Temperature scales: Celsius, Fahrenheit, Kelvin and Rankine

Temperature is a property of matter that represents the internal motion of the particles that make it up. The instrument used to measure it is the thermometer.

The most commonly used temperature scales today are:

  • Celsius or centigrade scale (ºC)
  • Fahrenheit Scale (ºF)
  • Kelvin scale (K)

There is a fourth staircase, the Rankine staircase, which is disused. Each scale is based on certain phenomena or fixed points, which served to define the range and degrees of measurement. For example, the Celsius scale was defined from the melting and boiling point of water.

comparison of the temperature scales celsius fahrenheit and kelvin
Thermometers where the three most used temperature scales are compared: Kelvin, Celsius and Fahrenheit.

Absolute zero is the coldest temperature that can be recorded. This happens because the velocity of the particles or their kinetic energy becomes zero, that is, the particles stop.

The equivalences of absolute zero at the different scales are:

  • Celsius: -273 ºC
  • Fahrenheit: -459.7 ºF
  • Kelvin: 0 K.

Fahrenheit scale

The Fahrenheit scale is the temperature scale used in the United States, Liberia, and the Bahamas, among others. Its symbol is ° F and it reads degrees Fahrenheit.

The physicist Daniel Fahrenheit (1686-1736) described the scale that bears his name in 1724. It is based on two fixed points: the temperature at which water freezes (32 ºF) and the temperature at which water bull (212) ºF). The difference between these two points is 180 degrees, so each degree represents 1/180 degrees.

Fahrenheit originally proposed the scale using three fixed points: the highest point was the temperature of the human body (96 ºF), the intermediate point was the temperature of the mixture of ice and water (32 ºF) and the lowest point was the temperature of a mixture of equal parts of ice, salt and water (0 ºF).

To convert degrees Fahrenheit from degrees Celsius the following formula is used:

Temperature in degrees Fahrenheit = (9/5 temperature in degrees Celsius) + 32

That is: the temperature in degrees Fahrenheit is equal to nine-fifths of the temperature in degrees Celsius plus 32. For example, if we want to convert the ambient temperature from 23 ºC to ºF we do the following:

TºF = 9/5 x (23 ºC) + 32 = 41.4 + 32 = 73.4 ºF.

Then, 23ºC is equal to 73.4 ºF. The Fahrenheit scale and the Celsius scale intersect at -40ºC, i.e. -40ºC equals -40ºF.

Celsius or Celsius scale

The Celsius scale is the most widely used temperature scale worldwide. Its symbol is ºC and it reads degrees Celsius or Celsius.

In 1742, the Swedish astronomer Anders Celsius (1701-1744) proposed two fixed points to make his temperature scale: the melting point of ice would represent 0 ºC and the boiling point of water would be 100 ºC.

The Celsius scale and the Kelvin scale are related by the formula:

Temperature in degrees Celsius (ºC) = Temperature in Kelvin (K) – 273.15

For example, we want to convert 300 K to centigrade. That’s why we subtract 273.15 to 300 K:

TºC = 300K-273.15 = 26.85 ºC

That is, 300K is 26.85 ºC.

Kelvin scale

The kelvin is the unit for temperature in the International System and the most widely used in the scientific context. The symbol is K and it reads kelvin. For example, the solar corona has a temperature of 1 million kelvin, while the interior of the Sun measures 10 million kelvin.

To define kelvin, we need to know that the triple point of water is the point where we can find water in all three states: liquid, solid, and gaseous.

This temperature was set at 273.16 K by an international agreement in 1954. Hence a kelvin is defined as the fraction 1 / 273.16 of the thermodynamic temperature of the triple point of water.

The Kelvin scale is the only one based on thermodynamic principles and not how a particular material behaves.

William Thomson (1824-1907), known as Lord Kelvin, was a pioneer in creating the concept of absolute temperature in thermodynamic terms. He insisted that the concept of absolute temperature should not be tied to any property of any particular material substance, and that temperature should be a measurable physical quantity.

Rankine scale

The Rankine scale is a thermodynamic temperature that has the symbol ºR and reads rankin degrees. It is named after the engineer and physicist William Rankine who proposed it in 1859.

The Rankine scale uses the degree as the Fahrenheit degree, but is measured from absolute zero as the Kelvin scale. This scale is currently obsolete.

Conversion formulas between temperature scales

Knowing the relationships between each temperature scale, we can make the corresponding conversions following the following formulas:

From ºC From K From ºF From ºR
A ºC TC= TK-273.15 TC= 5/9 (TF-32) TC= 5 / 9TR-273.15
AK T \K= Tc +273 TK= 5/9 (TF+459.67) TK= 5 / 9TR
A ºF TF= 9 / 5TC +32 TF= 9 / 5TK-459.67 TF= TR-459.67
A ºR TR= 9 / 5TC+491.67 TR= 9 / 5TK TR= TF+459.67

You may also be interested to see:


Machin, G. (2017) Chapter 4 Temperature scales: past, present and future: 1700-2050. A: Cooper, M., Grozler, J. Precise Dimensions A history of units from 1791-2018. IOP Publishing

Temperature and thermometric scales. In: Slavat, J (director) (1988) Salvat Encyclopedia of Science and Technology-volume 13. Salvat editors. Barcelona, ​​Spain.

Zain, S. (2021) Thermodynamics and Statistical Mechanics. IOP Publishing.

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