Celsius to Fahrenheit Formula Explained

4 min read•June 1, 2025•Reviewed: June 1, 2026

✓Reviewed by Apex Conversion Editorial Team · Last reviewed June 1, 2026

The formula for converting Celsius to Fahrenheit is °F = (°C × 9/5) + 32. The multiplication adjusts for the different size of each degree, and the +32 adjusts for the different zero points of the two scales. Both scales measure temperature, but they define their zero and their unit-size differently.

Unlike length or weight conversions, temperature requires two operations because the two scales don't share a common zero. Water freezes at 0°C but 32°F — a 32-unit offset. And each Celsius degree is 1.8× the size of a Fahrenheit degree, hence the ×9/5 (= ×1.8) factor.

The Formula

°F = (°C × 9/5) + 32
°F = (°C × 1.8) + 32  (equivalent)

Worked examples:
   0°C: (0 × 1.8) + 32 =  32°F  (water freezes)
  20°C: (20 × 1.8) + 32 = 68°F  (comfortable room temp)
  37°C: (37 × 1.8) + 32 = 98.6°F  (body temperature)
 100°C: (100 × 1.8) + 32 = 212°F  (water boils)
 -40°C: (-40 × 1.8) + 32 = -40°F  (scales meet here)

Quick mental estimate (within ~10%):
  Step 1: double the Celsius value
  Step 2: add 30
  Example: 20°C → 40 + 30 = 70°F  (exact: 68°F)

Why the Formula Has Two Steps

The Celsius scale sets 0° at water's freezing point and 100° at its boiling point at sea level. The Fahrenheit scale sets 32° at water's freezing point and 212° at its boiling point. The boiling-to-freezing range is 100 Celsius degrees but 180 Fahrenheit degrees, so each Celsius degree = 180/100 = 1.8 Fahrenheit degrees — hence ×1.8 (or ×9/5).

The +32 adjusts for the fact that the two scales have different zero points. 0°C is not 0°F — it is 32°F. So after scaling the degree size, you add 32 to shift the origin. Omitting either step gives a wrong answer.

Quick Tips

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Key anchors: 0°C = 32°F, 20°C = 68°F, 37°C = 98.6°F, 100°C = 212°F.
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Quick estimate: double the Celsius and add 30. Gives 68°F for 20°C as 70°F — close enough.
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Better estimate: multiply by 2 and subtract 10%, then add 32. For 20°C: 20×2=40, −4=36, +32=68°F (exact).
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−40 is the only temperature where Celsius and Fahrenheit are equal.
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For oven temperatures: 180°C = 356°F (approx. 350°F); 200°C = 392°F (approx. 400°F).