Lessons · Medicine foundations · Fahrenheit to Celsius

Fahrenheit to Celsius: subtract, then five ninths

Celsius is the Fahrenheit reading minus 32, multiplied by five ninths; going back is nine fifths, then add 32.

Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.

What it is for

One chart is in Fahrenheit, the reference range beside it is in Celsius, and the number you are being asked about sits between them. A tenth of a degree matters to whoever wrote the range, so guessing is not available.

How to think about it

Subtract 32 first, always, and give that its own line. Then multiply by 5 and divide by 9. Going the other way, multiply by 9 and divide by 5 first, and add the 32 last. The 32 is at the wrong end in exactly one of the two directions, and that is the whole difficulty.

Worked example

°C = (°F − 32) × 5 / 9

The conversion, with the subtraction inside the brackets so it happens first.

98.6 − 32 = 66.6, the degrees above freezing

The subtraction on its own line. This is not yet a temperature in Celsius.

66.6 × 5 / 9 = 37.0 °C

Now the scaling. Thirty-seven degrees Celsius.

Back the other way: 38.5 × 9 / 5 + 32 = 101.3 °F

Scale first, add the 32 last.

Your turn

A chart reads 104 °F. Write the line that converts it to Celsius.

(104 − 32) × 5 / 9 =  °C

The trap

Multiplying by five ninths before subtracting the 32. It gives 54.8 for a reading of 98.6, which is not a temperature anything alive has, and the arithmetic looks tidy the whole way.

Practise Fahrenheit to Celsius on HoneA question on it now, a coding challenge where there is one, and it is remembered for review. Free, no email needed.