Why Does Minus 40 Degrees Fahrenheit Equal Minus 40 Degrees Celsius?

When measuring temperature, whether it's your body, a roast chicken, or the weather, you have two main units to choose from: Celsius (or centigrade) and Fahrenheit. Kelvin is another option, but it's typically reserved for extreme temperatures, such as those found in space. Celsius and Fahrenheit differ significantly; for example, water freezes at 0 degrees Celsius but 32 degrees Fahrenheit.

Interestingly, these two scales converge at one icy point: minus 40 degrees. This occurs because a Celsius degree is larger than a Fahrenheit degree, allowing the scales to meet in the same way a faster runner can overtake a slower one.

But how does this work? Before diving into the explanation, let's explore the process of converting between Celsius and Fahrenheit.

Celsius Versus Fahrenheit

In the U.S., Fahrenheit is the standard for temperature measurement, while most other countries rely on Celsius. Both scales were developed in the 18th century by European scientists — Daniel Fahrenheit, a Dutch physicist and inventor, and Anders Celsius, a Swedish astronomer.

The two scales vary in several aspects. For instance, the freezing and boiling points of water differ significantly. In Fahrenheit, water freezes at 32 degrees and boils at 212 degrees, while in Celsius, it freezes at 0 degrees and boils at 100 degrees. Since Fahrenheit spans 180 degrees between freezing and boiling, compared to Celsius's 100 degrees, each Celsius degree is 1.8 times larger than a Fahrenheit degree.

Here's a simple guide to switching between the two temperature scales:

Understanding the relationship between Celsius and Fahrenheit is key: each Celsius degree equals 1.8 Fahrenheit degrees, or 9/5 when expressed as a fraction.

Because the two scales begin at different points — zero for Celsius and 32 for Fahrenheit — converting between them requires adjusting by 32.

To convert a temperature from Celsius to Fahrenheit, multiply the Celsius value by 1.8 and then add 32. This formula can be used:

F = (1.8 x C) + 32

For converting Fahrenheit to Celsius, start by subtracting 32 from the Fahrenheit temperature, then divide the result by 1.8 using this formula:

C = (F − 32) ÷ 1.8

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

The conversion also works in reverse: (-40F − 32) ÷ 1.8 = -40C

Why does this happen? Both scales must intersect at some point, and that point happens to be at minus 40 degrees. If you're curious about the mathematical explanation, continue reading.

How to Find the Converging Temperature for the Two Scales

If the exact point where Fahrenheit and Celsius meet is unknown, algebraic methods can be employed to determine the converging temperature.

To identify the temperature where both scales align, two key pieces of information are required.

Select a scale and denote the converging temperature as x. Place x on one side of the equation and convert it to the other scale on the opposite side.

For example, if x is in Celsius and placed on the left side, the right side will represent x in Fahrenheit. These two expressions can be set equal since they represent the same temperature.

To convert x into Fahrenheit, begin by multiplying x by 9/5, then add 32 to the result.

x = (9/5)x + 32

Next, we solve the equation 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 denotes the converging temperature in Fahrenheit, converting x to Celsius involves subtracting 32 and then multiplying by 5/9. This can be expressed as:

x = (x − 32) * (5/9)

Once 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