# Video: Converting from Celsius to Fahrenheit

What is −40°‎C in degrees Fahrenheit?

01:31

### Video Transcript

What is negative 40 degrees Celsius in degrees Fahrenheit?

In this exercise then, we’re doing a temperature conversion from a temperature in degrees Celsius to one in degrees Fahrenheit. Whenever we do that, it’s helpful to recall the conversion relationship between these two separate temperature scales. Given a temperature in degrees Celsius, we can call it 𝑇 sub C, if we multiply that temperature by nine-fifths and then add 32 to that result, we get the corresponding temperature in degrees Fahrenheit, we’ll call it 𝑇 sub F.

So, what we want to do is solve for 𝑇 sub F, given an input temperature of negative 40 degrees Celsius. To do that, we’ll use this conversion relationship, and we’ll insert negative 40 for our temperature in degrees Celsius. Multiplying negative 40 by nine-fifths, we get negative 360 divided by five. And that fraction is equal to negative 72. When we add positive 32 to negative 72, we get a result of negative 40. And it’s now that we put the correct units onto this result. That’s degrees Fahrenheit.

Now, at first this may seem strange. We started out with negative 40 in degrees Celsius, and we found that, apparently, that’s negative 40 in degrees Fahrenheit. In fact, there is nothing wrong with what we’ve done. Rather, what we’ve discovered is the one single temperature at which that temperature value in degrees Celsius is equal to the same temperature value in degrees Fahrenheit. There is no other temperature for which this is true, but it is true for negative 40. So, negative 40 degrees Celsius is negative 40 degrees Fahrenheit.