Celsius to Fahrenheit Formula (and Fahrenheit to Celsius)

To convert Celsius to Fahrenheit, multiply by 9/5 (that is, by 1.8) and add 32: °F = °C × 9/5 + 32. To go back, subtract 32 first and then multiply by 5/9: °C = (°F − 32) × 5/9. So 20 °C is 68 °F, 98.6 °F is 37 °C, and −40 is the one reading that is the same on both scales.

The quickest route here: open the Celsius to Fahrenheit converter and type the value. The Fahrenheit to Celsius converter does the reverse, and the Temperature converter shows Celsius, Fahrenheit, Kelvin and Rankine side by side. Everything runs in the browser, with nothing to install.

Where 9/5 and 32 come from

The scales disagree about two things, and each disagreement contributes one part of the formula.

• They start in different places. Water freezes at 0 °C but at 32 °F. That offset is the +32.
• Their degrees are different sizes. Between freezing and boiling there are 100 Celsius degrees but 180 Fahrenheit degrees, so one Celsius degree is 180 ÷ 100 = 1.8 Fahrenheit degrees. That is the 9/5.

Written out: °F = °C × 1.8 + 32 and °C = (°F − 32) ÷ 1.8. The order is not optional in the second: the subtraction undoes the offset before the division undoes the scaling.

Reference table: everyday temperatures

Celsius	Fahrenheit	What it is
−40 °C	−40 °F	The single point where both scales agree
−18 °C	−0.4 °F	A home freezer
0 °C	32 °F	Water freezes
10 °C	50 °F	A cool day
20 °C	68 °F	Ordinary room temperature
30 °C	86 °F	A hot day
37 °C	98.6 °F	Often quoted as body temperature
38 °C	100.4 °F	The figure many health services use for a fever
100 °C	212 °F	Water boils at sea level

Reference table: oven settings

Fahrenheit recipes rarely land on a round Celsius number. Ovens are not that accurate anyway, so cooks round to the nearest dial marking.

Fahrenheit	Exact Celsius	Dial setting normally used
300 °F	148.9 °C	150 °C
325 °F	162.8 °C	160 °C
350 °F	176.7 °C	175 or 180 °C
375 °F	190.6 °C	190 °C
400 °F	204.4 °C	200 °C
425 °F	218.3 °C	220 °C

Three worked examples

A warm day: 25 °C into Fahrenheit. Multiply first: 25 × 1.8 = 45. Then add the offset: 45 + 32 = 77 °F.

A temperature reading: 100.4 °F into Celsius. Subtract first: 100.4 − 32 = 68.4. Then divide: 68.4 ÷ 1.8 = 38 °C.

An American recipe: 350 °F into Celsius. 350 − 32 = 318, and 318 ÷ 1.8 = 176.67 °C. Set the oven to 175 or 180 °C; that gap is smaller than the swing of most domestic thermostats.

The "double it and add 30" shortcut, and how wrong it is

The popular mental trick is double the Celsius figure and add 30. It is exact at 10 °C and drifts by 0.2 °F for every degree you move away from it, always upwards.

Celsius	Shortcut (2 × °C + 30)	Exact	Error
0 °C	30 °F	32 °F	2 °F too low
10 °C	50 °F	50 °F	exact
20 °C	70 °F	68 °F	2 °F too high
25 °C	80 °F	77 °F	3 °F too high
30 °C	90 °F	86 °F	4 °F too high
37 °C	104 °F	98.6 °F	5.4 °F too high
100 °C	230 °F	212 °F	18 °F too high

Across normal weather, 0 °C to 30 °C, it is out by no more than 4 °F — close enough to decide what to wear, and not close enough for anything else. At body temperature it overshoots by 5.4 °F. The reverse trick, subtract 30 and halve, is exact at 50 °F and then runs low: 68 °F gives 19 °C instead of 20 °C, and 86 °F gives 28 °C instead of 30 °C.

What the formula assumes

• You are converting a temperature, not a difference. This matters more than it sounds; the next section covers it.
• It is a plain reading, with no pressure or altitude correction. Water boils at 100 °C at sea level and lower up a mountain. The conversion is unaffected; the meaning of the number is not.
• Decimals are real. Most whole Fahrenheit values become repeating decimals in Celsius. Rounding is your choice, not the formula's.

Converting a difference, a rise or a margin

A difference in temperature has no starting point, so it carries no offset. Convert it with 9/5 alone:

• a rise of 10 °C is a rise of 18 °F (10 × 1.8), not 50 °F
• a tolerance of ±5 °C is ±9 °F
• a drop of 10 °F is a drop of about 5.6 °C

This is the usual error in spreadsheets and translated manuals: "it rose by 15 degrees" is 27 °F, while "it is 15 degrees" is 59 °F.

Kelvin, in one paragraph

Kelvin uses Celsius-sized degrees but starts at absolute zero, so K = °C + 273.15. Room temperature at 20 °C is 293.15 K, and 0 K is −273.15 °C, or −459.67 °F. Kelvin takes no degree sign: 293.15 K, never 293.15 °K. From Fahrenheit, convert to Celsius first and then add 273.15. Because the degree size is shared, a difference of 5 °C is exactly 5 K. The Temperature converter also handles Rankine, which is to Fahrenheit what Kelvin is to Celsius.

Common problems, and what they mean

Your answer is far too big — around 90 °F for a mild day. You added 32 before multiplying. 20 °C is (20 × 1.8) + 32 = 68 °F, not (20 + 32) × 1.8 = 93.6 °F.

Your answer is far too small going from Fahrenheit. You divided before subtracting. 68 °F is (68 − 32) ÷ 1.8 = 20 °C, not (68 ÷ 1.8) − 32 = 5.8 °C.

Everything is out by roughly 32. A difference has been converted as if it were a reading, or the reverse. Ask whether your number is a point on the scale or a gap between two points.

A converted recipe gives a temperature no oven dial has. That is normal; round to the nearest 5 or 10 °C, as in the oven table above.

A negative value comes out positive. Check the minus sign survived the multiplication: −20 °C × 1.8 = −36, and −36 + 32 = −4 °F, not 68 °F.

Questions people ask

Which temperature is the same on both scales? Only −40. Solving °C = °C × 1.8 + 32 gives −40 as the one answer, which makes it a quick way to sanity-check any converter.

Is body temperature really 37 °C? It is the traditional average, and it converts to exactly 98.6 °F. Readings vary between people and across the day, so treat it as a reference point rather than a target.

Why 1.8 rather than 9/5? They are the same number: 9/5 suits fractions by hand, 1.8 suits a calculator.

How do I write the formula in a spreadsheet? With the Celsius value in cell A1: =A1*9/5+32 for Fahrenheit, and =(A1-32)*5/9 for the reverse.

Who still uses Fahrenheit? It is the everyday scale in the United States and a few other places. Most of the world uses Celsius for weather and cooking, and science uses Kelvin.

Next steps

• Convert the other way: Fahrenheit to Celsius
• See all four scales at once, Kelvin and Rankine included: Temperature converter
• Other everyday conversions: kg to lbs and cm to inches