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Celsius and Fahrenheit match at only one temperature

At minus 40 degrees, Celsius and Fahrenheit show the same number. The difference between the two scales explains why

Two glass thermometers with red columns at different heights, one in snow on slate, one on sunlit wood

Celsius and Fahrenheit show exactly the same number at minus 40 degrees. Minus 40 degrees Celsius is also minus 40 degrees Fahrenheit. The two scales put zero in different places and use different step sizes, so they meet at just one point.

The steps are different sizes

Celsius sets the temperature at which water freezes as 0 degrees and the temperature at which it boils as about 100 degrees, and divides the space between them into 100 steps. In Fahrenheit, the same range runs from 32 to 212 degrees, which makes 180 steps. So when Celsius rises by 1 degree, Fahrenheit rises by 1.8 degrees. The US National Institute of Standards and Technology (NIST) also explains that an interval of 1 Celsius degree equals an interval of 1.8 Fahrenheit degrees.

The starting points differ too. Water freezes at 0 degrees Celsius but at 32 degrees Fahrenheit. Put together, Fahrenheit is Celsius multiplied by 1.8 plus 32. Going the other way, subtract 32 from Fahrenheit and divide by 1.8 to get Celsius.

Why they meet at minus 40

At 0 degrees Celsius, the Fahrenheit number is 32 ahead. But each time Celsius drops 1 degree, Fahrenheit drops 1.8 degrees, so the gap between them shrinks by 0.8. Since 32 divided by 0.8 is 40, the gap reaches zero at minus 40, after Celsius has gone down another 40 degrees.

If it gets colder than that, the Fahrenheit number becomes smaller than the Celsius one. Minus 40 degrees is a temperature you only see in the depths of winter in Siberia or Antarctica, so you will almost never see the two numbers match in daily life.

How to estimate in your head

When you come across Fahrenheit in a US weather report or recipe, you can use a rough estimate instead of the exact formula. Subtract 30 from Fahrenheit and divide by 2 to get close to Celsius. For 68 degrees Fahrenheit, subtracting 30 from 68 and dividing by 2 gives 19 degrees, which is very close to the actual value of 20 degrees. Going the other way, double the Celsius number and add 30 to get Fahrenheit.

This estimate works well at weather-level temperatures, but it goes badly off at high temperatures. Calculating an oven temperature of 350 degrees Fahrenheit this way gives 160 degrees, but the real value is about 177 degrees. When the temperature really matters, as in cooking, it is better to use the exact formula that divides by 1.8.

Body temperature of 98.6 uses the same math

When someone in an American TV show has a fever over "100 degrees," that is Fahrenheit too. 100 degrees Fahrenheit is about 37.8 degrees Celsius. The 98.6 degrees Fahrenheit often called normal body temperature is simply 37 degrees Celsius converted.

There is no need to be surprised that Fahrenheit numbers look large. Because 1 Celsius degree equals 1.8 Fahrenheit degrees, the same change moves the number further in Fahrenheit.

Celsius times 1.8 plus 32 gives Fahrenheit. The two scales show the same number only once, at minus 40.

Notes and references · US NIST, SI Units – Temperature. Says 1 Celsius degree equals 1.8 Fahrenheit degrees and gives exact formulas. "Subtract 30, divide by 2" is this article's rough estimate; the error grows at high temperatures

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When Celsius rises by 1 degree, how many degrees does Fahrenheit rise?

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