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Conversions Between Celsius and Fahrenheit
Making equations to convert Celsius degrees to Fahrenheit degrees or Fahrenheit degrees to Celsius degrees, requires that you understand two important relationships.
Celsius Fahrenheit
degrees from water's freezing point to boiling point 100 180
water's freezing point temperature 0 32
  • The first relationship is a ratio.
    • The ratio of 100 to 180 is reduced to 5 to 9 by dividing both numbers by 20.
    • Multiplying by 5/9 will change °F to °C and multiplying by 9/5 will change °C to °F.
  • The second relationship is simple difference of 32°.
    • 32 must be added to °C to get °F or subtracted from °F to get °C.
Once we know these two relationships, we just decide which to do first. To calculate Fahrenheit when you know Celsius, first multiply by 9/5 and then add 32.
  • °F = (9/5)(°C) + 32

To calculate Celsius when you know Fahrenheit, first subtract 32 and then multiply by 5/9.

  • °C = (5/9)(°F – 32)
Another way to approach this problem is to use the fact that –40°F = –40°C.
  • °F = (9/5)(°C + 40) - 40
  • °C = (5/9)(°F + 40) - 40
Many students find these two equations less confusing because, in both, you add, then multiply, then subtract.
Image Credit: NASA
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