Temperature Scales Explained

Celsius, Fahrenheit, Kelvin, and Rankine are four different ways of writing the same underlying physical quantity: thermodynamic temperature. Each has a different zero point and a different degree size. Understanding the differences is the key to converting correctly.

Why Four Scales Exist

Temperature measurement predates the discovery of thermodynamics. Early scientists invented scales based on convenient reference points (the freezing and boiling points of water, the temperature of a salt-ice mixture, body temperature), and different traditions settled on different choices. By the time physicists realized temperature had an absolute zero, several scales were already in common use, and they all persisted.

Celsius (°C)

Proposed by Anders Celsius in 1742. Originally the scale ran backwards (0 for boiling, 100 for freezing); the modern orientation (0 for freezing, 100 for boiling) was adopted shortly after his death.

  • 0 °C = freezing point of water at 1 atm
  • 100 °C = boiling point of water at 1 atm
  • Used in science and in everyday life throughout most of the world
  • The SI accepts Celsius for use with SI: 0 °C = 273.15 K exactly

Fahrenheit (°F)

Proposed by Daniel Gabriel Fahrenheit in 1724. The zero point was based on a brine mixture; 32 °F was the freezing point of pure water, and 96 °F (later 98.6 °F) approximated human body temperature.

  • 32 °F = freezing point of water
  • 212 °F = boiling point of water
  • Used in the United States, and informally in a small number of other countries
  • The degree size is 5/9 of a Celsius degree

Kelvin (K)

The kelvin is the SI base unit of thermodynamic temperature. It is an absolute scale: 0 K is absolute zero, the temperature at which all classical thermal motion stops. There is no degree symbol; the unit is simply "kelvin" (lowercase for the unit name, uppercase for the symbol K).

  • 0 K = absolute zero
  • 273.15 K = freezing point of water
  • 373.15 K = boiling point of water at 1 atm
  • Same degree size as Celsius (1 K step = 1 °C step)
  • Defined since 2019 by fixing the Boltzmann constant to 1.380649 × 10⁻²³ J/K exactly

Rankine (°R)

An absolute scale based on the Fahrenheit degree size. Zero is absolute zero, and each degree is the same size as a Fahrenheit degree. It is used in some US engineering fields, especially thermodynamics with imperial units.

  • 0 °R = absolute zero
  • 491.67 °R = freezing point of water
  • 671.67 °R = boiling point of water at 1 atm
  • 1 °R = 5/9 K exactly

Comparison Table

Temperature scale comparison
Reference°C°FK°R
Absolute zero−273.15−459.6700
Water freezing032273.15491.67
Comfortable room2068293.15527.67
Human body3798.6310.15558.27
Water boiling (1 atm)100212373.15671.67

Exact Conversion Formulas

°F = (°C × 9/5) + 32
°C = (°F − 32) × 5/9
K = °C + 273.15
°C = K − 273.15
K = °F × 5/9 + 255.372
°F = K × 9/5 − 459.67
°R = (°C + 273.15) × 9/5
°R = °F + 459.67
K = °R × 5/9
°R = K × 9/5

All of these are exact. The offsets (273.15 and 32) and the ratio (9/5) are definitional and are not approximations.

Why Temperature Needs Explicit Formulas

Linear unit conversions (length, mass, volume) can all be done with a single multiplication: multiply by a scale factor. Temperature cannot, because it has both a scale factor and an offset. Celsius and Fahrenheit are the same at no point on the scale except the intersection at −40. There is no simple "multiply by 1.8" rule that works for both directions without also handling the 32 offset.

M-Convert therefore uses explicit forward and reverse functions for temperature, never a scale-factor multiplication. This guarantees correctness at every temperature, including negative values and extreme values.

Practical Conversion Tips

  • Rough Celsius to Fahrenheit: double the Celsius value and add 30. (Actual: 20 °C = 68 °F; the estimate gives 70 °F. Accurate to within about 5%.)
  • Rough Fahrenheit to Celsius: subtract 30 and halve. (Actual: 68 °F = 20 °C; estimate gives 19 °C.)
  • −40 is the intersection: at this single temperature, Celsius and Fahrenheit read the same.
  • Kelvin is C+273.15: a quick mental conversion is to add 273 for everyday purposes.
  • Rankine is F+459.67: used mostly in engineering, especially in the US.

Which Scale to Use

  • Science: Kelvin for thermodynamic calculations, Celsius for reporting results.
  • Weather (US): Fahrenheit.
  • Weather (elsewhere): Celsius.
  • Cooking: Celsius internationally, Fahrenheit in the US.
  • Engineering thermodynamics (US): Rankine for imperial units, Kelvin for SI.
  • Medicine: Celsius internationally, both in the US.