Celsius, Fahrenheit and Kelvin

Why temperature is not like length or weight

Converting a length or a mass is a single multiplication, because both scales measure the same thing from the same starting point. Temperature is different: each scale has its own zero, and two zeros are not in the same place. That is why every temperature formula has two parts, a scale factor and an offset.

The offset fixes where the scale starts. The factor fixes how big one degree is. Change either one and the whole number moves, which is why you cannot convert a temperature by multiplying by 1.8 alone. The definitions behind the factors are settled by international agreement, and the UnitUtils temperature converter applies them directly rather than through a rounded table of remembered pairs.

How the three scales are defined

Celsius puts zero at the freezing point of water and 100 at the boiling point of water at standard atmospheric pressure.

Fahrenheit uses a much smaller degree, so the same 100-degree span takes 180 Fahrenheit degrees: 32 °F to 212 °F. Because 180 ÷ 100 = 1.8, one Celsius degree is 1.8 Fahrenheit degrees. Fahrenheit's zero came from a laboratory freezing mixture rather than from anything in the natural world, which is why the 32 has to be added on every conversion.

Kelvin starts at absolute zero, the lowest temperature a body can reach, and is set so that a Kelvin degree is exactly the same size as a Celsius degree. Converting Celsius to kelvin needs no multiplication, only the addition of 273.15. The temperature section of the methodology sets out the arithmetic the converter uses.

The formulas

To go from Celsius to Fahrenheit, multiply by 9 ÷ 5 (that is, by 1.8) and add 32. To go the other way, subtract 32, then multiply by 5 ÷ 9. To go from Celsius to Kelvin, add 273.15.

Worked from Celsius, 20 °C gives 20 × 1.8 = 36, then 36 + 32 = 68 °F. A body temperature of 37 °C gives 37 × 1.8 = 66.6, then 66.6 + 32 = 98.6 °F. Running those in reverse, 100 °F is 100 − 32 = 68, then 68 × 5 ÷ 9 = 37.777… °C, which is 37.78 °C to two decimal places. In Kelvin, 20 °C is 20 + 273.15 = 293.15 K.

Minus 40 is worth knowing because it needs no arithmetic at all: −40 × 1.8 = −72, and −72 + 32 = −40. It is the one temperature where the two scales agree exactly without an adjustment. If you mostly need one direction, use the Celsius to Fahrenheit converter or the Fahrenheit to Celsius converter; the temperature converter covers all three scales including Kelvin.

Readings and differences do not convert the same way

This is the most common error with temperature. The offset belongs to a reading, not to a change. If a forecast says the temperature will be 10 °C higher than it is now, that is a difference, and you convert it by multiplying by 1.8 alone: 10 °C is 18 °F. A difference of 50 °F is a difference of 27.78 °C.

Adding the 32 to a difference would be meaningless, which is why a recipe that says increase the oven by 25 degrees is not the same as setting it to 25 degrees.

A rough shortcut, and where it breaks

For a quick estimate, double the Celsius figure and add 30. It gives 70 for 20 °C where the exact answer is 68 °F, which is close enough for a coat check or a comment on the weather. It is exactly right at 10 °C, where doubling gives 20 and adding 30 gives 50, the same as 10 × 1.8 + 32.

The error is 0.2 Fahrenheit degrees for every degree away from 10 °C: too low below 10 °C and too high above it. At 0 °C the shortcut reads 30 instead of 32, two degrees low. At 37 °C it reads 104 instead of 98.6, 5.4 degrees high. Use the real formula whenever the number matters.

Reference points

The freezing and boiling points in that table hold at standard atmospheric pressure, 101,325 pascals. At altitude water boils at a lower temperature, so a stated recipe temperature is a reading that assumes a pressure rather than a property of the water alone.

What the converter will not do

The UnitUtils temperature converter rejects anything colder than absolute zero. A figure of −300 °C is not a temperature that can be measured, whatever the scales are called, and no conversion of it is meaningful.

Results come back to six significant figures unless you ask for a fixed number of decimal places, so 100 °F reads as 37.7778 °C by default and 37.78 °C to two places. Choose the rounding to suit the job: a cooking or laboratory figure rarely needs more than one decimal place, and more digits than the original measurement do not add accuracy.