Celsius to Fahrenheit Conversion

Also known as C to F · F to C · fahrenheit to celsius · celsius to fahrenheit formula · 9/5 plus 32 · convert temperature · degrees C to degrees F

θF=95θC+32\theta_F = \tfrac{9}{5}\,\theta_C + 32

Units aren’t used in this calculation — every value is a plain number.

Worked example: 25 C → 77 Fpress Try an example to run it live, then adjust anything.

Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value.

Learning zone

Two scales, two arbitrary choices of zero, and one fixed relationship between them. Daniel Fahrenheit set his zero in 1724 at the coldest temperature he could reliably reproduce, a brine of ice, water and ammonium chloride, and put body temperature near 96 so that the range would divide neatly in halves. Anders Celsius proposed his in 1742 with the fixed points at the freezing and boiling of water, and — a detail people enjoy — with zero at boiling and 100 at freezing. It was inverted after his death, most likely by Carl Linnaeus, who wanted a thermometer for his greenhouses that read upward.

Because there are 180 Fahrenheit degrees between the freezing and boiling points where there are 100 Celsius degrees, one Celsius degree is 180/100=9/5180/100 = 9/5 Fahrenheit degrees. That ratio is the multiplication, and the 32 is simply where the Fahrenheit scale had already put the freezing point.

The distinction that matters in practice is between a reading and an interval. A reading needs both the multiplication and the offset. A temperature difference needs only the ratio: a rise of 10 Celsius degrees is a rise of 18 Fahrenheit degrees, and adding 32 to it is the single commonest error in the topic. Engineering notation puts the degree sign after the letter to mark the difference — 10 C° is an interval, 10 °C is a temperature — and this site keeps them as separate unit types for the same reason.

The two scales cross at −40, which is worth memorising as a check: any conversion routine that does not return −40 for −40 has a sign error in it.

Celsius to Fahrenheit Conversion
θF=95θC+32\theta_F = \tfrac{9}{5}\,\theta_C + 32
Where
  • θC\theta_C= Celsius reading (°C)
  • θF\theta_F= Fahrenheit reading (°F)
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