Fahrenheit to Celsius Formula Explained
Derive C = (F - 32) x 5/9 from the two fixed points of water, and see how wrong the common mental shortcut is.
Where 5/9 and 32 come from
On the Celsius scale water freezes at 0 and boils at 100 - a 100-degree span. On the Fahrenheit scale the same two points are 32 and 212 - a 180-degree span. So one Celsius degree equals 180/100 = 9/5 Fahrenheit degrees, and the conversion is C = (F - 32) x 5/9. The 32 is an offset, not a multiplier, which is why temperature conversion cannot be done with a single factor.
Worked examples
| Fahrenheit | Working | Celsius |
|---|---|---|
| 32 F | (32 - 32) x 5/9 | 0 C |
| 72 F | (72 - 32) x 5/9 | 22.2222 C |
| 98.6 F | (98.6 - 32) x 5/9 | 37 C |
| 212 F | (212 - 32) x 5/9 | 100 C |
| -40 F | (-40 - 32) x 5/9 | -40 C |
The mental shortcut and its error
Subtract 30 then halve is the common approximation. It is exact at 50 F and drifts as you move away.
| F | Exact C | (F - 30) / 2 | Error |
|---|---|---|---|
| 0 F | -17.78 C | -15 C | 2.78 C |
| 32 F | 0 C | 1 C | 1 C |
| 50 F | 10 C | 10 C | 0 C |
| 72 F | 22.22 C | 21 C | -1.22 C |
| 98.6 F | 37 C | 34.3 C | -2.7 C |
| 212 F | 100 C | 91 C | -9 C |
| 350 F | 176.67 C | 160 C | -16.67 C |
Reverse and Kelvin
- F = C x 9/5 + 32
- K = C + 273.15
- The two scales meet at -40, the only number that is the same on both.
Related pages
Frequently Asked Questions
Why is there a 32 in the formula?
Because the Fahrenheit and Celsius zero points differ: water freezes at 32 F but at 0 C.
At what temperature are F and C equal?
At -40. It is the only value where both scales show the same number.
Is (F - 30) / 2 accurate?
It is exact at 50 F and drifts away from it; the error table on this page shows the drift at common temperatures.