Formulas for Fahrenheit and Celsius Conversions

Other methods can also help with quicker conversions.

Celsius thermometer
(Petr Kratochvil/publicdomainpictures.net)

Fahrenheit and Celsius are two temperature measurements. Fahrenheit is most common in the United States, while Celsius is the norm in most other Western nations, though it is also used in the U.S. You can use tables that show common conversions between Fahrenheit and Celsius and vice versa as well as online converters, but knowing how to convert one scale to the other is important for obtaining accurate temperature readings.

Formulas are the most common tools for conversions, but other methods allow you to do quick approximate conversions in your head. Understanding how the scales were invented and what they measure can make converting between the two a bit easier.

History and Background

Germany physicist Daniel Gabriel Fahrenheit invented the Fahrenheit scale in 1724. He needed a way to measure temperature because he had invented the mercury thermometer 10 years earlier in 1714. The Fahrenheit scale divides the freezing and boiling points of water into 180 degrees, where 32 F is the freezing point of water and 212 F is its boiling point.

The Celsius temperature scale, which is also referred to as the centigrade scale, was invented several years later in 1741 by Swedish astronomer Anders Celsius. Centigrade literally means consisting of or divided into 100 degrees: The scale has 100 degrees between the freezing point (0 C) and boiling point (100 C) of water at sea level.

Using Formulas

To convert Celsius to Fahrenheit, you can use two basic formulas. If you know the temperature in Fahrenheit and want to convert it to Celsius, first subtract 32 from the temperature in Fahrenheit and multiply the result by five/ninth. The formula is:

C = 5/9 x (F-32)

where C is Celsius

To clarify the idea, use an example.

Suppose you have a temperature of 68 F. Follow these steps:

  1. 68 minus 32 is 36
  2. 5 divided by 9 is 0.5555555555555
  3.  Multiply the repeating decimal by 36
  4. Your solution is 20

Using the equation would show:

C = 5/9 x (F-32)

C = 5/9 x (68-32)

C = 5/9 x 36

C = 0.55 x 36

C = 19.8, which rounds to 20

So, 68 F is equal to 20 C.

Convert 20 degrees Celsius to Fahrenheit to check your work, as follows:

  1. 9 divided by 5 is 1.8
  2. 1.8 multiplied by 20 is 36
  3. 36 plus 32 = 68

Using the Celsius to Fahrenheit formula would show:

F = [(9/5)C] + 32

F = [(9/5) x 20] + 32

F = [1.8 x 20] + 32

F = 36 + 32

F = 68

Quick Approximation Method

To convert Celsius to Fahrenheit, you can also do a quick approximation of the temperature in Fahrenheit by doubling the temperature in Celsius, subtracting 10 percent of your result and adding 32.

For example, suppose that you read that temperature in a European city you plan to visit today is 18 C. Being used to Fahrenheit, you need to convert to know what to wear for your trip. Double the 18, or  2 x 18 = 36. Take 10 percent of 36 to yield 3.6, which rounds to 4. You would then calculate: 36 - 4 = 32 and then add 32 and 32 to get 64 F. Bring a sweater on your trip but not a big coat.

As another example, suppose the temperature of your European destination is 29 C.

Calculate the approximate temperature in Fahrenheit as follows:

  1. 29 doubled = 58 (or 2 x 29 = 58) 
  2. 10 percent of 58 = 5.8, which rounds to 6
  3. 58 - 6 = 52
  4. 52 + 32 = 84

The temperature in your destination city will be 84 F—a nice warm day: Leave your coat at home.

A Quick Trick: Memorize Your 10 Blocks

If accuracy is not critical, memorize the conversions from Celsius to Fahrenheit in increments of 10 C. The following table lists the range for the most common temperatures you might experience in many U.S. and European cities. Note that this trick only works for C to F conversions.

0 C

32 F

10 C

52 F

20 C

68 F

30 C

86 F

40 C

104 F