At What Temperature Are Celsius & Fahrenheit Identical But Have Opposite Signs?

The Magic Number

• The temperature at which the Celsius and Fahrenheit scales give an identical reading but with opposite signs occurs between 11 and 12 degrees, specifically 11.42857 degrees, rounded to five decimal places. When it's 11.42857 degrees above zero Fahrenheit, it's 11.42857 degrees below zero Celsius.
  
  

Scales

• On the Celsius scale, pure water under standard atmospheric conditions -- at sea level, in other words -- freezes at 0 degrees and boils at 100 degrees. On the Fahrenheit scale, water freezes at 32 degrees and boils at 212 degrees. So a 100-degree span of temperatures on the Celsius scale is the same as a 180-degree span in Fahrenheit. Every increase or decrease of 1 degree C equals an increase or decrease of 1.8 degrees F. Put another way, 1 degree of Celsius temperature equals 5/9 of a Fahrenheit degree, and 1 degree of Fahrenheit temperature equals 9/5 of a Celsius degree. These fractions, plus the 32-degree difference between equivalent temperatures at 0 Celsius, form the basis for conversions between the two scales.
  
  

F to C

• To convert a reading from Fahrenheit to Celsius, first subtract 32 from the Fahrenheit temperature, then multiply the result by 5/9. The equation looks like this:
  
  (F-32) x 5/9 = C
  
  For our "magic" temperature, start with the Fahrenheit reading and subtract 32:
  
  11.42857 - 32 = -20.57143
  
  Them multiply the result by 5/9, and round to five decimal places:
  
  -20.57143 x 5/9 = -11.42857
  
  

C to F

• To convert a reading from Celsius to Fahrenheit, first multiply the Celsius temperature by 9/5, then add 32. The equation looks like this:
  
  (C x 9/5) + 32 = F
  
  For our "magic" temperature, start with the Celsius reading and multiply by 9/5:
  
  -11.42857 x 9/5 = -20.571426
  
  Then add 32 to the result, and round to five decimal places:
  
  -20.571426 + 32 = 11.42857