Convert Fahrenheit to Celsius: Definition, Formula, Facts

What Is Fahrenheit to Celsius Formula?

We can convert a given temperature in Fahrenheit scale to the Celsius scale using the Fahrenheit to Celsius formula. The Fahrenheit to Celsius formula is also commonly referred to as the F to C formula. The F to C formula is used to convert temperature from Fahrenheit to Celsius. 

Fahrenheit to Celsius conversion is used to convert a given temperature from the scale of Fahrenheit to Celsius. You know that temperature is the measurement of how hot or cold a body, an environment, or an object is. 

The temperature can be measured in degree-Fahrenheit scale or degree-Celsius scale. These are the most commonly used scales. The symbol used to represent Fahrenheit is $^\circ\text{F}$. Similarly, the symbol used for Celsius is $^\circ\text{C}$. The Fahrenheit scale is mostly used in the United States, while the Celsius scale is used worldwide.

Fahrenheit to Celsius Formula

The Fahrenheit to Celsius formula (F to C formula) that converts the given temperature value from $^\circ\text{F}$ to $^\circ\text{C}$ is given by :

$^\circ\text{C} = \frac{5}{9} \times (^\circ\text{F}\;-\;32)$ 

where,

$C =$ Measure of temperature in degree Celsius $(^\circ\text{C})$.

$F =$ Measure of temperature in degree Fahrenheit $(^\circ\text{F})$.

How to Convert Farenheit to Celcius

To convert any temperature from Farenheit to Celsius, we follow the given steps:

Step 1: Subtract 32 from the temperature given in Fahrenheit.

Step 2: Next, multiply the difference value by 5.

Step 3: Divide the product by 9.

Example: Convert $98.6 ^\circ\text{F}$ to celsius.

Step 1: Subtract 32 from 98.6

           $98.6\;−\;32 = 66.6$

Step 2: Multiply 66.6 by 5.

         $66.6 \times 5 = 333$

Step 3: Divide 333 by 9.

           $333 \div 9 = 37$

Hence, $98.6 ^\circ\text{F} = 37 ^\circ\text{C}$.

Definition of Fahrenheit

Fahrenheit, denoted by the symbol $^\circ\text{F}$ or F alone in scientific usages, is a temperature scale in which water freezes at 32 degrees and boils at 212 degrees. It is more popularly used in the United States.

The scale was devised by Gabriel Daniel Faherenheit in 1714, an instrument maker of the eighteenth century born in Germany.

The temperature in Fahrenheit is written as $32 ^\circ\text{F},\; 98.6 ^\circ\text{F}$, and so on.

Definition of Celsius

The symbol used for Celsius is $^\circ\text{C}$. On this scale, $0^\circ$ is the freezing point of water and $100^\circ$ is the boiling point of water. 

The Celsius scale was invented in 1742 by the Swedish astronomer Anders Celsius. It is also called the centigrade scale because of the 100 intervals between the defined points.The temperature in celsius is written as $100 ^\circ\text{C},\; 0\; ^\circ\text{C}$, and so on.

Relationship between Fahrenheit and Celsius

The two scales have different boiling points and the freezing points of water. 

The two scales are directly proportional to each other. If the temperature in the Celsius scale increases, then the equivalent temperature in the Fahrenheit scale will also increase. 

The relationship is given by

$^\circ\text{C} = \frac{5}{9}\times (^\circ\text{F}\;-\; 32)$

Celsius Scale	Fahrenheit Scale
The boiling point of water is $100\;^\circ$\text{C}$.	The boiling point of water is $212\;^\circ\text{F}$.
The freezing point of water is $0\;^\circ\text{C}$.	The freezing point of water is $32\;^\circ\text{F}$.
Normal body temperature is $37\;^\circ\text{C}$.	Normal body temperature is $98.6\;^\circ\text{F}$.

Fahrenheit to Celsius Equation

The derivation of the relation between Fahrenheit and Celsius could be proved with the help of the mathematical equation, as mentioned below.

As the freezing point of water in Celsius scale is $0\;^\circ\text{C}$ and in Fahrenheit scale is $32\; ^\circ\text{F}$, we get the equation,

$C\;−\;0 = F\;−\;32$

Dividing it by the total number of intervals in the scale (100 degree interval for celsius scale and 180 degree interval for fahrenheit scale), we get

$\frac{(C\;−\;0)}{100}  = \frac{(F\;−\;32)}{180}$  

$\frac{C}{100}  = \frac{F\;-\;32}{180}$

$\frac{C}{5}  = \frac{F\;-\;32}{9}$        

$^\circ\text{C} = \frac{5}{9}\times(^\circ\text{F}\;-\;32)$  

where, 

F is Temperature in Fahrenheit.

C is Temperature in Celsius.

Fahrenheit to Celsius Conversion Table

The following table shows a few temperature values that are converted from Fahrenheit to Celsius.

Fahrenheit	Celsius
$-40\;^\circ\text{F}$	$-40.00\;^\circ\text{C}$
$-20\;^\circ\text{F}$	$-28.89\;^\circ\text{C}$
$-10\;^\circ\text{F}$	$-23.33\;^\circ\text{C}$
$-5\;^\circ\text{F}$	$-20.56\;^\circ\text{C}$
$0\;^\circ\text{F}$	$-17.78\;^\circ\text{C}$
$10\;^\circ\text{F}$	$-12.22\;^\circ\text{C}$
$20\;^\circ\text{F}$	$-6.67\;^\circ\text{C}$
$30\;^\circ\text{F}$	$-1.11\;^\circ\text{C}$
$32\;^\circ\text{F}$	$0\;^\circ\text{C}$ (Freezing point of water)
$50\;^\circ\text{F}$	$10\;^\circ\text{C}$
$68\;^\circ\text{F}$	$20\;^\circ\text{C}$
$86\;^\circ\text{F}$	$30\;^\circ\text{C}$
$98.6\;^\circ\text{F}$	$37\;^\circ\text{C}$ (Normal body temperature)
$104\;^\circ\text{F}$	$40\;^\circ\text{C}$
$176\;^\circ\text{F}$	$80\;^\circ\text{C}$
$194\;^\circ\text{F}$	$90\;^\circ\text{C}$
$212\;^\circ\text{F}$	$100\;^\circ\text{C}$(Boiling point of water)

Facts about the Fahrenheit to Celsius Formula

• The first known use of Fahrenheit was in 1753.
• Celsius (or centigrade) is a temperature scale named after the Swedish astronomer Anders Celsius $(1701\;–\;1744)$, who first proposed such a system two years before his death. 
• The Fahrenheit and Celsius scales are equal at $-40\;^\circ\text{C}$ and $-40\;^\circ\text{F}$.
• Absolute zero is the lowest temperature possible. At a temperature of absolute zero there is no motion and no heat. Absolute zero occurs at a temperature of $-273.15$ degrees Celsius, or at $-460$ degrees Fahrenheit.

Conclusion

In this article, we learned that we can convert temperature of any substance from Farenheit to Celsius by using the C to F formula:

                                              $^\circ\text{C} = \frac{5}{9}\times(^\circ\text{F}\;-\;32)$

Solved Examples on the Fahrenheit to Celsius Formula

1. Convert $32\;^\circ\text{F}$ to C using the Fahrenheit to Celsius formula.

Solution:

The given temperature in Fahrenheit $= 32\;^\circ\text{F}$

We know that the formula for Fahrenheit to Celsius is

  $^\circ\text{C} = \frac{5}{9} \times (^\circ\text{F}\;-\;32)$

Substitute the value of Fahrenheit in the Fahrenheit to Celsius formula,

 $^\circ\text{C} = \frac{5}{9} \times (32\;-\;32)$

 $^\circ\text{C} = \frac{5}{9} \times 0  = 0\;^\circ\text{C}$

Thus, $32\;^\circ\text{F} = 0\;^\circ\text{C}$.

2. Convert $100^\circ\text{F}$ to Celsius.

Solution:

The given temperature in Fahrenheit, $^\circ\text{F} = 100\;^\circ\text{F}$.

We know that the formula for Fahrenheit to Celsius is 

  $^\circ\text{C} = \frac{5}{9}\times (^\circ\text{F} \;-\; 32)$

Now substitute the values in the formula,

  $^\circ\text{C} = \frac{5}{9}\times (100 \;-\; 32)$

  $^\circ\text{C} = \frac{5}{9} \times 68$

  $^\circ\text{C} = \frac{340}{9}$

$^\circ\text{C} = 37.78$

Therefore, $100\;^\circ\text{F} = 37.78\;^\circ\text{C}$.

3. Convert $- 5\;^\circ\text{F}$ to Celsius.

Solution: 

The Fahrenheit to Celsius formula is $^\circ\text{C} = \frac{5}{9}\times (^\circ\text{F} \;-\; 32)$

Substituting the values in the formula, we get

  $^\circ\text{C} = \frac{5}{9}\times(\;-5\;-\;32)$

  $^\circ\text{C} = \frac{5}{9}\times (\;-\;37)$

  $^\circ\text{C} = \frac{-\;185}{9}$

  $^\circ\text{C} = -20.56$

Hence,  $−5\;^\circ\text{F} =  −20.56\;^\circ\text{C}$.

4. Convert $-\; 20^\circ\text{F}$ to Celsius.

Solution: 

The Fahrenheit to celsius formula is 

 $^\circ\text{C} = \frac{5}{9}\times(^\circ\text{F}\;-\;32)$

Substituting the values in the formula, we get

$^\circ\text{C} = \frac{5}{9}\times(\;-\;20\;-\;32)$

$^\circ\text{C} = \frac{5}{9}\times(\;-52)$

 $^\circ\text{C} = \frac{-260}{9}$

$^\circ\text{C} =  \;−28.89$

Hence,  $−20\;^\circ\text{F} =  −28.89\;^\circ\text{C}$.

5. Convert $40\;^\circ\text{F}$ to Celsius.

Solution: 

The Fahrenheit to celsius formula is $^\circ\text{C} = \frac{5}{9}\times(^\circ\text{F}\;-\;32)$

Substituting the values in the formula, we get

 $^\circ\text{C} = \frac{5}{9}\times(40\;-\;32)$

 $^\circ\text{C} = \frac{5}{9}\times8$

 $^\circ\text{C} = \frac{40}{9}$

$^\circ\text{C} =  4.44$

Hence,  $40\;^\circ\text{F} =  4.44\;^\circ\text{C}$.

Practice Problems on the Fahrenheit to Celsius Formula

Frequently Asked Questions on the Fahrenheit to Celsius Formula