Celsius, Fahrenheit and Kelvin: How the Scales Relate
By Scientific Converters · Updated · Factors from NIST SP 811 and the BIPM SI Brochure
Short answer: °F = °C × 1.8 + 32 and K = °C + 273.15 exactly; a temperature difference converts without the offset, so a 10 °C rise is an 18 °F rise.
The exact formulas
- °F = °C × 9/5 + 32 · °C = (°F − 32) × 5/9
- K = °C + 273.15 · °C = K − 273.15
- °R = °F + 459.67 · K = °R × 5/9
All of these are exact definitions. The kelvin is the SI base unit, fixed since 2019 by the Boltzmann constant; Celsius is the kelvin shifted by 273.15; Fahrenheit and Rankine use degrees 5/9 the size of a kelvin.
Reference points
| Point | °C | °F | K | °R |
|---|---|---|---|---|
| Absolute zero | -273.15 °C | -459.67 °F | 0 K | 0 °R |
| Liquid nitrogen boils | -195.8 °C | -320.44 °F | 77.35 K | 139.23 °R |
| −40 (scales meet) | -40 °C | -40 °F | 233.15 K | 419.67 °R |
| Water freezes (1 atm) | 0 °C | 32 °F | 273.15 K | 491.67 °R |
| Standard air (68 °F) | 20 °C | 68 °F | 293.15 K | 527.67 °R |
| Body temperature | 37 °C | 98.6 °F | 310.15 K | 558.27 °R |
| Water boils (1 atm) | 100 °C | 212 °F | 373.15 K | 671.67 °R |
| Autoclave cycle | 121 °C | 249.8 °F | 394.15 K | 709.47 °R |
| Moderate oven | 180 °C | 356 °F | 453.15 K | 815.67 °R |
Temperatures vs temperature differences
A thermometer reading converts with the offset. A change, rise or tolerance converts with the factor only. A process that heats water by 10 °C heats it by 18 °F, not by 50 °F. Likewise a ±0.5 °C sensor tolerance is ±0.9 °F, and a temperature difference of 1 °C equals exactly 1 K. Heat-transfer coefficients, specific heats and thermal expansion coefficients use temperature differences, so they convert without the 32 or 273.15.
When you need kelvin or Rankine
Any formula that multiplies or divides by temperature needs an absolute scale: the ideal gas law (PV = nRT), standard-to-actual flow corrections, radiation (σT⁴) and Arrhenius rate laws. Doubling a Celsius value does not double the thermal energy: 20 °C to 40 °C is only a 6.82 % rise in absolute temperature.
Mental shortcuts
- °C → °F: double and add 30 (good to about ±2 °F between 0 and 30 °C).
- °F → °C: subtract 30 and halve.
- Memorable pairs: 10 °C = 50 °F, 16 °C ≈ 61 °F, 28 °C ≈ 82 °F (digits reversed), −40 °C = −40 °F.