How Can Minus 40 Fahrenheit Equal Minus 40 Celsius?

minus 40 on thermometer scale — It's a super-cold temperature that you're unlikely to encounter in either scale, but it's curious that minus 40 is the same whether it's Fahrenheit or Celsius. Novikov Aleksey/Shutterstock

If you're interested in taking the temperature of something — say, your own body or a roast chicken or the temperature outdoors — there are two different units of measurement available to you: Celsius (or centigrade) and Fahrenheit. There's another called Kelvin, but it's used to measure really far-spectrum temperatures, like what you'd find in outer space. Celsius and Fahrenheit use completely different measurements — for instance, water freezes at 0 degrees Celsius, but 32 degrees Fahrenheit.

However, the two temperature scales happen to intersect at one frigid position: minus 40 degrees. The reason is that, because a degree in Celsius is larger than one in Fahrenheit, the two meet up in the same way a runner who's moving faster than another runner can eventually lap the slower guy.

But how? Before we answer that, let's look at converting Celsius and Fahrenheit.

Celsius Versus Fahrenheit

If you live in the U.S., you probably use Fahrenheit, but most other places in the world use Celsius. Both were invented in the early- to mid-18th century by European scientists — Dutch physicist and inventor Daniel Fahrenheit and Swedish astronomer Anders Celsius.

The two scales differ in a couple of ways. First, the freezing and boiling points of water are different. In Fahrenheit, water freezes at 32 degrees and boils at 212 degrees, whereas in Celsius, water freezes at 0 degrees and boils at 100 degrees. Because there are 180 degrees between freezing and boiling in Fahrenheit and only 100 degrees between the two in Celsius, each degree is 1.8 times larger in Celsius than in Fahrenheit.

Here's how to easily convert between the two scales:

It's important to know that for every Celsius degree, there are 1.8 Fahrenheit degrees (or 9/5 degrees, to put it in a fraction).

Since the two scales start at different numbers — zero and 32 — converting between the two involves adding or subtracting 32.

To convert Celsius to Fahrenheit, multiply the temperature in Celsius by 1.8, then add 32. You can use this formula:

F = (1.8 x C) + 32

If you want to convert from Fahrenheit to Celsius, subtract 32 from the Fahrenheit temperature, then divide the result by 1.8 using this formula:

C = (F − 32)÷ 1.8

So, (1.8 x -40C) + 32 = -40F

It works the other way too. (-40F − 32) ÷ 1.8 = -40C

So, why is that? Both scales have to converge somewhere and minus 40 degrees just happens to be the spot. If you'd like to know the mathematical reason, keep reading.

How to Find the Converging Temperature for the Two Scales

If you don't know the point at which Fahrenheit and Celsius converge, you can use a little algebraic manipulation to solve for the converging temperature.

There are two things you need to know to find the temperature where the two scales have the same value.

How many degrees in one scale are equal to a degree in the other. (Answer: There are 5/9 of 1 Celsius degree in a Fahrenheit degree. There are 9/5 Fahrenheit degrees in 1 Celsius degree.)
The offset between the freezing point in each scale. (Answer: Since Celsius is zero at freezing and Fahrenheit is 32 degrees at freezing, the offset between the two scales is 32 degrees Fahrenheit.)

Pick a scale and call the convergent temperature in that scale x. Put x on one side of the equation, and on the other side convert x into the other scale.

For instance, if you choose x to be in Celsius and put that on the left side of the equation; on the right side will be the value of x in Fahrenheit. We can set those two quantities equal to each other because we know they're the same temperature.

To convert x to Fahrenheit, first multiply x by 9/5, then add 32.

x = (9/5)x + 32

Now, we solve for x:

x − (9/5)x = 32

(1 − 9/5)x = 32

(-4/5)x = 32

(-5/4)(-4/5)x = (-5/4)32

x = -(5/4) * 32

x = -(160/4)

x = -40 Fahrenheit

If x represents the convergent temperature in Fahrenheit, to convert x to Celsius, first subtract 32 and then multiply x by 5/9. That is:

x = (x − 32) * (5/9)

Again, solve for x:

(9/5)x = x − 32

(9/5)x − x = -32

(9/5 − 1)x = -32

(4/5)x = -32

x = -(5/4)32

x = -(160/4)

x = -40