The formula, both ways
The two terms do different jobs and both are necessary. The 9/5 accounts for the degrees being different sizes: there are 100 Celsius degrees between the freezing and boiling points of water and 180 Fahrenheit degrees across the same range, and 180/100 is 9/5. The 32 accounts for the scales starting in different places, since water freezes at 0°C but at 32°F.
This is why every other conversion on this site is a single multiplication and this one is not. Multiplying a Celsius temperature by 1.8 and forgetting the offset produces an answer that is 32 degrees wrong at every point on the scale.
Minus forty, the one point they agree
There is exactly one temperature where the two scales give the same number, and it is −40. Set the formulas equal and solve, and −40 falls out as the unique solution. It is a genuinely useful fact in cold climates, where −40 needs no unit at all, and a good sanity check on a conversion: if your method does not return −40 for −40, your method is wrong.
Fahrenheit's zero was not arbitrary either — it was set at the coldest temperature Daniel Fahrenheit could reliably reproduce in 1724, using a brine of ice, water and ammonium chloride. Human body temperature was meant to land near 96 on his original scale. Subsequent recalibration moved it to 98.6°F, which is 37°C exactly and which is itself only an average rather than a fixed value.
Mental shortcuts, ranked
The double and add 30 method is the most common: 20°C becomes roughly 70°F against a true 68. It is good enough for weather and drifts badly at extremes — at 100°C it gives 230 against a true 212.
A better version is double, subtract a tenth, add 32. For 20: double to 40, subtract 4, add 32, giving exactly 68. That is the real formula rearranged, since 2 − 0.2 is 1.8. It costs one extra step and is exact.
Going the other way, subtract 30 and halve gets you close: 70°F becomes 20°C against a true 21.1. For cooking, where an oven at 180°C versus 350°F is a 2°F difference nobody can taste, approximations are fine. For anything medical or industrial they are not.
Kelvin, and why science uses it
Kelvin uses the same degree size as Celsius but starts at absolute zero, so K = °C + 273.15 with no multiplication needed. The tool above shows the Kelvin equivalent alongside Fahrenheit when converting from Celsius.
The reason it matters is that Kelvin has no negative values and a true zero, which means ratios are meaningful: 200 K really is twice as hot as 100 K in a way that 20°C is not twice 10°C. Any calculation involving gas laws or thermal radiation requires absolute temperature, and using Celsius in those formulas is a classic and severe error.
Frequently asked questions
What is 20 degrees Celsius in Fahrenheit?
68°F exactly. Multiply by 9/5 to get 36, then add 32. The common double-and-add-30 shortcut gives 70, which is two degrees high.
Why do I have to add 32?
Because the scales have different zero points as well as different degree sizes. Water freezes at 0°C but 32°F, so the 9/5 handles the degree size and the 32 handles the offset.
At what temperature are Celsius and Fahrenheit the same?
Minus 40. It is the only point where the two scales coincide, and it makes a useful check: any conversion method that does not return −40 for −40 is wrong.