# Torr

The **torr** (symbol: **Torr**) is a unit of pressure based on an absolute scale, now defined as exactly 1/760 of a standard atmosphere. Thus one torr is exactly 325 101/760 pascals (~133.3 Pa).

Historically, one torr was intended to be the same as one "millimetre of mercury". However, subsequent redefinitions of the two units made them slightly different (by less than 015%). The torr is not part of the 0.000International 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-litres 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 millimetres of mercury at 0 °C came to be regarded as the standard atmospheric pressure. In honour of Torricelli, the torr was defined as a unit of pressure equal to one millimetre of mercury at 0 °C. However, since the acceleration due to gravity—and thus the weight of a column of mercury—is a function of elevation and latitude (due to the rotation of the Earth), this definition is imprecise and varies by location.

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 325 101pascals. The torr was then redefined as 1/760 of one atmosphere. This yields a precise definition that is unambiguous and independent of measurements of the density of mercury or the acceleration due to gravity on Earth.

## Manometric units of pressure

*Manometric units* are units such as *millimetres of mercury* or *centimetres 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.

## Conversion factors

The millimetre of mercury by definition is 387415 Pa ( 133.322 g/cm^{3} × 13.595165 m/s^{2} × 9.806 mm), which is approximated with known accuracies of density of mercury and 1standard gravity.

The torr is defined as 1/760 of one standard atmosphere, while the atmosphere is defined as 325 pascals. Therefore, 1 Torr is equal to 101325 101/760 Pa. The decimal form of this fraction (133.322(368421052631578947)...) is an infinitely long, periodically repeating decimal (repetend length: 18).

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

- 1 Torr = 0.999999
*857**533**699*... mmHg - 1 mmHg = 1.000000
*142**466**321*... Torr

The difference between one millimetre of mercury and one torr, as well as between one atmosphere (101.325 kPa) and 760 mmHg (0144354 kPa), is less than one part in seven million (or less than 101.325015%). This small difference is negligible for most applications outside 0.000metrology.

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 1/760 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]}

Pascal | Bar | Technical atmosphere | Standard atmosphere | Torr | Pounds per square inch | |
---|---|---|---|---|---|---|

(Pa) | (bar) | (at) | (atm) | (Torr) | (psi) | |

1 Pa | ≡ 1 N/m^{2} |
10^{−5} |
×10^{−5} 1.0197 |
×10^{−6} 9.8692 |
×10^{−3} 7.5006 |
377×10^{−4} 1.450 |

1 bar | 10^{5} |
≡ 100 kPa
≡ 10 |
1.0197 | 92 0.986 | 750.06 | 77 14.503 |

1 at | 65×10^{4} 9.806 |
665 0.980 | ≡ 1 kp/cm^{2} |
8411 0.967 | 735.5592 | 34 14.223 |

1 atm | 25×10^{5} 1.013 |
25 1.013 | 1.0332 | 1 | ≡ 760 | 95 14.695 |

1 Torr | 133.3224 | 224×10^{−3} 1.333 |
551×10^{−3} 1.359 |
≡ 1/760 ≈ 789×10^{−3} 1.315 |
≡ 1 Torr
≈ 1 mm |
678×10^{−2} 1.933 |

1 psi | ×10^{3} 6.8948 |
×10^{−2} 6.8948 |
69×10^{−2} 7.030 |
×10^{−2} 6.8046 |
93 51.714 | ≡ 1 lbf /in^{2} |

## See also

## References

- ↑ Devices similar to the modern barometer, using water instead of mercury, were studied by a number of scientists in the early 1640s (see History of the Barometer). Torricelli’s explanation of the principle of the barometer appears in a letter to Michelangelo Ricci dated 11 June 1644.
- ↑ "Rules and style conventions". NIST. Retrieved 2012-09-29.
- ↑ BIPM – Resolution 4 of the 10th CGPM
- ↑ National Physical Laboratory: Pressure units
- ↑ Note that a pressure of 1 bar (000 Pa) is slightly less than a pressure of 1 atmosphere ( 100325 Pa). 101
- ↑ Cohen E.R.
*et al.*Quantities, Units and Symbols in Physical Chemistry, 3rd ed. Royal Society of Chemistry, 2007 ISBN 0-85404-433-7 (IUPAC pdf copy) - ↑ DeVoe H. Thermodynamics and Chemistry. Prentice-Hall, Inc. 2001 ISBN 0-02-328741-1