In the formulas below, we use the mathematical standard computer conventions for algebraic and numeric expressions. The characters ([ ]) represent order of calculations, / represents division, * represents multiplication, - subtraction, + addition and = is equal. It is very important to follow the order of operations as different results can be obtained giving inaccurate results.
The common scales for most temperature expressions are Celsius and Fahrenheit while Kelvin, Réaumur, and Rankine are used for specialized scientific applications.
Celsius and Fahrenheit
Tc = (5/9)*(Tf-32); Tc = temperature in degrees Celsius, Tf = temperature in degrees Fahrenheit
For example, assume you have a Fahrenheit temperature of 98.6 degrees and you desire to convert it into degrees on the Celsius scale. Using the above formula, you would first subtract 32 from the Fahrenheit temperature and get 66.6 as a result. Then you multiply 66.6 by five-ninths and get the converted value of 37 degrees Celsius.
Below is the formula to convert a Celsius scale temperature into degrees on the Fahrenheit(commonly misspelled Farenheit) scale. As you might guess, it is the exact opposite of converting Fahrenheit to Celsius.
Tf = (9/5)*Tc+32; Tc = temperature in degrees Celsius, Tf = temperature in degrees Fahrenheit
Assume that you have a Celsius scale temperature of 100 degrees and you wish to convert it into degrees on the Fahrenheit scale. Using the stated formula, you first multiply the Celsius scale temperature reading by nine-fifths and get a result of 180. Then add 32 to 180 and get the final converted result of 212 degrees on the Fahrenheit scale.
Below is another accepted conversion method that works just as well and perhaps might be easier to remember. No matter which direction you want to covert, Fahrenheit to Celsius or Celsius to Fahrenheit, always first add 40 to the number. Next, multiply by 5/9 or 9/5 just like the first method. Then, always subtract out the 40 you just added to yield the final result. To remember whether to use 5/9 or 9/5 when converting from Fahrenheit to Celsius or Celsius to Fahrenheit, just simply remember, F (for Fahrenheit) begins with the same letter as Fraction. 5/9 is always a Fraction; while 9/5 is also a fraction, in this form, it is Clearly a whole number plus a fraction (1 and 4/5). Thus, if you want to convert Fahrenheit (F) to Celsius (C), then use the Fraction 5/9; Celsius (C) to Fahrenheit (F), use the other, 9/5, which is Clearly not just a fraction.
For an example of this method, we'll use the values we used in the initial example, 98.6 F and 37 C, which are equal.
To convert from F to C, try these calculations manually.
98.6 + 40 = 138.6, and 138.6 * 5/9 = 77. For the final calculation, remove the 40. 77 - 40 = 37
To convert from C to F, try these calculations manually.
37 + 40 = 77, and 77 * 9/5 = 138.6. For the final calculation, remove the 40. 138.6 - 40 = 98.6
In summary, add 40, (F to C) multiply by Fraction...(C to F) multiply by the other, subtract 40. Go figure...
The Celsius temperature scale is still sometimes referred to as the "centigrade" scale. Centigrade means "consisting of or divided into 100 degrees;" the Celsius scale, devised by Swedish Astronomer Andres Celsius (1701-1744) for scientific purposes, has 100 degrees between the freezing point of 0 degrees and boiling point of 100 degrees of pure water at sea level air pressure, 29.92 inches of mercury. That pressure criteria is often called an atmosphere, or more commonly, standard pressure. The term Celsius was adopted in 1948 by an international conference on weights and measures. This is the most widely used scale in the world.
On the Fahrenheit scale, used primarily in the United States, the freezing point of water is 32 degrees and the boiling point is 212 degrees while measured at standard pressure. Zero degrees Fahrenheit was the coldest temperature that the German born scientist Gabriel Daniel Fahrenheit could create with a mixture of ice and ordinary salt. He is credited with the invention of the mercury thermometer and introduced it and his scale in 1714 in Holland, where he lived most of his life. His thermometer was based on the original design papers by Galileo for a temperature and pressure measuring device.
Scientists use a third scale for unique measurements, called the absolute or Kelvin scale. This scale was invented by William Thomson, also know as Lord Kelvin, a British scientist who made important discoveries about heat in the 1800's. Scientists have determined that the coldest it can get, in theory, is minus 273.15 degrees Celsius. This temperature has never actually been reached, though scientists have come close. The value, minus 273.15 degrees Celsius, is called absolute zero. At this temperature scientists believe that molecular motion would stop. You can't get any colder than that. The Kelvin scale uses this number as zero. To get other temperatures in the Kelvin scale, you add 273 degrees to the Celsius temperature. Conversion is very straight forward, though, strangely enough, the word degree is not used with the Kelvin scale.
A now somewhat obsolete scale is used in specific calculations and measurements. It was created by R A F de Réaumur (1683-1757) a French scientist. He knew nothing of Fahrenheit's work and did not use mercury, but did produce a good working thermometer. He used the freezing point of water as his zero mark, and put the boiling point at 80 degrees. This scale was widely used in the 18th and 19th centuries, especially in France, in scientific communities. He has a greater claim to fame for much of the other scientific work he did.
W J M Rankine (1820-1872), a Scottish engineer, created his scale, which was merely the Kelvin scale using the Fahrenheit degree instead of the Celsius. It has also had some wide use in scientific communities but is of no practical use in other areas of measurement.
Kelvin, Réaumur, and Rankine
a °C = (4/5)a °Réaumur = [32 + (9/5)a] °F
b °Réaumur = (5/4)b °C = [32 + (9/4)b] °F
c °F = (5/9)(c - 32) °C = (4/9)(c - 32) °Réaumur
t °C = (t + 273.15) K
TK K = (TK - 273.15) °C = [1.80 * (TK - 273.15) + 32] °F = 1.80 TK °Rankine