Temperature Scales: Celsius, Kelvin, and Fahrenheit

The Celsius scale sets 0 °C at the freezing point of water and 100 °C at its boiling point at normal pressure, the Kelvin scale starts at absolute zero (0 K = −273.15 °C) and uses the same size of degree as Celsius, and the Fahrenheit scale sets water to freeze at 32 °F and boil at 212 °F. In brief: T(K) = T(°C) + 273.15, and T(°F) = 1.8 × T(°C) + 32. The kelvin is the SI unit of temperature, and many physics formulas, such as the gas laws, need temperatures in kelvins.

Weather reports in the United States use Fahrenheit, most of the world uses Celsius, and scientists use kelvins. Converting between them is a basic skill. This guide describes the three scales, explains absolute zero and how to convert between scales, compares fixed points in a table, works through conversions and corrects common mistakes.

What is the Celsius scale?

The Celsius scale (formerly centigrade) is defined by two reference points for water at standard atmospheric pressure: 0 °C (ice melting) and 100 °C (boiling), divided into 100 equal steps. Today it is defined from the kelvin: t(°C) = T(K) − 273.15. Normal human body temperature is about 37 °C, and a comfortable room is around 20 to 22 °C.

What is the Kelvin scale?

The Kelvin scale is an absolute scale, whose zero is absolute zero: the lowest possible temperature, at which the particles have minimal thermal motion, which is −273.15 °C. A change of 1 K is the same as a change of 1 °C. Kelvins are written without the degree sign (300 K, not 300 °K). Since 2019, the kelvin is defined by fixing the value of the Boltzmann constant, k = 1.380649 × 10⁻²³ J/K. Because the scale starts at true zero, temperatures in kelvins are proportional to the average kinetic energy of the particles, and they are never negative. Equations such as pV = nRT, or Stefan’s law, must use kelvins.

What is the Fahrenheit scale?

On the Fahrenheit scale, water freezes at 32 °F and boils at 212 °F, so there are 180 degrees between them, compared with 100 on the Celsius scale. Each Fahrenheit degree is therefore 5/9 of a Celsius degree. The conversion formulas:

• °F = (9/5) × °C + 32 = 1.8 × °C + 32
• °C = (5/9) × (°F − 32)

The two scales give the same number at −40 (−40 °C = −40 °F). Fahrenheit is used in everyday life in the United States and a few other countries.

Fixed points compared

Worked example: conversions

1. °C to K: 25 °C = 25 + 273.15 = 298.15 K, which is usually rounded to 298 K.
2. K to °C: liquid nitrogen boils at 77 K: 77 − 273.15 = −196 °C.
3. °C to °F: 37 °C = 1.8 × 37 + 32 = 66.6 + 32 = 98.6 °F.
4. °F to °C: 100 °F = (5/9) × (100 − 32) = (5/9) × 68 = 37.8 °C.
5. Temperature differences: a rise of 20 °C is a rise of 20 K, but 1.8 × 20 = 36 °F.
6. Check of the point −40: 1.8 × (−40) + 32 = −72 + 32 = −40 °F.

How were the scales developed?

Daniel Fahrenheit created the first reliable mercury thermometer in 1714 and his scale in 1724. Anders Celsius proposed a scale with 100 degrees between the two points in 1742, originally with 0 for boiling and 100 for freezing, which was inverted after his death. Lord Kelvin proposed an absolute scale in 1848, based on the efficiency of heat engines. The International Temperature Scale and, in 2019, the redefinition of the kelvin in terms of the Boltzmann constant followed.

Which mistakes are common?

Mistake 1: Using Celsius in gas law or radiation formulas

Convert to kelvins first. Using °C gives wrong results, and 0 °C is not a zero temperature.

Mistake 2: Converting the difference as a temperature

A difference of 10 °C is 10 K, but 18 °F. Do not add 273.15 or 32 to a difference.

Mistake 3: Writing “degrees Kelvin”

The unit is the kelvin (K), with no degree sign.

Mistake 4: Thinking that 20 °C is twice as warm as 10 °C

Ratios are meaningful only on the absolute scale: 293 K is not twice 283 K.