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Fahrenheit

Temperature scale

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Thermometer with Fahrenheit and Celsius units
Stilfehler · Public domain

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For much of the 20th century, the Fahrenheit scale was defined by two fixed points with a 180 °F separation: the temperature at which pure water freezes was defined as 32 °F and the boiling point of water was defined to be 212 °F, both at sea level and under standard atmospheric pressure. It is now formally defined using the Kelvin scale.

It continues to be used in the United States (including its unincorporated territories), its freely associated states in the Western Pacific (Palau, the Federated States of Micronesia and the Marshall Islands), which all use the United States National Weather Service, and one British Overseas Territory—the Cayman Islands.

Fahrenheit is still used alongside the Celsius scale in other countries that use the U.S. meteorological service, such as Antigua and Barbuda, Saint Kitts and Nevis, the Bahamas, and Belize. A handful of British Overseas Territories, including the Virgin Islands, Montserrat, Anguilla, and Bermuda, also still use both scales. All other countries now use Celsius ("centigrade" until 1948), which was developed 18 years after the Fahrenheit scale.

Definition and conversion

Historically, on the Fahrenheit scale the freezing point of water was 32 °F, and the boiling point was 212 °F (at standard atmospheric pressure). This put the boiling and freezing points of water 180 degrees apart. Therefore, a degree on the Fahrenheit scale was 1⁄180 of the interval between the freezing point and the boiling point. On the Celsius scale, the freezing and boiling points of water were originally defined to be 100 degrees apart. A temperature interval of 1 °F was equal to an interval of 5⁄9 degrees Celsius. With the Fahrenheit and Celsius scales now both defined by the kelvin, this relationship was preserved, a temperature interval of 1 °F being equal to an interval of 5⁄9 K and of 5⁄9 °C. The Fahrenheit and Celsius scales intersect numerically at −40 in the respective unit (i.e., −40 °F corresponds to −40 °C).

Absolute zero is 0 K, −273.15 °C, or −459.67 °F. The Rankine temperature scale uses degree intervals of the same size as those of the Fahrenheit scale, except that absolute zero is 0 °R – the same way that the Kelvin temperature scale matches the Celsius scale, except that absolute zero is 0 K.

The combination of degree symbol (°) followed by an uppercase letter F is the conventional symbol for the Fahrenheit temperature scale. A number followed by this symbol (and separated from it with a space) denotes a specific temperature point (e.g., "Gallium melts at 85.5763 °F"). A difference between temperatures or an uncertainty in temperature is also conventionally written the same way as well, e.g., "The output of the heat exchanger experiences an increase of 72 °F" or "Our standard uncertainty is ±5 °F". However, some authors instead use the notation "An increase of 50 F°" (reversing the symbol order) to indicate temperature differences. Similar conventions exist for the Celsius scale, see Celsius § Temperatures and intervals.

Conversion (specific temperature point)

For an exact conversion between degrees Fahrenheit and Celsius, and kelvins of a specific temperature point, the following formulae can be applied. Here, f is the value in degrees Fahrenheit, c the value in degrees Celsius, and k the value in kelvins:

  • f °F to c °C: c = ⁠f − 32/1.8⁠
  • c °C to f °F: f = c × 1.8 + 32
  • f °F to k K: k = ⁠f + 459.67/1.8⁠
  • k K to f °F: f = k × 1.8 − 459.67

There is also an exact conversion between Celsius and Fahrenheit scales making use of the correspondence −40 °F ≘ −40 °C. Again, f is the numeric value in degrees Fahrenheit, and c the numeric value in degrees Celsius:

  • f °F to c °C: c = ⁠f + 40/1.8⁠ − 40
  • c °C to f °F: f = (c + 40) × 1.8 − 40

Conversion (temperature difference or interval)

When converting a temperature interval between the Fahrenheit and Celsius scales, only the ratio is used, without any constant (in this case, the interval has the same numeric value in kelvins as in degrees Celsius):

  • f °F to c °C or k K: c = k = ⁠f/1.8⁠
  • c °C or k K to f °F: f = c × 1.8 = k × 1.8

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