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Temperature Converter (°C ↔ °F ↔ K ↔ °R)

Temperature Converter (°C ↔ °F ↔ K ↔ °R)

Convert temperature between Celsius, Fahrenheit, Kelvin and Rankine — all in one calculation.

Scaled value (°C) —
Scaled value (°F) —
Scaled value (K) —
Scaled value (°R) —
Formule 
TEMPERATURE CONVERSIONS

  °C → °F   : T_F = T_C × 9/5 + 32
  °F → °C   : T_C = (T_F − 32) × 5/9

  °C → K    : T_K = T_C + 273.15    (absolute zero = −273.15 °C)
  K  → °C   : T_C = T_K − 273.15

  K  → °R   : T_R = T_K × 9/5      (Rankine — US thermodynamics)

REFERENCE POINTS
  −273.15 °C = 0 K         absolute zero (no thermal motion)
       0 °C  = 32 °F       water freezing point (1 atm)
     100 °C  = 212 °F      water boiling point (1 atm)
      37 °C  = 98.6 °F     human body temperature
     −40 °C  = −40 °F      the only point where °C = °F
Temperature scales — engineering range (−50 to +150 °C)❄ Absolute zero−273,15 °C = 0 K= −459,67 °F−40 °C−40 °F233,15 K°C = °F0 °C32 °F273,15 Kwater freezes37 °C98,6 °F310,15 Kbody temp100 °C212 °F373,15 Kwater boils1 °C = 1 K (same size) · 1 °F = 1 °R (same size) · 1 °C = 1.8 °F

Where do these four scales come from?

Each scale was created at a time when no global standard existed. Understanding their origins sheds light on how they are still used today.

Celsius (°C) — Anders Celsius, 1742

In 1742 at Uppsala University, the Swedish astronomer Anders Celsius proposed a linear scale built on two reference points that were easy to reproduce: the freezing point and the boiling point of water at standard atmospheric pressure. Ironically, Celsius originally defined it upside-down (0 = boiling, 100 = freezing). It was flipped after his death by Linnaeus in 1745 to give us the modern form.

The Celsius scale is now the worldwide scientific and industrial standard, except in the United States for domestic use. It is officially defined from the Kelvin: 0 °C = 273.15 K.

Fahrenheit (°F) — Daniel Gabriel Fahrenheit, 1724

A German physicist based in Amsterdam, Fahrenheit built the first reliable mercury thermometer in 1714. To calibrate his instruments he needed stable reference points:

  • 0 °F = the lowest temperature he could reliably reproduce (a brine of water, ice and ammonium chloride)
  • 96 °F = human body temperature (later refined to 98.6 °F)
  • The freezing point of water then fell at 32 °F and boiling at 212 °F — exactly 180 degrees apart (a deliberate geometric choice).

The Fahrenheit scale gives 1.8 times more resolution than Celsius (180 degrees vs 100 over the same water-to-steam interval), which mattered in the era of analogue thermometers. That is why it stuck in the United States, Liberia, the Bahamas and a few territories.

Kelvin (K) — Lord Kelvin (William Thomson), 1848

The Irish physicist William Thomson — later Lord Kelvin — showed in 1848 that there exists an absolute minimum temperature below which one cannot go: 0 K = −273.15 °C, the point where all thermal motion ceases. This discovery is the foundation of modern thermodynamics.

The Kelvin scale became the SI base unit for temperature, indispensable whenever you manipulate:

  • the ideal gas law (PV = nRT)
  • radiation (Stefan-Boltzmann law)
  • Carnot efficiency
  • any expression where temperature appears in a denominator

Important convention: write “300 K”, not “300 °K” — the Kelvin unit does not take the “degree” symbol.

Rankine (°R) — William Rankine, 1859

The Fahrenheit cousin of Kelvin. The Scottish engineer William Rankine, a pioneer of thermodynamics, proposed in 1859 an absolute scale with Fahrenheit-sized degrees. The zero is the same (0 °R = 0 K = −459.67 °F), but the gap between degrees matches the Fahrenheit.

Used almost exclusively in US thermodynamics (process equipment, gas turbines, US industrial HVAC) where engineers still reason in °F and need an absolute variant for ideal-gas calculations.

Which scale should you use?

ContextPreferred scale
Industrial process (Europe, Asia, worldwide)Celsius
Industrial process (US)Fahrenheit
Thermodynamics, physics, scienceKelvin
US thermodynamics (heat engines)Rankine or Kelvin
Meteorology, instrumentationCelsius (international) / Fahrenheit (US)

Worth remembering:

  • −40 ° is the only point where °C and °F coincide
  • A step of 1 °C = 1.8 °F = 1 K = 1.8 °R (degrees are the same “size” in Celsius and Kelvin, and the same in Fahrenheit and Rankine)
  • PID controllers, sensor calibrations and international calibration reports are almost always expressed in °C

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