Celsius, Fahrenheit and Kelvin Explained

Three scales, one quantity

Celsius, Fahrenheit and Kelvin all measure temperature, but they place zero in different spots and use different step sizes. Celsius and Kelvin share the same step: a change of one degree Celsius is exactly a change of one kelvin. Fahrenheit uses a smaller step, so a change of one degree Celsius equals a change of 1.8 degrees Fahrenheit.

Unlike length or mass, temperature scales do not simply differ by a multiplying factor. Converting between Celsius and Fahrenheit involves both a multiplication and an offset, which is why temperature conversions trip people up more than other conversions.

A few reference points help to see how the three line up. Water freezes at 0 °C, 32 °F and 273.15 K. A mild room at 20 °C is 68 °F and 293.15 K. A reading of 37 °C is 98.6 °F and 310.15 K, and water boiling at standard pressure is 100 °C, 212 °F and 373.15 K. Each pair differs by the same arithmetic you will see below.

Celsius

The Celsius scale is used for everyday temperatures in most of the world. Anders Celsius proposed a scale in 1742 with 0 at the boiling point of water and 100 at the freezing point, which is the reverse of what we use now. Within a few years it was flipped, and the version with 0 at freezing and 100 at boiling became standard. Until 1948 it was called centigrade; that year the 9th General Conference on Weights and Measures renamed the unit the degree Celsius.

Today the Celsius scale is defined through the kelvin: 0 °C is 273.15 K. The familiar fixed points of water, freezing at 0 °C and boiling at 100 °C, remain a good description of everyday conditions at normal atmospheric pressure, but they are no longer how the scale is formally defined.

Fahrenheit

Daniel Gabriel Fahrenheit proposed his scale in 1724. His early zero point came from a mixture of ice, water and a salt, ammonium chloride, and the scale was later adjusted so that water froze at 32 and, at standard atmospheric pressure, boiled at 212. That puts 180 degrees between freezing and boiling, against 100 on the Celsius scale, and explains the ratio of 9 to 5.

Fahrenheit is the everyday scale in the United States and a few other places, including some Pacific island states and the Cayman Islands. Some countries show both scales. It is now defined through the kelvin as well: absolute zero is −459.67 °F.

Kelvin

The kelvin is the SI base unit of thermodynamic temperature. Its zero is absolute zero, the lowest temperature possible in principle, so the scale has no negative values. By convention it is written K with no degree sign, so “300 K” is correct and “300 °K” is not; the older name “degree Kelvin” was dropped in the 1960s.

Since 20 May 2019 the kelvin has been defined by fixing the Boltzmann constant at exactly 1.380649 × 10⁻²³ joules per kelvin. Before that, it was defined using the triple point of water, set at exactly 273.16 K. That value is now a measured quantity with a tiny uncertainty, while the Boltzmann constant is exact. Scientists use kelvin because formulas in physics and chemistry relate temperature to energy and need a scale that starts from zero.

The formulas

These are the relationships to remember.

• Celsius to Fahrenheit: °F = °C × 9/5 + 32
• Fahrenheit to Celsius: °C = (°F − 32) × 5/9
• Celsius to kelvin: K = °C + 273.15
• Kelvin to Celsius: °C = K − 273.15

Take 20 °C. Multiply by 1.8 to get 36, add 32, and the answer is 68 °F. For 100 °F, subtract 32 to get 68, then multiply by 5/9 to get 37.78 °C. A temperature of 300 K is 300 − 273.15 = 26.85 °C, and 26.85 × 1.8 + 32 = 80.33 °F. To move between Fahrenheit and kelvin, go through Celsius first.

For a quick mental estimate from Celsius to Fahrenheit, double the number and add 30. For 20 °C that gives 70 °F against an exact 68 °F, close enough to decide what to wear. The estimate drifts further as temperatures get higher or lower, so use the exact formula when it matters. One curiosity: −40 is the single temperature where the Celsius and Fahrenheit scales agree, because −40 × 1.8 + 32 = −40.

Readings versus differences

The offset only applies to readings, not to differences. If the temperature rises by 10 °C, it rises by 10 K and by 18 °F. A forecast that is 5 °C warmer than yesterday is 9 °F warmer, not 41. Mixing the two is the most common error in temperature conversion, and it appears whenever someone adds 32 to a difference.

The scales also have physical limits. Nothing can be colder than absolute zero, which is 0 K, −273.15 °C or −459.67 °F, so a value below that has no meaning. A unit converter such as this one rejects temperatures below absolute zero for this reason, and you can read the result from any of the three scales at once.