The Celsius to Fahrenheit formula, explained
The formula is multiply by 1.8, then add 32. This guide is about why — which is what stops the usual mistakes, and what tells you when the 32 does not belong.
By Akash Yadav Updated 19 October 2026
In one line
The formula
To convert a temperature in degrees Celsius to degrees Fahrenheit, multiply by 1.8 and then add 32. In symbols:
°F = °C × 1.8 + 32
The other way: °C = (°F − 32) ÷ 1.8
Worked once, slowly: 20 °C × 1.8 = 36, and 36 + 32 = 68 °F. There is no third step. The Celsius to Fahrenheit converter does this arithmetic as you type, and shows each step underneath the answer.
Why
Where the 1.8 and the 32 come from
Every other conversion on this site is a single multiplication, because the units agree about where zero is: nothing weighs zero pounds and something else. Celsius and Fahrenheit do not agree. Water freezes at 0 °C and at 32 °F — the same temperature, two different numbers — so the first job is to line the two scales up. That is the 32.
Then the degrees are different sizes. Between the freezing and boiling points of water there are 100 Celsius degrees and 180 Fahrenheit degrees, so the ratio is 180 ÷ 100 = 1.8 (the same number as 9/5). A Celsius degree is the bigger of the two: it covers in one step what Fahrenheit takes 1.8 steps to cover.
Historically the ordering is the other way round from what the arithmetic suggests: Fahrenheit's scale came first, in 1724, and Celsius published his in 1742 — upside down, with 0 at boiling. The modern scale has kept his name and reversed his direction.
Kelvin is the third scale, and it needs none of this. A kelvin is the same size as a Celsius degree, so that conversion is a single shift — add 273.15 — with no multiplier and no 32. If you are converting for a lab rather than for a forecast, see Celsius to Kelvin.
Worked
Three examples, one of them negative
A room, 22 °C. 22 × 1.8 = 39.6, and 39.6 + 32 = 71.6 °F.
An oven, 180 °C. 180 × 1.8 = 324, and 324 + 32 = 356 °F. That is why a recipe written for a US oven says 350 °F: 180 °C is not a round number in Fahrenheit, so the recipe rounds it. The oven temperature guide works through the whole dial, gas marks included.
Below freezing, −10 °C. −10 × 1.8 = −18, and −18 + 32 = 14 °F. The formula needs no special case below zero: the multiplier is applied to the reading first and the 32 is added afterwards, so −10 °C lands at a positive Fahrenheit number.
The trap
A reading is not a step
The commonest way to get this conversion wrong is to apply it to a difference. If a room warms from 15 °C to 20 °C, the change is 5 Celsius degrees, and the change in Fahrenheit is 5 × 1.8 = 9 °F — not 9 plus 32. Adding the 32 to a difference overstates it by exactly 32 degrees.
One Celsius degree of change is 1.8 Fahrenheit degrees of change. The 32 fixes where the scales put zero; a difference does not have a zero to fix, so it never carries it.
Checks
Five points worth carrying in your head
- 0 °C is 32 °F, and 100 °C is 212 °F — the 180-degree span the 1.8 comes from.
- 20 °C is 68 °F — a comfortable room, and the handiest anchor for weather.
- 37 °C is 98.6 °F — the usual figure for body temperature, worth knowing to sanity-check a thermometer.
- −40 is the one place the two scales agree: −40 °C is -40 °F, which makes a useful test of any converter, including this one.
- A change of 1 °C is a change of 1.8 °F — the same fact as the 1.8, said a different way.
Reverse
Going the other way
Subtract 32 first, then divide by 1.8 — in that order, always. Dividing before subtracting is the classic mistake and it does not give a slightly wrong answer, it gives a meaningless one: 68 °F the correct way is (68 − 32) ÷ 1.8 = 20 °C, and the wrong way round comes out at 5.8 °C.
The Fahrenheit to Celsius converter does it in the right order and shows the subtraction before the division, if you would rather watch it happen.
Mental arithmetic
Without a calculator: double it and add 30
For weather conversation, the exact formula is rarely needed. Double the Celsius number and add 30: 20 °C becomes 70 instead of 68, and 30 °C becomes 90 instead of 86. Close enough to decide on a coat.
It is exact at 10 °C, where the estimate and the formula both give 50, and it drifts as the numbers get bigger: at 30 °C it runs 4 degrees hot, and at oven temperatures it is not usable at all — 200 °C comes out as 430 where the exact answer is 392. Use it at a bus stop, not at a baking tray.
Common questions
Questions the formula raises
Why is the multiplier 1.8 and not 2?
Because 180 Fahrenheit degrees cover the same span as 100 Celsius degrees, and 180 ÷ 100 = 1.8 exactly — both freezing and boiling are defined points on both scales, so there is no rounding hiding in it. The "×2" in the mental shortcut is a deliberate approximation, and the section above shows how much it costs.
Does the formula work below zero?
Yes, unchanged. The multiplier applies to the reading and the 32 is added afterwards, so negative numbers need no special case — which is exactly how −40 °C lands on −40 °F.
Is there a version without decimals?
Yes: °F = °C × 9/5 + 32. 9/5 is 1.8 written as a fraction, so the two forms are the same formula. Whichever one your mental arithmetic prefers is the right one to use.
Is the centigrade formula the same?
Yes. Centigrade is the old name for the Celsius scale. The General Conference on Weights and Measures renamed it in 1948, and the scale itself did not change, so °F = °C × 1.8 + 32 works whichever name a recipe or textbook uses. For oven settings, the oven guide has the table, and the chart covers everything from −40 °C to 300 °C if you want to look a value up instead of calculating it.
Use it
Converters in this guide
Every figure in this guide is computed at build time from the same conversion engine as the converters it links to, and the factors behind it are the defining standards listed on the methodology page. Nothing here is typed by hand from a template.
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