Converting °C and °F

The idea

Fahrenheit = (9/5) × Celsius + 32 and Celsius = (5/9) × (Fahrenheit – 32), so 0 °C = 32 °F.

One thermometer, two scales

Some thermometers have two scales. At 0 °C the Fahrenheit scale does not read 0. It reads 32 °F.

If 0 °C is 32 °F, what does the Fahrenheit scale read at 25 °C?

• 25 °F
• 57 °F
• 77 °F

Slide the temperature

Slide the temperature in one scale and read the other. The two steps below show how one number turns into the other. Try both directions.

Multiply, then add 32

Fahrenheit = 9/5 × Celsius + 32 and Celsius = 5/9 × (Fahrenheit − 32), so 0 °C = 32 °F.

From °C to °F, multiply by 9/5, then add 32. For 25 °C: 25 × 9/5 = 45, then 45 + 32 = 77 °F.

From °F to °C, subtract 32, then multiply by 5/9. For 77 °F: 77 − 32 = 45, then 45 × 5/9 = 25 °C.

The scales start at different places, so they are not in proportion: 25 : 77 and 100 : 212 are not the same ratio.

Notes

Fahrenheit = 9/5 × Celsius + 32 and Celsius = 5/9 × (Fahrenheit − 32), so 0 °C = 32 °F.

Check yourself

What is 30 °C in °F?

Answer: 86 °F

30 × 9/5 = 54, then 54 + 32 = 86 °F.

What is 95 °F in °C?

Answer: 35 °C

95 − 32 = 63, then 63 × 5/9 = 35 °C.

A student uses a proportion, 100 : 212 :: 25 : ?, to convert 25 °C. What does it give? (in °F)

Answer: 53 °F

212 × 25 ÷ 100 = 53. But 25 °C is really 77 °F, so the proportion is wrong.

Why can a proportion not convert between °C and °F?

• The scales start at different places: 0 °C is 32 °F, not 0 °F — correct. Yes! In a proportion, 0 goes with 0. Here 0 °C goes with 32 °F, so you must also add 32.
• Fahrenheit numbers are bigger. Bigger numbers are not the problem. For example, 2 : 4 and 20 : 40 are in proportion. The trouble is the 32.
• Temperatures cannot be put in a ratio. Any two numbers can be put in a ratio. The ratios just come out different each time: 25 : 77 and 100 : 212.