Celsius to Fahrenheit Calculator

To convert from Celsius to Fahrenheit is simple: multiply by 9/5 (or 1.8) and then add 32.

The calculator above can be used both ways. If you enter a value into one of the fields, the result will appear in the other field, along with values in kelvin, rankine and four more historical temperature scales.

It also supports conversions that most other sites leave out. Instead of converting a temperature value, you can convert a change in temperature.

Formula:

The conversion of Celsius to Fahrenheit is as follows:

The conversion to the opposite direction is as follows:

9/5 is the ratio of size between two temperature units. Celsius divides the range from zero to boiling point into 100 equal parts while Fahrenheit divides it into 180 equal parts. When you divide 180 by 100, you get 1.8.

The 32 is an offset because the two temperature scales have different zero points. Water freezes at 0 degrees Celsius and 32 degrees Fahrenheit.

A full example:

Let's take a mild spring day with a temperature of 21.5 degrees Celsius. First we multiply.

Then we add the offset.

So 21.5 degrees Celsius is the same as 70.7 degrees Fahrenheit. This can be checked in reverse: if you subtract 32 from 70.7, you get 38.7, and if you multiply 38.7 by 5/9, you get 21.5.

The values shown are not difference values.

This is often a source of confusion. When the weather forecast says that the temperature will rise by 10 degrees Celsius, it means that it will rise by 18 degrees Fahrenheit and not 50.

With this ratio the offset can be completely ignored. When you subtract one measurement from another, the offset is cancelled out.

The reason for this is simple algebra. When you convert two measurements and then subtract one from the other, those two 32s cancel out leaving just the 1.8.

This rule applies to anything measured in differences, such as tolerance bands on data tables, temperature swings during the night, temperature gradients and especially heating rates. An oven set to heat at 300 degrees Fahrenheit per hour has a heating rate of 166.7 degrees Celsius per hour. Subtracting 32 by mistake gives a value that is 148.9 lower than the correct one, which is more than ten percentage points difference.

The metric system has another advantage: because the kelvin and Celsius have the same unit size, a temperature change of 12 degrees (Celsius) is exactly the same as a change of 12 kelvins. The only difference is in the displayed values, with there being a fixed difference of 273.15.

Practical mental arithmetic methods

The rule everyone repeats is to double the temperature and add 30. At 25 degrees Celsius this gives a result of 80 but the actual value is 77 which is close enough to decide whether or not to put on a jacket.

The error is exactly one fifth of a degree celsius for every deviation from the temperature of 10 degrees celsius. At 10 degrees celsius it's completely correct, at 30 degrees celsius it's 4 degrees higher and at minus 10 degrees celsius it's 4 degrees lower.

There is a technique called the "rule of thumb" but it's really not a rule of thumb. You double the Celsius value, subtract one-tenth and then add 32. Doubling and subtracting one-tenth gives you a multiple of the original value, which is 1.8. So if we have 100 degrees Celsius, for example, 200 minus 20 plus 32 would give us 212. This is the actual boiling point and it's completely accurate.

The origins of both temperature scales

Daniel Fahrenheit published his temperature scale in 1724. He set the freezing point of a salt water solution as zero and placed body temperature at the upper end of a range divided into 96 equal parts. So these numbers seem rather arbitrary today. His thermometer was very stable, and because of its reliability this temperature scale spread.

In 1742, Anders Celsius proposed a temperature scale based on the freezing and boiling points of water with one hundred units. His original version had the opposite direction - the boiling point was at zero and the freezing point at 100 - and he used this method for the rest of his life.

After his death the direction of this temperature scale was reversed. To avoid confusion with degrees of angle measure, the official designation was changed from "percent degree" to "degree Celsius" in 1948.

All temperature tables:

The following seven conversions all use Celsius as input, which is also the input used in the result area.

Kelvin and Rankine are absolute temperature scales corresponding to the Celsius and Fahrenheit respectively. As their zero point is not based on water properties but rather at absolute zero, they do not use a degree symbol.

The Delisle temperature scale is an exception; because the direction of the scale is reversed, temperatures decrease as numbers increase, with zero being the boiling point.

Useful temperatures to remember:

If you memorize a few corresponding values, you can make most everyday conversions without any calculations.

Why minus 40 is special:

To set the two temperature scales equal to each other, we solve for F equals C. So if F is equal to C, then C is equal to the value of 1.8C plus 32. So negative 0.8 degrees Celsius corresponds to a value of 32 and C is negative 40.

Since two lines with different slopes can only intersect once, -40 is the only value at which the two temperature scales read the same number. Entering this value into either tool will show the intersection point on the graph.