# Celsius to Fahrenheit Conversion (°C to °F) –  Definition, Examples

Home » Math Vocabulary » Celsius to Fahrenheit Conversion (°C to °F) –  Definition, Examples

## What Is Celsius to Fahrenheit Conversion?

Celsius to Fahrenheit is a temperature conversion from the Celsius scale to the Fahrenheit scale.

To convert a temperature from Celsius to Fahrenheit, we use a straightforward formula known as the Celsius to Fahrenheit formula or the C to F formula.

Temperature scales help in measuring how hot or cold a body is.

What Is Celsius?

The Celsius temperature scale is one of the most commonly used scales to measure everyday temperatures. The Celsius scale is used by the international system of units (SI). The freezing point and the boiling point of water are 0°C and 100°C respectively.

What Is Fahrenheit?

Fahrenheit is the most commonly used scale to measure the temperature in the US. The freezing point and the boiling point of water in the Fahrenheit scale measures are 32 °F and  212 °F respectively.

## Celsius to Fahrenheit Formula

The formula to convert Celsius to Fahrenheit is given by:

°F = °C $\times \frac{9}{5}$ + 32

where,

• C = temperature in degree Celsius (°C).
• F = temperature in degree Fahrenheit (°F).

The formula can also be written as

°F = ( °C × 1.8)+32 (since $\frac{9}{5}$ = 1.8)

## How to Convert Celsius to Fahrenheit

Let’s understand the Celsius to Fahrenheit conversion with the help of examples.

Example 1: Suppose we have to convert 30 °C to °F.

We get

°F = °C $\times \frac{9}{5}$ + 32

°F = 30 $\times \frac{9}{5}$ + 32

°F = 6 $\times$ 9 + 32

°F = 54 + 32

°F = 86 °F

Example 2: 40 degree celsius to fahrenheit

40 °C = 40 $\times \frac{9}{5}$ + 32 = 72 + 32 = 104 °F

## Derivation of Celsius to Fahrenheit Formula

The freezing point of water in Fahrenheit is 32 °F.

The boiling point of water in Fahrenheit is 212 °F.

Difference = 212 °F – 32 °F = 180 °F.

Similarly, the freezing point of water in Celsius is 0 °C.

The boiling point of water in Celsius is 100°C.

Difference = 100 °C – 0 °C = 100 °C

Fahrenheit and Celsius are directly proportional to each other. If the temperature on the Celsius scale rises, the temperature on the Fahrenheit scale also rises and vice versa. So, we will form a linear equation of the form y = mx + b.

Celsius to fahrenheit equation: °F = m °C + b

m = Rate of change = The ratio of the difference in temperatures

Ratio $= \frac{180}{100} = \frac{9}{5}$

For b, we need the temperature in Fahrenheit scale when the temperature in celsius is 0°C. It is 32 °F.

Thus, we get the formula

°F $= \frac{9}{5}\times$ °C + 32

## Shortcut Method for Celsius to Fahrenheit Conversion

As mentioned earlier, − 40 °C = − 40 °F.

Also, the ratio of the difference in temperatures is 9:5.

To convert a given temperature from Celsius to Fahrenheit, we can also use the following simple steps:

• Multiply by 1.8 or 95.
• Subtract 40.

Example: 37 °C.

## Facts about Celsius to Fahrenheit Scale

• The Celsius scale is widely used in most countries, while the Fahrenheit scale is primarily used in the United States.
• Freezing point of water in Celsius is 0 °C and in Fahrenheit is 32 °F.
• Boiling point of water in Celsius is 100 °C and in Fahrenheit is 212 °F.
• 0 Degrees Celsius to Fahrenheit = 32 °F
• 1 Degree Celsius to Fahrenheit = 33.8 °F

## Conclusion

In this article, we learned how to convert temperature from Celsius to Fahrenheit scale. We discussed and derived the formula for the Celsius to Fahrenheit scale. Let’s solve a few examples and MCQs for practice.

## Solved Examples on Celsius to Fahrenheit Conversion

1. What is the temperature in Fahrenheit of 20 °C?

Solution:

°F = °C $\times \frac{9}{5}$ + 32

°F = 20 $\times \frac{9}{5}$ + 32

°F = 4 × 9+32

°F =36+32

°F = 68 °F

2. Convert 140 °C to Fahrenheit.

Solution:

°F = °C $\times \frac{9}{5}$ + 32

°F = 140 $\times \frac{9}{5}$ + 32

°F = 28 × 9 + 32

°F = 252 + 32

°F = 284 °F

3. Find the temperature at which both Celsius and Fahrenheit scales show the same temperature.

Solution:

Let x °F = x °C

°F = °C $\times \frac{9}{5}$ + 32

x = x $\times \frac{9}{5}$ + 32

x – $\frac{9x}{5}$ = 32

$\frac{-4x}{5}$ = 32

x = – 40

Thus, – 40°C =  – 40 °F

4. What is the value of 65°C in Fahrenheit?

Solution:

°F = °C $\times \frac{9}{5}$ + 32

°F = 65 $\times \frac{9}{5}$ + 32

°F = 13 × 9 + 32

°F = 117 + 32

°F = 149 °F

5. Convert 36°C to Fahrenheit.

Solution: °F = °C $\times \frac{9}{5}$ + 32

°F = 36 $\times \frac{9}{5}$ + 32

= 64.8 + 32 = 96.8°F.

## Practice Problems on Celsius to Fahrenheit Scale

1

### On converting 125 °C to Fahrenheit, we get _____.

257 °F
267 °F
157 °F
167 °F
CorrectIncorrect
°F = °C $\times \frac{9}{5}$ + 32
°F = 125 $\times \frac{9}{5}$ + 32
°F = 225 + 32 = 257 °F.
2

### Convert 90°C to Fahrenheit.

149 °F
194 °F
198 °F
294 °F
CorrectIncorrect
°F = °C $\times \frac{9}{5}$ + 32
°F = 90 $\times \frac{9}{5}$ + 32
°F = 162 + 32 = 194 °F.
3

### Find the temperature in Fahrenheit of 45°C.

93 °F
103 °F
113 °F
133 °F
CorrectIncorrect
°F = °C $\times \frac{9}{5}$ + 32
°F = 45 $\times \frac{9}{5}$ + 32
°F = 81 + 32 = 113 °F.
4

### What is 75°C in Fahrenheit?

75 °F
107 °F
125 °F
167 °F
CorrectIncorrect
°F = °C $\times \frac{9}{5}$ + 32
°F = 75 $\times \frac{9}{5}$ + 32
°F = 135 + 32 = 167 °F.
5

### What is the temperature in Fahrenheit of 120 °C?

248 °F
268 °F
208 °F
348 °F
CorrectIncorrect
°F = °C $\times \frac{9}{5}$ + 32
°F = 120 $\times \frac{9}{5}$ + 32 = 216 + 32 = 248 °F.

To convert temperature from Fahrenheit to Celsius, we use the formula: °C = (°F-32) $\times \frac{5}{9}$

where

• C = Measure of temperature in degree Celsius (°C).
• K = Measure of temperature in degree Fahrenheit (°K).

The freezing point and boiling point of water in the Kelvin scale are 273.15°K and 373.15°K,  respectively.

For converting temperature from Fahrenheit to Kelvin, we use the formula: °K=(°F-32) $\times \frac{5}{9}$ + 273.15

where

• F = temperature in degree Fahrenheit (°F).
• K = temperature in degree Kelvin (°K).

The formula to convert Celsius to Kelvin is given by: °C = °K – 273.15.

where

• C = temperature in degree Celsius (°C).
• K = temperature in degree Kelvin (°K).

The formula to convert Celsius to Kelvin is given by: °K = °C + 273.15.

where,

• C = temperature in degree celsius (°C).
• K = temperature in degree Kelvin (°K).