheit: What's the Difference?
The primary difference between Celsius and Fahrenheit is their starting points and degree sizes. Celsius is based on the metric system where 0° is the freezing point of water and 100° is the boiling point. Fahrenheit is an older imperial scale where water freezes at 32° and boils at 212°.
While the Fahrenheit scale is more granular (180 degrees between freezing and boiling vs 100 in Celsius), the Celsius scale is much more common in scientific and international contexts. You can how to change Celsius into Fahrenheit easily for any value using our specialized tools.
Formula vs Calculator: Which Should You Use?
Deciding whether to use the Celsius to Fahrenheit formula or an online calculator depends on your specific needs:
- Use the Formula when: You are in a classroom setting, taking an exam, or want to practice mental math using our easy doubling method.
- Use a Calculator when: You have a long list of temperatures to convert, need high-precision decimal results, or are in a hurry during cooking or travel.
Both methods use the same consistent mathematical logic to help you understand how to change Celsius into Fahrenheit accurately.
Specific Temperature Conversion FAQ
At what temperature are Celsius and Fahrenheit equal?
The two scales intersect at -40 degrees. This means -40°C is exactly the same as -40°F—the point of thermal equilibrium between the two systems.
How do I convert 37.3°C to Fahrenheit for medical use?
For a medical temperature like 37.3°C, use the calculation: (37.3 × 1.8) + 32 = 99.14°F. This is slightly above the average adult body temperature of 98.6°F and may indicate a low-grade fever.
How do I convert 180°C to Fahrenheit for baking?
For oven settings, the conversion is: (180 × 1.8) + 32 = 356°F. Most recipes will round this to 350°F or 375°F depending on the required baking precision and oven calibration.
For quick and accurate conversions, try our Celsius to Fahrenheit calculator. Celsius to Fahrenheit Converter.