The Celsius to Fahrenheit Formula
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.
Need to calculate conversions quickly? Use our C to F Calculator for instant results.
How to Use the Formula
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
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 = 180/5 = 36
Step 2: Add 32 to the result
36 + 32 = 68
Final Result:
20°C = 68°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.
Why 9/5 and +32?
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.
Common Celsius to Fahrenheit Conversions
For a complete reference, see our Celsius to Fahrenheit Conversion Chart.
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 C to F formula:
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 close to the exact value of 86°F.
Frequently Asked Questions About the Celsius to Fahrenheit Formula
The formula for converting Celsius to Fahrenheit is: °F = (°C × 9/5) + 32. This equation means you multiply the Celsius temperature by 9/5 (or 1.8) and then add 32 to get the Fahrenheit temperature.
The easiest way to convert Celsius to Fahrenheit mentally is to use the approximation formula: °F ≈ (°C × 2) + 30. This method is not exact but gives a close estimate for everyday temperatures. For example, 20°C ≈ (20×2)+30 = 70°F (actual value is 68°F).
The equation to convert Celsius to Fahrenheit is: °F = (°C × 9/5) + 32. Multiply the Celsius temperature by 9/5 (or 1.8), then add 32 to the result. For example, 25°C = (25 × 9/5) + 32 = 45 + 32 = 77°F.
The fraction 9/5 (which equals 1.8) is used in the formula because there are 180 degrees between the freezing and boiling points of water on the Fahrenheit scale (32°F to 212°F), but only 100 degrees on the Celsius scale (0°C to 100°C). The ratio 180/100 simplifies to 9/5.
We add 32 in the formula because 0°C equals 32°F. The freezing point of water is 32°F on the Fahrenheit scale, so this offset accounts for the different starting points of the two temperature scales.
To convert 30°C to Fahrenheit, use the formula: °F = (30 × 9/5) + 32. Calculate 30 × 9/5 = 54, then add 32 to get 86°F. So, 30°C = 86°F.
Celsius and Fahrenheit are equal at -40 degrees. That is, -40°C = -40°F. This is the intersection point of the two temperature scales.
To convert 37.3°C to Fahrenheit, use the formula: °F = (37.3 × 9/5) + 32. Calculate 37.3 × 9/5 = 67.14, then add 32 to get 99.14°F. So, 37.3°C ≈ 99.1°F. This is slightly above normal body temperature (98.6°F) and may indicate a mild fever.
To convert 180°C to Fahrenheit, use the formula: °F = (180 × 9/5) + 32. Calculate 180 × 9/5 = 324, then add 32 to get 356°F. So, 180°C = 356°F. This is a common baking temperature for many recipes.
For quick and accurate conversions, try our C to F Calculator.