### Millimetres of mercury

For the standard botanical author abbreviation Torr., see John Torrey.

The torr (symbol: Torr) is a traditional unit of pressure, now defined as exactly 1/760 of a standard atmosphere, which in turn is defined as exactly 101325 pascals. Thus one torr is exactly 101325/760 ≈ 133.3 pascals.

Historically, one torr was intended to be the same as one "millimeter of mercury". However, subsequent redefinitions of the two units made them slightly different (by less than 0.000015%). The torr is not part of the International System of Units (SI), but it is often combined with the metric prefix milli to name one millitorr (mTorr) or 0.001 Torr.

The unit was named after Evangelista Torricelli, an Italian physicist and mathematician who discovered the principle of the barometer in 1644.[1]

## Nomenclature and common errors

The unit's name "torr" is written in lower case, while its symbol ("Torr") is always written with upper-case initial; including in combinations with prefixes and other units, as in "mTorr" (millitorr) or "Torr·L/s" (torr-liters per second).[2] The symbol (uppercase) should be used with prefix abbreviations (thus, mTorr and millitorr are correct, but mtorr and milliTorr are not).

The torr is sometimes incorrectly denoted by the symbol "T", which is the SI symbol for the tesla. The misspelled symbol "Tor" is also encountered, and is always incorrect.

## History

Torricelli attracted considerable attention when he demonstrated the first mercury barometer to the general public. He is credited with giving the first modern explanation of atmospheric pressure. Scientists at the time were familiar with small fluctuations in height that occurred in barometers. When these fluctuations were explained as a manifestation of changes in atmospheric pressure, the science of meteorology was born.

Over time, 760 millimeters of mercury came to be regarded as the standard atmospheric pressure. In honor of Torricelli, the torr was defined as a unit of pressure equal to one millimeter of mercury.

In 1954, the definition of the atmosphere was revised by the 10e Conférence Générale des Poids et Mesures (10th CGPM)[3] to the currently accepted definition: one atmosphere is equal to 101325 pascals. The torr was then redefined as 1760 of one atmosphere. This was necessary in place of the definition of the torr as one millimetre of mercury, because the pressure exerted by a column of mercury depends not only on the height of the column but on both the temperature and the acceleration due to gravity.

## Manometric units of pressure

Manometric units are units such as millimeters of mercury or centimeters of water that depend on an assumed density of a fluid and an assumed acceleration due to gravity. The use of these units is discouraged.[4] Nevertheless, manometric units are routinely used in medicine and physiology, and they continue to be used in areas as diverse as weather reporting and scuba diving.

Manometric results in medicine are sometimes given in torr. This is usually incorrect, since the torr and the millimeter of mercury are not precisely the same thing. Pressures obtained with a manometer (or its transducer equivalent) should be reported in millimeters of mercury.

## Conversion factors

The millimeter of mercury by definition is 133.322387415 Pa (13.5951 g/cm3 × 9.80665 m/s2 × 1 mm ), which is approximated with known accuracies of density of mercury and gravitational acceleration.

The torr is defined as 1/760 of one standard atmosphere, while the atmosphere is defined as 101,325 pascals. Therefore, 1 Torr is equal to 101325760 Pa. The decimal form of this fraction (133.322368421052...) is an infinitely long, periodically repeating decimal, as is its reciprocal.

The relationship between the torr and the millimeter of mercury is:

• 1 Torr = 0.999999857533699... mmHg
• 1 mmHg = 1.000000142466321... Torr

The difference between one millimeter of mercury and one torr, as well as between one atmosphere (101.325 kPa) and 760 mmHg (101.325014435-2 kPa), is less than one part in seven million (or less than 0.000015%). This small difference is negligible for most applications outside metrology.

Other units of pressure include:

• The bar (symbol: bar), defined as 100 kPa exactly.
• The atmosphere (symbol: atm), defined as 101.325 kPa exactly.
• The torr (symbol: Torr), defined as 1760 atm exactly.

These four pressure units are used in different settings. For example, the bar is used in meteorology to report atmospheric pressures.[5] The torr is used in high-vacuum physics and engineering.[6][7]

Pressure units
Pascal Bar Technical atmosphere Standard atmosphere Torr Pounds per square inch
(Pa) (bar) (at) (atm) (Torr) (psi)
1 Pa ≡ 1 N/m2 10−5 1.0197×10−5 9.8692×10−6 7.5006×10−3 1.450377×10−4
1 bar 105 ≡ 106 dyn/cm2 1.0197 0.98692 750.06 14.50377
1 at 0.980665 ×105 0.980665 ≡ 1 kp/cm2 0.9678411 735.5592 14.22334
1 atm 1.01325 ×105 1.01325 1.0332 p0 ≡ 760 14.69595
1 Torr 133.3224 1.333224×10−3 1.359551×10−3 1.315789×10−3 ≈ 1 mmHg 1.933678×10−2
1 psi 6.8948×103 6.8948×10−2 7.03069×10−2 6.8046×10−2 51.71493 ≡ 1 lbF/in2